Engineering Risk Management Special topic: Beer Game Copyright Old Dominion University, 2017 All rights reserved Revised Class Schedule Lac-Megantic Case Study Part 1: Timeline of events Part 2: Timeline + causal chain of events Part 3: Instructions Evaluate your causal-chain (network) Which are the root causes? Which events have the most causes? What are the relationship of the causes? Which causes have the most influence? Part 4: Instructions Consider these recommendations from TSB Which nodes in your causal chain will be addressed by which of these recommendations? Recap How would you summarize the steps in conducting post-event analysis of an accident? Beer Game Case Study The beer game was developed at MIT in the 1960s. It is an experiential learning business simulation game created by a group of professors at MIT Sloan School of Management in early 1960s to demonstrate a number of key principles of supply chain management. The game is played by teams of four players, often in heated competition, and takes at least one hour to complete.  Beer Game Case Study Beer Game Case Study A truck driver delivers beer once each week to the retailer. Then the retailer places an order with the trucker who returns the order to the wholesaler. There’s a four week lag between ordering and receiving the beer. The retailer and wholesaler do not communicate directly. The retailer sells hundreds of products and the wholesaler distributes many products to a large number of customers. Beer Game Case Study The Retailer Week 1: Lover’s Beer is not very popular but the retailer sells four cases per week on average. Because the lead time is four weeks, the retailer attempts to keep twelve cases in the store by ordering four cases each Monday when the trucker makes a delivery. Week 2: The retailer’s sales of Lover’s beer doubles to eight cases, so on Monday, he orders 8 cases. Week 3: The retailer sells 8 cases. The trucker delivers four cases. To be safe, the retailer decides to order 12 cases of Lover’s beer. Week 4: The retailer learns from some of his younger customers that a music video appearing on TV shows a group singing “I’ll take on last sip of Lover’s beer and run into the sun.” The retailer assumes that this explains the increased demand for the product. The trucker delivers 5 cases. The retailer is nearly sold out, so he orders 16 cases. Beer Game Case Study The Retailer Week 5: The retailer sells the last case, but receives 7 cases. All 7 cases are sold by the end of the week. So again on Monday the retailer orders 16 cases. Week 6: Customers are looking for Lover’s beer. Some put their names on a list to be called when the beer comes in. The trucker delivers only 6 cases and all are sold by the weekend. The retailer orders another 16 cases. Week 7: The trucker delivers 7 cases. The retailer is frustrated, but orders another 16 cases. Week 8: The trucker delivers 5 cases and tells the retailer the beer is backlogged. The retailer is really getting irritated with the wholesaler, but orders 24 cases. Beer Game Case Study The Wholesaler The wholesaler distributes many brands of beer to a large number of retailers, but he is the only distributor of Lover’s beer. The wholesaler orders 4 truckloads from the brewery truck driver each week and receives the beer after a 4 week lag. The wholesaler’s policy is to keep 12 truckloads in inventory on a continuous basis. Week 6: By week 6 the wholesaler is out of Lover’s beer and responds by ordering 30 truckloads from the brewery. Week 8: By the 8th week most stores are ordering 3 or 4 times more Lovers’ beer than their regular amounts. Week 9: The wholesaler orders more Lover’s beer, but gets only 6 truckloads. Week 10: Only 8 truckloads are delivered, so the wholesaler orders 40. Week 11: Only 12 truckloads are received, and there are 77 truckloads in backlog, so the wholesaler orders 40 more truckloads. Beer Game Case Study The Wholesaler Week 12: The wholesaler orders 60 more truckloads of Lover’s beer. It appears that the beer is becoming more popular from week to week. Week 13: There is still a huge backlog. Weeks 14-15: The wholesaler receives larger shipments from the brewery, but orders from retailers begin to drop off. Week 16: The trucker delivers 55 truckloads from the brewery, but the wholesaler gets zero orders from retailers. So he stops ordering from the brewery. Week 17: The wholesaler receives another 60 truckloads. Retailers order zero. The wholesaler orders zero. The brewery keeps sending beer. Beer Game Case Study The Brewery The brewery is small but has a reputation for producing high quality beer. Lover’s beer is only one of several products produced at the brewery. Week 6: New orders come in for 40 gross. It takes two weeks to brew the beer. Week 14: Orders continue to come in and the brewery has not been able to catch up on the backlogged orders. The marketing manager begins to wonder how much bonus he will get for increasing sales so dramatically. Week 16: The brewery catches up on the backlog, but orders begin to drop off. Week 18: By week 18 there are no new orders for Lover’s beer. Week 19: The brewery has 100 gross of Lover’s beer in stock, but no orders. So the brewery stops producing Lover’s beer. Weeks 20-23. No orders. Beer Game Case Study At this point all the players blame each other for the excess inventory. Conversations with wholesale and retailer reveal an inventory of 93 cases at the retailer and 220 truckloads at the wholesaler. The marketing manager figures it will take the wholesaler a year to sell the Lover’s beer he has in stock. The retailers must be the problem. The retailer explains that demand increased from 4 cases per week to 8 cases. The wholesaler and marketing manager think demand mushroomed after that, and then fell off, but the retailer explains that didn’t happen. Demand stayed at 8 cases per week. Since he didn’t get the beer he ordered, he kept ordering more in an attempt to keep up with the demand. The marketing manager plans his resignation. Homework 4 Read the case and answer 1+6 questions. 0th What should go right? 1st What can go wrong? 2nd What are the causes and consequences? 3rd What is the likelihood of occurrence? 4rd What can be done to detect, control, and manage them? 5th What are the alternatives? 6th What are the effects beyond this particular time? Homework 4 In 500 words or less, summarize lessons learned in this beer game as it relates to supply chain risk management. Apply one of the tools (CCA, HAZOP, FMEA, etc.) to the case. Work individually and submit before Monday midnight (Feb. 20th). No class on Monday (Feb. 20th).

Engineering Risk Management Special topic: Beer Game Copyright Old Dominion University, 2017 All rights reserved Revised Class Schedule Lac-Megantic Case Study Part 1: Timeline of events Part 2: Timeline + causal chain of events Part 3: Instructions Evaluate your causal-chain (network) Which are the root causes? Which events have the most causes? What are the relationship of the causes? Which causes have the most influence? Part 4: Instructions Consider these recommendations from TSB Which nodes in your causal chain will be addressed by which of these recommendations? Recap How would you summarize the steps in conducting post-event analysis of an accident? Beer Game Case Study The beer game was developed at MIT in the 1960s. It is an experiential learning business simulation game created by a group of professors at MIT Sloan School of Management in early 1960s to demonstrate a number of key principles of supply chain management. The game is played by teams of four players, often in heated competition, and takes at least one hour to complete.  Beer Game Case Study Beer Game Case Study A truck driver delivers beer once each week to the retailer. Then the retailer places an order with the trucker who returns the order to the wholesaler. There’s a four week lag between ordering and receiving the beer. The retailer and wholesaler do not communicate directly. The retailer sells hundreds of products and the wholesaler distributes many products to a large number of customers. Beer Game Case Study The Retailer Week 1: Lover’s Beer is not very popular but the retailer sells four cases per week on average. Because the lead time is four weeks, the retailer attempts to keep twelve cases in the store by ordering four cases each Monday when the trucker makes a delivery. Week 2: The retailer’s sales of Lover’s beer doubles to eight cases, so on Monday, he orders 8 cases. Week 3: The retailer sells 8 cases. The trucker delivers four cases. To be safe, the retailer decides to order 12 cases of Lover’s beer. Week 4: The retailer learns from some of his younger customers that a music video appearing on TV shows a group singing “I’ll take on last sip of Lover’s beer and run into the sun.” The retailer assumes that this explains the increased demand for the product. The trucker delivers 5 cases. The retailer is nearly sold out, so he orders 16 cases. Beer Game Case Study The Retailer Week 5: The retailer sells the last case, but receives 7 cases. All 7 cases are sold by the end of the week. So again on Monday the retailer orders 16 cases. Week 6: Customers are looking for Lover’s beer. Some put their names on a list to be called when the beer comes in. The trucker delivers only 6 cases and all are sold by the weekend. The retailer orders another 16 cases. Week 7: The trucker delivers 7 cases. The retailer is frustrated, but orders another 16 cases. Week 8: The trucker delivers 5 cases and tells the retailer the beer is backlogged. The retailer is really getting irritated with the wholesaler, but orders 24 cases. Beer Game Case Study The Wholesaler The wholesaler distributes many brands of beer to a large number of retailers, but he is the only distributor of Lover’s beer. The wholesaler orders 4 truckloads from the brewery truck driver each week and receives the beer after a 4 week lag. The wholesaler’s policy is to keep 12 truckloads in inventory on a continuous basis. Week 6: By week 6 the wholesaler is out of Lover’s beer and responds by ordering 30 truckloads from the brewery. Week 8: By the 8th week most stores are ordering 3 or 4 times more Lovers’ beer than their regular amounts. Week 9: The wholesaler orders more Lover’s beer, but gets only 6 truckloads. Week 10: Only 8 truckloads are delivered, so the wholesaler orders 40. Week 11: Only 12 truckloads are received, and there are 77 truckloads in backlog, so the wholesaler orders 40 more truckloads. Beer Game Case Study The Wholesaler Week 12: The wholesaler orders 60 more truckloads of Lover’s beer. It appears that the beer is becoming more popular from week to week. Week 13: There is still a huge backlog. Weeks 14-15: The wholesaler receives larger shipments from the brewery, but orders from retailers begin to drop off. Week 16: The trucker delivers 55 truckloads from the brewery, but the wholesaler gets zero orders from retailers. So he stops ordering from the brewery. Week 17: The wholesaler receives another 60 truckloads. Retailers order zero. The wholesaler orders zero. The brewery keeps sending beer. Beer Game Case Study The Brewery The brewery is small but has a reputation for producing high quality beer. Lover’s beer is only one of several products produced at the brewery. Week 6: New orders come in for 40 gross. It takes two weeks to brew the beer. Week 14: Orders continue to come in and the brewery has not been able to catch up on the backlogged orders. The marketing manager begins to wonder how much bonus he will get for increasing sales so dramatically. Week 16: The brewery catches up on the backlog, but orders begin to drop off. Week 18: By week 18 there are no new orders for Lover’s beer. Week 19: The brewery has 100 gross of Lover’s beer in stock, but no orders. So the brewery stops producing Lover’s beer. Weeks 20-23. No orders. Beer Game Case Study At this point all the players blame each other for the excess inventory. Conversations with wholesale and retailer reveal an inventory of 93 cases at the retailer and 220 truckloads at the wholesaler. The marketing manager figures it will take the wholesaler a year to sell the Lover’s beer he has in stock. The retailers must be the problem. The retailer explains that demand increased from 4 cases per week to 8 cases. The wholesaler and marketing manager think demand mushroomed after that, and then fell off, but the retailer explains that didn’t happen. Demand stayed at 8 cases per week. Since he didn’t get the beer he ordered, he kept ordering more in an attempt to keep up with the demand. The marketing manager plans his resignation. Homework 4 Read the case and answer 1+6 questions. 0th What should go right? 1st What can go wrong? 2nd What are the causes and consequences? 3rd What is the likelihood of occurrence? 4rd What can be done to detect, control, and manage them? 5th What are the alternatives? 6th What are the effects beyond this particular time? Homework 4 In 500 words or less, summarize lessons learned in this beer game as it relates to supply chain risk management. Apply one of the tools (CCA, HAZOP, FMEA, etc.) to the case. Work individually and submit before Monday midnight (Feb. 20th). No class on Monday (Feb. 20th).

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Biomedical Signal and Image Processing (4800_420_001) Assigned on September 12th, 2017 Assignment 4 – Noise and Correlation 1. If a signal is measured as 2.5 V and the noise is 28 mV (28 × 10−3 V), what is the SNR in dB? 2. A single sinusoidal signal is found with some noise. If the RMS value of the noise is 0.5 V and the SNR is 10 dB, what is the RMS amplitude of the sinusoid? 3. The file signal_noise.mat contains a variable x that consists of a 1.0-V peak sinusoidal signal buried in noise. What is the SNR for this signal and noise? Assume that the noise RMS is much greater than the signal RMS. Note: “signal_noise.mat” and other files used in these assignments can be downloaded from the content area of Brightspace, within the “Data Files for Exercises” folder. These files can be opened in Matlab by copying into the active folder and double-clicking on the file or using the Matlab load command using the format: load(‘signal_noise.mat’). To discover the variables within the files use the Matlab who command. 4. An 8-bit ADC converter that has an input range of ±5 V is used to convert a signal that ranges between ±2 V. What is the SNR of the input if the input noise equals the quantization noise of the converter? Hint: Refer to Equation below to find the quantization noise: 5. The file filter1.mat contains the spectrum of a fourth-order lowpass filter as variable x in dB. The file also contains the corresponding frequencies of x in variable freq. Plot the spectrum of this filter both as dB versus log frequency and as linear amplitude versus linear frequency. The frequency axis should range between 10 and 400 Hz in both plots. Hint: Use Equation below to convert: Biomedical Signal and Image Processing (4800_420_001) Assigned on September 12th, 2017 6. Generate one cycle of the square wave similar to the one shown below in a 500-point MATLAB array. Determine the RMS value of this waveform. [Hint: When you take the square of the data array, be sure to use a period before the up arrow so that MATLAB does the squaring point-by-point (i.e., x.^2).]. 7. A resistor produces 10 μV noise (i.e., 10 × 10−6 V noise) when the room temperature is 310 K and the bandwidth is 1 kHz (i.e., 1000 Hz). What current noise would be produced by this resistor? 8. A 3-ma current flows through both a diode (i.e., a semiconductor) and a 20,000-Ω (i.e., 20-kΩ) resistor. What is the net current noise, in? Assume a bandwidth of 1 kHz (i.e., 1 × 103 Hz). Which of the two components is responsible for producing the most noise? 9. Determine if the two signals, x and y, in file correl1.mat are correlated by checking the angle between them. 10. Modify the approach used in Practice Problem 3 to find the angle between short signals: Do not attempt to plot these vectors as it would require a 6-dimensional plot!

Biomedical Signal and Image Processing (4800_420_001) Assigned on September 12th, 2017 Assignment 4 – Noise and Correlation 1. If a signal is measured as 2.5 V and the noise is 28 mV (28 × 10−3 V), what is the SNR in dB? 2. A single sinusoidal signal is found with some noise. If the RMS value of the noise is 0.5 V and the SNR is 10 dB, what is the RMS amplitude of the sinusoid? 3. The file signal_noise.mat contains a variable x that consists of a 1.0-V peak sinusoidal signal buried in noise. What is the SNR for this signal and noise? Assume that the noise RMS is much greater than the signal RMS. Note: “signal_noise.mat” and other files used in these assignments can be downloaded from the content area of Brightspace, within the “Data Files for Exercises” folder. These files can be opened in Matlab by copying into the active folder and double-clicking on the file or using the Matlab load command using the format: load(‘signal_noise.mat’). To discover the variables within the files use the Matlab who command. 4. An 8-bit ADC converter that has an input range of ±5 V is used to convert a signal that ranges between ±2 V. What is the SNR of the input if the input noise equals the quantization noise of the converter? Hint: Refer to Equation below to find the quantization noise: 5. The file filter1.mat contains the spectrum of a fourth-order lowpass filter as variable x in dB. The file also contains the corresponding frequencies of x in variable freq. Plot the spectrum of this filter both as dB versus log frequency and as linear amplitude versus linear frequency. The frequency axis should range between 10 and 400 Hz in both plots. Hint: Use Equation below to convert: Biomedical Signal and Image Processing (4800_420_001) Assigned on September 12th, 2017 6. Generate one cycle of the square wave similar to the one shown below in a 500-point MATLAB array. Determine the RMS value of this waveform. [Hint: When you take the square of the data array, be sure to use a period before the up arrow so that MATLAB does the squaring point-by-point (i.e., x.^2).]. 7. A resistor produces 10 μV noise (i.e., 10 × 10−6 V noise) when the room temperature is 310 K and the bandwidth is 1 kHz (i.e., 1000 Hz). What current noise would be produced by this resistor? 8. A 3-ma current flows through both a diode (i.e., a semiconductor) and a 20,000-Ω (i.e., 20-kΩ) resistor. What is the net current noise, in? Assume a bandwidth of 1 kHz (i.e., 1 × 103 Hz). Which of the two components is responsible for producing the most noise? 9. Determine if the two signals, x and y, in file correl1.mat are correlated by checking the angle between them. 10. Modify the approach used in Practice Problem 3 to find the angle between short signals: Do not attempt to plot these vectors as it would require a 6-dimensional plot!

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Book review The Shareholder Value Myth: How Putting Shareholders First Harms Investors, Corporations, and the Public by Lynn Stout Provide 1) a 900 word review of this book (word range 900-1,200) and 2) a 350 word reflection where you force yourself to relate the message of the book . As per the format of the review, I like the ones done by the folks of the WSJ. This is an example: http://forums.delphiforums.com/diversecity/messages?msg=17531.1264 or http://www.wsj.com/articles/book-review-how-adam-smith-can-change-your-life-by-russ-roberts-1413846808?KEYWORDS=book+reviews

Book review The Shareholder Value Myth: How Putting Shareholders First Harms Investors, Corporations, and the Public by Lynn Stout Provide 1) a 900 word review of this book (word range 900-1,200) and 2) a 350 word reflection where you force yourself to relate the message of the book . As per the format of the review, I like the ones done by the folks of the WSJ. This is an example: http://forums.delphiforums.com/diversecity/messages?msg=17531.1264 or http://www.wsj.com/articles/book-review-how-adam-smith-can-change-your-life-by-russ-roberts-1413846808?KEYWORDS=book+reviews

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AIM: Assignment consists of a group project that aims at producing a paper on the topic assigned to each group. Production data analysis and evaluating the well performance are two major tasks for any production engineer. The main variables affecting the well performance are listed separately below. It is required for each group to investigate the effect of assigned variable (variables) on data analysis and well performance. Apart from submission of the paper all students will need to attend a short meeting to answer questions about the produced paper which demonstrates the contribution of each member of each team to the submitted work. Assessment Criteria: The assessment consists of two elements, as bellow: Element 1 (50%): Papers. Assessed based on:  Quality of the contents (20 %)  Attitude and understanding (20%)  Figures and Tables (clarity and proper captioning) (20%)  Formatting (20%)  Referencing (20%)

AIM: Assignment consists of a group project that aims at producing a paper on the topic assigned to each group. Production data analysis and evaluating the well performance are two major tasks for any production engineer. The main variables affecting the well performance are listed separately below. It is required for each group to investigate the effect of assigned variable (variables) on data analysis and well performance. Apart from submission of the paper all students will need to attend a short meeting to answer questions about the produced paper which demonstrates the contribution of each member of each team to the submitted work. Assessment Criteria: The assessment consists of two elements, as bellow: Element 1 (50%): Papers. Assessed based on:  Quality of the contents (20 %)  Attitude and understanding (20%)  Figures and Tables (clarity and proper captioning) (20%)  Formatting (20%)  Referencing (20%)

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Lab #02 Relationship between distance & illumination As engineers, we deal with the effects of light on many projects. The first key to working with light is understanding how the light waves propagate. Once we understand light waves, we will test a manufacturers claim that lower wattage fluorescent bulbs output the same quantity of light as incandescent bulbs. This experiment is designed for you to work as a class to collect data regarding a given light source and then, working within your individual group, attempt to determine the re-lationship(s) between the measured parameter (lux) and the distance (meter) from the source. Measure and record data, in the manner described below, as a class. Work on your so-lutions as a group of 2-3. Your first task is to develop a mathematical formula, or a simple relationship that predicts the amount of lux that can be expected at a given distance from the light source. Purpose: The purpose of this assignment is to accomplish the following goals: • Gain experience collecting data in a controlled, systematic fashion. • Practice working as a group to infer relationships between variables from your collected data. • Use the data you collect to draw conclusions. In this case, to evaluate the hypothesis that the fluorescent and incandescent bulb output the same quantity of light. • Become accustomed to working in teams (note, teamwork often requires individual work as well). • Learn to balance workload across your team. (Individuals will be responsible for certain tasks, and ensure they are performed on time and to the desired quality level. • Demonstrate to me what your group’s attention to detail is, as well as your ability to construct a written explanation of work. Problem: What effect does distance have on the lux, intensity, emitted from a light source and are the 5 light bulbs producing the same intensity light? Use the rough protocol listed below and the data sheet provided to collect your data, then complete the assignment outlined below. 1. Set up a light source on one of the lab tables. 2. Using the illumination meter, measure the lux at 0.5 meter increments from the source back to 3 meters from the source. • Be sure the keep the meter perpendicular to the horizontal line from the source at all times! 3. Record your measurements on your data sheets. 4. Measurements should be taken in a random order 5. Repeat the experiment 3 times, using different people and a different order of collection and different colors. Assignment Requirements: 1. Create the appropriate graph(s) to express the data you have collected. Your report must, at the minimum, contain the following: a. An X-Y Scatter plot showing the data from both bulbs. The chart should follow all conventions taught in lecture, and display the equation for the trend-line you choose. b. A column or bar chart of your choosing showing the difference, if any, between the two bulbs. 2. Write an introduction, briefly explaining what you are accomplishing with this exper-iment. 3. Create a hierarchal outline that states, step by step, each activity that was performed to conduct the experiment and analyze the experimental data. 4. Anova analysis for data collected 5. Write a verbal explanation of what each of the charts from requirement #1 are showing. 6. Include, at the end of the document, a summary of all the tasks required to complete the assignment, including the 5 listed above, and which member or members of the group were principally responsible for completing those tasks. This should be in the form of a simple list. 7. Write at least 3 possible applications of the experiment with detailed explanation. DUE DATE: This assignment is to be completed and turned in at the beginning of your laboratory meeting during the week of 18th February Microsoft office package: Excel: Insert, page layout tab functions, Mean, standard deviation, graph functions

Lab #02 Relationship between distance & illumination As engineers, we deal with the effects of light on many projects. The first key to working with light is understanding how the light waves propagate. Once we understand light waves, we will test a manufacturers claim that lower wattage fluorescent bulbs output the same quantity of light as incandescent bulbs. This experiment is designed for you to work as a class to collect data regarding a given light source and then, working within your individual group, attempt to determine the re-lationship(s) between the measured parameter (lux) and the distance (meter) from the source. Measure and record data, in the manner described below, as a class. Work on your so-lutions as a group of 2-3. Your first task is to develop a mathematical formula, or a simple relationship that predicts the amount of lux that can be expected at a given distance from the light source. Purpose: The purpose of this assignment is to accomplish the following goals: • Gain experience collecting data in a controlled, systematic fashion. • Practice working as a group to infer relationships between variables from your collected data. • Use the data you collect to draw conclusions. In this case, to evaluate the hypothesis that the fluorescent and incandescent bulb output the same quantity of light. • Become accustomed to working in teams (note, teamwork often requires individual work as well). • Learn to balance workload across your team. (Individuals will be responsible for certain tasks, and ensure they are performed on time and to the desired quality level. • Demonstrate to me what your group’s attention to detail is, as well as your ability to construct a written explanation of work. Problem: What effect does distance have on the lux, intensity, emitted from a light source and are the 5 light bulbs producing the same intensity light? Use the rough protocol listed below and the data sheet provided to collect your data, then complete the assignment outlined below. 1. Set up a light source on one of the lab tables. 2. Using the illumination meter, measure the lux at 0.5 meter increments from the source back to 3 meters from the source. • Be sure the keep the meter perpendicular to the horizontal line from the source at all times! 3. Record your measurements on your data sheets. 4. Measurements should be taken in a random order 5. Repeat the experiment 3 times, using different people and a different order of collection and different colors. Assignment Requirements: 1. Create the appropriate graph(s) to express the data you have collected. Your report must, at the minimum, contain the following: a. An X-Y Scatter plot showing the data from both bulbs. The chart should follow all conventions taught in lecture, and display the equation for the trend-line you choose. b. A column or bar chart of your choosing showing the difference, if any, between the two bulbs. 2. Write an introduction, briefly explaining what you are accomplishing with this exper-iment. 3. Create a hierarchal outline that states, step by step, each activity that was performed to conduct the experiment and analyze the experimental data. 4. Anova analysis for data collected 5. Write a verbal explanation of what each of the charts from requirement #1 are showing. 6. Include, at the end of the document, a summary of all the tasks required to complete the assignment, including the 5 listed above, and which member or members of the group were principally responsible for completing those tasks. This should be in the form of a simple list. 7. Write at least 3 possible applications of the experiment with detailed explanation. DUE DATE: This assignment is to be completed and turned in at the beginning of your laboratory meeting during the week of 18th February Microsoft office package: Excel: Insert, page layout tab functions, Mean, standard deviation, graph functions

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-1- Department of Engineering ELE3DDE: Electronic Design Automation – 2015 Assignment: Traffic Light Controller: Design, Synthesis and Test DUE: Code Submission and Demonstration, Wednesday, September 9 Report, 2pm Monday, September 14 Students will work on this assignment individually – developing their own design and producing their own independent report Task: A traffic signal controller is required for an intersection of two cross roads in a busy town centre that also has considerable pedestrian traffic. All four approaches to the intersection have standard traffic lights (Red, Amber and Green) and a traffic sensor (active low), which can detect the presence of approaching traffic. Assume that when a car passes over a sensor, it produces a low signal for approximately three (3) seconds. Thus a constant stream of traffic would produce a continuous low signal (i.e. assume that debouncing for these sensors has already been performed in the sensor circuitry). The intersection also has pedestrian crossing signals (Walk, Don’t Walk (flashing), and Don’t Walk (constantly illuminated), and pedestrian call buttons (simple push button switches) at each of the four crossing points. As a digital design engineer, you have been asked to produce an FPGA prototype for the Traffic Light Controller and assigned the following tasks (i) Produce a VHDL design for the Traffic Light Controller meeting the specifications outlined below. (ii) Produce a test bench for your VHDL design and via simulation confirm that your design functions correctly. (iii) Produce a space efficient, fully tested working prototype, suitable for demonstration to the client. (i.e. implement your design in the ALTERA, Cyclone II FPGA on the ALTERA DE2 board). (iv) Produce a report of your work, including a discussion on the efficiency of your design. (v) All code generated for you design must be included in your report. If you have pages and pages of VHDL code (particularly if you generated them with HDL Designer), these should be included in your report as an appendix. Prototype. The design will be implemented using the ALTERA, Cyclone II (EP2C35F672C6) device on the ALTERA DE2 board. See Appendix or DE2 Board Manual for device I/O pins. The four traffic lights will be represented via the 7-segment displays HEX7 – HEX4, with segment ‘a’ representing a red light, segment ‘g’ representing a yellow light and segment ‘d’ representing a green light. With the traffic sensors in the road represented by four slide switches (SW17, SW15, SW13 & SW11). The emergency Amber flash switch should be connected to slide switch SW3. -2- The pedestrian call buttons will be represented by the push buttons, KEY0, KEY1, KEY2 and KEY3. With 7-segment displays HEX3 – HEX0 used to represent the pedestrian signals for the crossing of the intersection, in the following manner: Walk (segment ‘d’ on), Don’t Walk – flashing (segment ‘a’ flashing), and Don’t Walk (segment ‘a’ on continuously). For timing the development board has a 50MHz clock. Shown above is a diagram of a seven-segment display indicating how segments ‘a’, ‘g’ and ‘d’ are used to represent the red, yellow and green lights, of a traffic light, respectively on HEX7 – HEX4. While below shows seven-segment display indicating how segments ‘a’ and ‘d’ are used to indicate Don’t Walk and Walk respectively on HEX3 – HEX0. Design Specifications – Basic Design. The road traffic lights are to operate using the sequence RedGreenAmberRed according to the timing and requirements outlined below. Whenever the lights for one road are Green or Amber the crossroad must always display a red signal. All traffic lights must display a red signal for two seconds between changeovers. In their inactive state all pedestrian signals will display “Don’t Walk – continuous” (segment ‘a’ continuously on), independent of the changes in the traffic signals. The pedestrian signal can be activated following a pedestrian call being registered (by an appropriate push button(s) being pressed) and will operate in the sequence “Walk”  “Don’t Walk – flash”  “Don’t Walk – continuous” with the timing and requirements outlined below. As this intersection carries considerable pedestrian traffic the town planners have decided that the traffic sequence will contain a dedicated pedestrian crossing only period, where pedestrians may walk between any two points of the intersection (including through the middle of the intersection). Rather than embedding the pedestrian crossing sequences in with the road traffic sequence – as you are probably more familiar with. Thus whenever any traffic flow enabling signal is active (i.e. Green or Amber on) the pedestrian signals will be inactive (i.e. “Don’t Walk – continuous”) and vice versa, whenever the pedestrian signals are active (“Walk” or “Don’t Walk – flash”) all road traffic lights remain red. a d e f g c b a d e f g c b -3- Traffic Light sequence and timing When all automotive sensors are inactive the default sequence is: Green Road 1 14 sec Amber Road 1 4 sec Red Roads 1/2 2 sec Green Road 2 14 sec Amber Road 2 4 sec Red Roads 1/2 2 sec For both Roads 1 & 2, if any traffic is detected after the road has been showing green for 9 seconds, then the Green time will be extended by a further 10 seconds (i.e. making the Green time 24 seconds for that road, on that sequence. The amber and red/red times remain at 4 and 2 seconds respectively – for all sequences. Thus if both Road 1 and Road 2 have heavy traffic (i.e. traffic still detected after 9 seconds of green signal) then the sequence will be: Green Road 1 24 sec Amber Road 1 4 sec Red Roads 1/2 2 sec Green Road 2 24 sec Amber Road 2 4 sec Red Roads 1/2 2 sec Also, should Road 1 have heavy traffic and Road 2 have only light or no traffic (i.e. no traffic detected after 9 seconds of green signal) then the sequence will be: Green Road 1 24 sec Amber Road 1 4 sec Red Roads 1/2 2 sec Green Road 2 14 sec Amber Road 2 4 sec Red Roads 1/2 2 sec And alternatively, should Road 2 have heavy traffic and Road 1 have only light or no traffic (i.e. no traffic detected after 9 seconds of green signal) then the sequence will be: Green Road 1 14 sec Amber Road 1 4 sec Red Roads 1/2 2 sec Green Road 2 24 sec Amber Road 2 4 sec Red Roads 1/2 2 sec When a pedestrian crossing sequence is required this is always inserted after the Road 2 sequence, following the 2 seconds of red in both directions. Pushing a pedestrian crossing button (outside of the “Walk” period) will register a “pedestrian call” and a pedestrian crossing sequence will be inserted as soon as the next Road 2 sequence is complete. Should a pedestrian call be registered at only one site, then the pedestrian crossing sequence will be: -4- : Red Roads 1/2 2 sec “Walk” (‘d’ on) 18 sec (still Red Roads 1/2) “Don’t Walk Flashing” (‘a’ flashing) 6 sec (still Red Roads 1/2) “Don’t Walk” (‘a’ on) 2 sec (still Red Roads 1/2) Green Road 1 : : Alternatively, should a pedestrian call be registered at more than one site, then the “Walk” portion of the pedestrian crossing sequence will be extended by a further 8 seconds, thus: : Red Roads 1/2 2 sec “Walk” (‘d’ on) 26 sec (still Red Roads 1/2) “Don’t Walk Flashing” (‘a’ flashing) 6 sec (still Red Roads 1/2) “Don’t Walk” (‘a’ on) 2 sec (still Red Roads 1/2) Green Road 1 : : All pedestrian calls will be cleared as soon as the “Walk” (‘d’ on) signal is activated, and will not register again until the “Walk” (‘d’ on) signal is no longer active. Any pedestrian calls (i.e. a pedestrian button push) made during the “Don’t Walk Flashing” signal will be registered as a call towards the next sequence and have no effect on the current length of the “Don’t Walk Flashing” signal. As an example, if the automotive traffic is “heavy” in both directions, and there is also a heavy demand on the pedestrian crossing, then the total sequence would be: : Green Road 1 24 sec Amber Road 1 4 sec Red Roads 1/2 2 sec Green Road 2 24 sec Amber Road 2 4 sec Red Roads 1/2 2 sec “Walk” (‘d’ on) 26 sec (still Red Roads 1/2) “Don’t Walk Flashing” (‘a’ flashing) 6 sec (still Red Roads 1/2) “Don’t Walk” (‘a’ on) 2 sec (still Red Roads 1/2) Green Road 1 24 sec : The traffic controller system must respond to road sensor changes within one second. (Hint – The core of your design may include a state machine that is clocked at 1Hz). Although, you may need a faster clock to register the pedestrian call buttons. Incorporate an emergency Amber flash switch in your design (SW3). When activated the system should move to the ‘Red both directions’ state as soon as possible (i.e. it must go through four seconds of amber if currently green or amber, or through six seconds of “Don’t Walk Flashing” should a pedestrian sequence be active. Then after two seconds of ‘Red both directions’ plus “Don’t Walk” (‘a’ on) it should flash amber at 1Hz in both directions. In this state all pedestrian -5- signals will remain continuously showing “Don’t Walk” and no pedestrian call buttons will be registered. The design must also include an reset (active low), which will immediately place the lights on both roads in the Red state, plus all pedestrian signals showing “Don’t Walk” continuously, hold for two seconds, and then move to normal operations. You should use SW0 for the reset. For the purposes of testing and demonstrating this assignment, you should include a state clock speed modification option (i.e. x4); under “test switch” control (SW2). This will enable an option of viewing (and testing) the sequence changes more quickly. Finally, so that each design is unique, arrange for a selectable option (using SW1) where your student number is displayed on the 7-segment displays. Clearly when the student number is being displayed the traffic light status cannot be shown, although normal operations should continue in the background. That is, SW1 controls a multiplexer that selects between traffic light and student number data to be displayed. There is no need to include this section in your report, as it is not part of the Traffic Light Controller design. However, it is required for the demonstration. Design Specifications – Enhanced Design. Add additional features to enhance your design. 1. Implement the “Walk”/”Don’t Walk” on the LCD display. 2. Display a count of the current ‘seconds’ for a particular state in the sequence. i.e. count up the seconds in “green-red”, then “amber-red”, then “red-red”, then “red-green” etc. 3. Implement Green right turn arrows on the cross roads. Use the four slide switches (SW16, SW14, SW12 & SW10) for the right turn sensors. If a North or East direction road has an right turn sensors that is active prior to the intended green cycle of that road then an additional 6 seconds inserted into the sequence showing “Green Arrow” and “Green” in one direction with “Red” in the opposite direction (i.e. South or West). After the 6 seconds have elapsed the “Green Arrow” is switched off while the “Green” remains on with “Red” still showing in the opposite direction. After a further four seconds the “Red” in opposite direction changes to “green” and the sequence continues normally. Alternatively, the right turn arrow for South or East direction roads is inserted at the end of the green sequence, as follows. If a South or West has an active right turn sensor then at the end of the common “Green” time for that road then an additional ten seconds is added to the sequence to accommodate the “Green Arrow”. This consists of four seconds of “Amber” in the corresponding opposite direction, with “Green” still showing in the South or East direction, followed by “Red” in the opposite direction, and “Green Arrow” with “Green” still on for a further 6 seconds. The cycle then moves to “Amber” in the South or East direction with the “Green Arrow” off and “Red” showing in the opposite direction for four seconds. After that is the “All Red” state for two seconds and then the start of a new sequence. For the purposes of the demonstration HEX7 & HEX6 are North & South respectively, while HEX5 & HEX4 are East & West respectively. As an example the following is a heavy traffic sequence with right turns. Red All Roads 2 sec Green and Green Arrow On North Road (South Red) 6 sec Green North Road with Green Arrow off (South Red) 4 sec Green North & South Roads 24 sec -6- Amber North Road with Green South Road 4 sec Red North Road with Green South Road 2 sec Green and Green Arrow On South Road (North Red) 6 sec Amber with Green Arrow off South Road (North Red) 4 sec Red All Roads 2 sec Green and Green Arrow On East Road (West Red) 6 sec Green East Road with Green Arrow off (West Red) 4 sec Green East & West Roads 24 sec Amber East Road with Green West Road 4 sec Red East Road with Green West Road 2 sec Green and Green Arrow On West Road (East Red) 6 sec Amber with Green Arrow off West Road (East Red) 4 sec Red All Roads 2 sec Shown above is a diagram of a seven-segment display indicating how segment ‘c’ is used to indicate a green right turn arrow in a traffic light, in conjunction with ‘a’, ‘g’ and ‘d’ representing the red, yellow and green lights. Notes/Hints: (i) A pedestrian signal sequence will only occur if a pedestrian call button has been pressed (and hence registered); otherwise it will remain in the continuous “Don’t Walk” state. (ii) The decision to extend a traffic signal sequence from 14 to 24 seconds should be made between the 10 and 14 second mark (inclusive). i.e. read the traffic sensors between these times. (iii) It is recommended that you practice implementing some of the basic functions on the DE2 Board first and build on this before implementing the entire design. At the end of the day, a partially implemented prototype that works will be easier to demonstrate than an entire design that does not work at all. (iv) There are many different ways of describing timing circuits in VHDL, not all are synthesisable. (v) At this stage it may be safer to stick with the standard ieee libraries, while it is possible to set up your own libraries – great care needs to be exercised. a d e f g c b -7- (vi) If you use a package – keep it in your work library, download it to the same folder as your design files (for the Quartus II compiler) and compile it (using the Quartus II compiler) before compiling your vending machine design. (vii) MOST IMPORTANT – the Quartus II compiler does NOT like integers of different ranges being assigned to each other – even though this may compile and simulate correctly in ModelSim. For your assignment report YOU ARE REQUIRED TO SUBMIT THE FOLLOWING: (a) Block diagrams of your design, showing the hierarchy of the design and signals at each level. You can use HDL Designer or another drawing package if you wish. To assist the explanation of your design (e) it may be appropriate to embed these in the written text. (b) Printout(s) of your Traffic Light Controller design (inc. VHDL code). Key parts of the design graphics/code should be included in the main body of the report, along with the explanation of the design. With the complete design code included as an appendix. Reset Amber Flash Road 1 Lights Pedestrian Signals Pedestrian Call Buttons Display Student No. Traffic Sensors Test Road 2 Lights -8- (c) Printout(s) of your test bench (stimulus) file(s). Where key to the understanding of the testing methodology and simulation results these should included in the main body of the report. Otherwise, a complete set of testbench code must be included as an appendix. (d) Test data (i.e. annotated printouts of simulation results and summary of on board testing); <<PLEASE keep your simulation printouts to the point, to minimize page usage. E.g. ~3-4 pages with several simulations on each page is good, but 6+ pages of simulations is likely to be a waste of space and effort. You must provide annotated simulations of your main blocks and top level design performing key functions. It is accepted that you will not be able to demonstrate absolutely every possible case on paper - choose the most important ones, and use your demonstration for the rest. For example, if your design is working correctly it will be obvious that your 7 segment display driver is also working correctly. This will be seen in the simulation of higher level blocks as well as the demonstration, and therefore doesn’t require a separate simulation printout>> (e) A concise (two – three pages writing) explanation of your design and your testing methodologies (i.e. how your circuit works, and why your test results demonstrate that it is functioning correctly), also include comments on any particular innovative ideas you have implemented in your design; (f) Include a summary of the FPGA resource usage of your completed design. Briefly comment on the general efficiency of your design, remember that, typically the smaller the design the lower the cost (as it may fit in a smaller/cheaper device), and the lower the power consumption. Are there any areas where you think the design could save some resources by being implemented differently? You are not required to make changes to the VHDL just brief comment(s). (Half page plus resource usage summary). Submission (by 2pm Monday, September 14):  Your complete report (including code) must be converted to an OCR compatible (i.e. searchable) PDF file and submitted to the Design Assignment drop box on the LMS site for this subject. No paper copies are required.  When you submit your assignment it will be checked automatically by the Turnitin software for similarity with past and present work, web sites, books etc. Any report with a high Turnitin similarity index will be scrutinised for potential plagiarism.  It is highly recommended that you submit a draft copy of your assignment report, to the draft Turnitin drop box (on LMS) and check the generated Turnitin report before finalising your submission. If you submit plagiarised work (that is work copied from others – including code) it will most likely be identified and your assignment deemed unsatisfactory! YOU WILL BE REQUIRED TO SUBMIT YOUR DESIGN CODE AND DEMONSTRATE YOUR DESIGN IN PRACTICAL CLASS SESSION IN THE WEEK PRIOR TO THE REPORT DUE DATE (i.e. September 9). Jim Whittington August 2015 -9- APPENDIX – Altera DE2 Board, Switch, LED, 7-Segment Display and Clock pins The following information is taken from the Altera DE2 Board Manual Signal Name FPGA Pin Description SW0 PIN_N25 Slide Switch[0] SW1 PIN_N26 Slide Switch[1] SW2 PIN_P25 Slide Switch[2] SW3 PIN_AE14 Slide Switch[3] SW4 PIN_AF14 Slide Switch[4] SW5 PIN_AD13 Slide Switch[5] SW6 PIN_AC13 Slide Switch[6] SW7 PIN_C13 Slide Switch[7] SW8 PIN_B13 Slide Switch[8] SW9 PIN_A13 Slide Switch[9] SW10 PIN_N1 Slide Switch[10] SW11 PIN_P1 Slide Switch[11] SW12 PIN_P2 Slide Switch[12] SW13 PIN_T7 Slide Switch[13] SW14 PIN_U3 Slide Switch[14] SW15 PIN_U4 Slide Switch[15] SW16 PIN_V1 Slide Switch[16] SW17 PIN_V2 Slide Switch[17] Table-1 Altera DE2 Board Slide Switch Pin Assignments Signal Name FPGA Pin Description KEY0 PIN_G26 Pushbutton[0] KEY1 PIN_N23 Pushbutton [1] KEY2 PIN_P23 Pushbutton [2] KEY3 PIN_W26 Pushbutton [3] Table-2 Altera DE2 Board Push Button Pin Assignments Signal Name FPGA Pin Description LEDR0 PIN_AE23 Red LED[0] LEDR1 PIN_AF23 Red LED[1] LEDR2 PIN_AB21 Red LED[2] LEDR3 PIN_AC22 Red LED[3] LEDR4 PIN_AD22 Red LED[4] LEDR5 PIN_AD23 Red LED[5] LEDR6 PIN_AD21 Red LED[6] LEDR7 PIN_AC21 Red LED[7] LEDR8 PIN_AA14 Red LED[8] LEDR9 PIN_Y13 Red LED[9] LEDR10 PIN_AA13 Red LED[10] LEDR11 PIN_AC14 Red LED[11] LEDR12 PIN_AD15 Red LED[12] -10- LEDR13 PIN_AE15 Red LED[13] LEDR14 PIN_AF13 Red LED[14] LEDR15 PIN_AE13 Red LED[15] LEDR16 PIN_AE12 Red LED[16] LEDR17 PIN_AD12 Red LED[17] LEDG0 PIN_AE22 Green LED[0] LEDG1 PIN_AF22 Green LED[1] LEDG2 PIN_W19 Green LED[2] LEDG3 PIN_V18 Green LED[3] LEDG4 PIN_U18 Green LED[4] LEDG5 PIN_U17 Green LED[5] LEDG6 PIN_AA20 Green LED[6] LEDG7 PIN_Y18 Green LED[7] LEDG8 PIN_Y12 Green LED[8] Table-3 Altera DE2 LED Pin Assignments Signal Name FPGA Pin Description HEX0[0] PIN_AF10 HEX0 Segment a HEX0[1] PIN_AB12 HEX0 Segment b HEX0[2] PIN_AC12 HEX0 Segment c HEX0[3] PIN_AD11 HEX0 Segment d HEX0[4] PIN_AE11 HEX0 Segment e HEX0[5] PIN_V14 HEX0 Segment f HEX0[6] PIN_V13 HEX0 Segment g HEX1 [0] PIN_V20 HEX1 Segment a HEX1 [1] PIN_V21 HEX1 Segment b HEX1 [2] PIN_W21 HEX1 Segment c HEX1 [3] PIN_Y22 HEX1 Segment d HEX1 [4] PIN_AA24 HEX1 Segment e HEX1 [5] PIN_AA23 HEX1 Segment f HEX1 [6] PIN_AB24 HEX1 Segment g HEX2 [0] PIN_AB23 HEX2 Segment a HEX2 [1] PIN_V22 HEX2 Segment b HEX2 [2] PIN_AC25 HEX2 Segment c HEX2 [3] PIN_AC26 HEX2 Segment d HEX2 [4] PIN_AB26 HEX2 Segment e HEX2 [5] PIN_AB25 HEX2 Segment f HEX2 [6] PIN_Y24 HEX2 Segment g HEX3 [0] PIN_Y23 HEX3 Segment a HEX3 [1] PIN_AA25 HEX3 Segment b HEX3 [2] PIN_AA26 HEX3 Segment c HEX3 [3] PIN_Y26 HEX3 Segment d HEX3 [4] PIN_Y25 HEX3 Segment e HEX3 [5] PIN_U22 HEX3 Segment f -11- HEX3 [6] PIN_W24 HEX3 Segment g HEX4 [0] PIN_U9 HEX4 Segment a HEX4 [1] PIN_U1 HEX4 Segment b HEX4 [2] PIN_U2 HEX4 Segment c HEX4 [3] PIN_T4 HEX4 Segment d HEX4 [4] PIN_R7 HEX4 Segment e HEX4 [5] PIN_R6 HEX4 Segment f HEX4 [6] PIN_T3 HEX4 Segment g HEX5 [0] PIN_T2 HEX5 Segment a HEX5 [1] PIN_P6 HEX5 Segment b HEX5 [2] PIN_P7 HEX5 Segment c HEX5 [3] PIN_T9 HEX5 Segment d HEX5 [4] PIN_R5 HEX5 Segment e HEX5 [5] PIN_R4 HEX5 Segment f HEX5 [6] PIN_R3 HEX5 Segment g HEX6 [0] PIN_R2 HEX6 Segment a HEX6 [1] PIN_P4 HEX6 Segment b HEX6 [2] PIN_P3 HEX6 Segment c HEX6 [3] PIN_M2 HEX6 Segment d HEX6 [4] PIN_M3 HEX6 Segment e HEX6 [5] PIN_M5 HEX6 Segment f HEX6 [6] PIN_M4 HEX6 Segment g HEX7 [0] PIN_L3 HEX7 Segment a HEX7 [1] PIN_L2 HEX7 Segment b HEX7 [2] PIN_L9 HEX7 Segment c HEX7 [3] PIN_L6 HEX7 Segment d HEX7 [4] PIN_L7 HEX7 Segment e HEX7 [5] PIN_P9 HEX7 Segment f HEX7 [6] PIN_N9 HEX7 Segment g Table-4 Altera DE2 Board 7-Segment Display Pin Assignments Signal Name FPGA Pin Description CLOCK_27 PIN_D13 27 MHz Clock CLOCK_50 PIN_N2 50 MHz Clock EXT_CLOCK PIN_P26 External Clock Input (SMA) Table-5 Altera DE2 Board Clock Pin Assignments

-1- Department of Engineering ELE3DDE: Electronic Design Automation – 2015 Assignment: Traffic Light Controller: Design, Synthesis and Test DUE: Code Submission and Demonstration, Wednesday, September 9 Report, 2pm Monday, September 14 Students will work on this assignment individually – developing their own design and producing their own independent report Task: A traffic signal controller is required for an intersection of two cross roads in a busy town centre that also has considerable pedestrian traffic. All four approaches to the intersection have standard traffic lights (Red, Amber and Green) and a traffic sensor (active low), which can detect the presence of approaching traffic. Assume that when a car passes over a sensor, it produces a low signal for approximately three (3) seconds. Thus a constant stream of traffic would produce a continuous low signal (i.e. assume that debouncing for these sensors has already been performed in the sensor circuitry). The intersection also has pedestrian crossing signals (Walk, Don’t Walk (flashing), and Don’t Walk (constantly illuminated), and pedestrian call buttons (simple push button switches) at each of the four crossing points. As a digital design engineer, you have been asked to produce an FPGA prototype for the Traffic Light Controller and assigned the following tasks (i) Produce a VHDL design for the Traffic Light Controller meeting the specifications outlined below. (ii) Produce a test bench for your VHDL design and via simulation confirm that your design functions correctly. (iii) Produce a space efficient, fully tested working prototype, suitable for demonstration to the client. (i.e. implement your design in the ALTERA, Cyclone II FPGA on the ALTERA DE2 board). (iv) Produce a report of your work, including a discussion on the efficiency of your design. (v) All code generated for you design must be included in your report. If you have pages and pages of VHDL code (particularly if you generated them with HDL Designer), these should be included in your report as an appendix. Prototype. The design will be implemented using the ALTERA, Cyclone II (EP2C35F672C6) device on the ALTERA DE2 board. See Appendix or DE2 Board Manual for device I/O pins. The four traffic lights will be represented via the 7-segment displays HEX7 – HEX4, with segment ‘a’ representing a red light, segment ‘g’ representing a yellow light and segment ‘d’ representing a green light. With the traffic sensors in the road represented by four slide switches (SW17, SW15, SW13 & SW11). The emergency Amber flash switch should be connected to slide switch SW3. -2- The pedestrian call buttons will be represented by the push buttons, KEY0, KEY1, KEY2 and KEY3. With 7-segment displays HEX3 – HEX0 used to represent the pedestrian signals for the crossing of the intersection, in the following manner: Walk (segment ‘d’ on), Don’t Walk – flashing (segment ‘a’ flashing), and Don’t Walk (segment ‘a’ on continuously). For timing the development board has a 50MHz clock. Shown above is a diagram of a seven-segment display indicating how segments ‘a’, ‘g’ and ‘d’ are used to represent the red, yellow and green lights, of a traffic light, respectively on HEX7 – HEX4. While below shows seven-segment display indicating how segments ‘a’ and ‘d’ are used to indicate Don’t Walk and Walk respectively on HEX3 – HEX0. Design Specifications – Basic Design. The road traffic lights are to operate using the sequence RedGreenAmberRed according to the timing and requirements outlined below. Whenever the lights for one road are Green or Amber the crossroad must always display a red signal. All traffic lights must display a red signal for two seconds between changeovers. In their inactive state all pedestrian signals will display “Don’t Walk – continuous” (segment ‘a’ continuously on), independent of the changes in the traffic signals. The pedestrian signal can be activated following a pedestrian call being registered (by an appropriate push button(s) being pressed) and will operate in the sequence “Walk”  “Don’t Walk – flash”  “Don’t Walk – continuous” with the timing and requirements outlined below. As this intersection carries considerable pedestrian traffic the town planners have decided that the traffic sequence will contain a dedicated pedestrian crossing only period, where pedestrians may walk between any two points of the intersection (including through the middle of the intersection). Rather than embedding the pedestrian crossing sequences in with the road traffic sequence – as you are probably more familiar with. Thus whenever any traffic flow enabling signal is active (i.e. Green or Amber on) the pedestrian signals will be inactive (i.e. “Don’t Walk – continuous”) and vice versa, whenever the pedestrian signals are active (“Walk” or “Don’t Walk – flash”) all road traffic lights remain red. a d e f g c b a d e f g c b -3- Traffic Light sequence and timing When all automotive sensors are inactive the default sequence is: Green Road 1 14 sec Amber Road 1 4 sec Red Roads 1/2 2 sec Green Road 2 14 sec Amber Road 2 4 sec Red Roads 1/2 2 sec For both Roads 1 & 2, if any traffic is detected after the road has been showing green for 9 seconds, then the Green time will be extended by a further 10 seconds (i.e. making the Green time 24 seconds for that road, on that sequence. The amber and red/red times remain at 4 and 2 seconds respectively – for all sequences. Thus if both Road 1 and Road 2 have heavy traffic (i.e. traffic still detected after 9 seconds of green signal) then the sequence will be: Green Road 1 24 sec Amber Road 1 4 sec Red Roads 1/2 2 sec Green Road 2 24 sec Amber Road 2 4 sec Red Roads 1/2 2 sec Also, should Road 1 have heavy traffic and Road 2 have only light or no traffic (i.e. no traffic detected after 9 seconds of green signal) then the sequence will be: Green Road 1 24 sec Amber Road 1 4 sec Red Roads 1/2 2 sec Green Road 2 14 sec Amber Road 2 4 sec Red Roads 1/2 2 sec And alternatively, should Road 2 have heavy traffic and Road 1 have only light or no traffic (i.e. no traffic detected after 9 seconds of green signal) then the sequence will be: Green Road 1 14 sec Amber Road 1 4 sec Red Roads 1/2 2 sec Green Road 2 24 sec Amber Road 2 4 sec Red Roads 1/2 2 sec When a pedestrian crossing sequence is required this is always inserted after the Road 2 sequence, following the 2 seconds of red in both directions. Pushing a pedestrian crossing button (outside of the “Walk” period) will register a “pedestrian call” and a pedestrian crossing sequence will be inserted as soon as the next Road 2 sequence is complete. Should a pedestrian call be registered at only one site, then the pedestrian crossing sequence will be: -4- : Red Roads 1/2 2 sec “Walk” (‘d’ on) 18 sec (still Red Roads 1/2) “Don’t Walk Flashing” (‘a’ flashing) 6 sec (still Red Roads 1/2) “Don’t Walk” (‘a’ on) 2 sec (still Red Roads 1/2) Green Road 1 : : Alternatively, should a pedestrian call be registered at more than one site, then the “Walk” portion of the pedestrian crossing sequence will be extended by a further 8 seconds, thus: : Red Roads 1/2 2 sec “Walk” (‘d’ on) 26 sec (still Red Roads 1/2) “Don’t Walk Flashing” (‘a’ flashing) 6 sec (still Red Roads 1/2) “Don’t Walk” (‘a’ on) 2 sec (still Red Roads 1/2) Green Road 1 : : All pedestrian calls will be cleared as soon as the “Walk” (‘d’ on) signal is activated, and will not register again until the “Walk” (‘d’ on) signal is no longer active. Any pedestrian calls (i.e. a pedestrian button push) made during the “Don’t Walk Flashing” signal will be registered as a call towards the next sequence and have no effect on the current length of the “Don’t Walk Flashing” signal. As an example, if the automotive traffic is “heavy” in both directions, and there is also a heavy demand on the pedestrian crossing, then the total sequence would be: : Green Road 1 24 sec Amber Road 1 4 sec Red Roads 1/2 2 sec Green Road 2 24 sec Amber Road 2 4 sec Red Roads 1/2 2 sec “Walk” (‘d’ on) 26 sec (still Red Roads 1/2) “Don’t Walk Flashing” (‘a’ flashing) 6 sec (still Red Roads 1/2) “Don’t Walk” (‘a’ on) 2 sec (still Red Roads 1/2) Green Road 1 24 sec : The traffic controller system must respond to road sensor changes within one second. (Hint – The core of your design may include a state machine that is clocked at 1Hz). Although, you may need a faster clock to register the pedestrian call buttons. Incorporate an emergency Amber flash switch in your design (SW3). When activated the system should move to the ‘Red both directions’ state as soon as possible (i.e. it must go through four seconds of amber if currently green or amber, or through six seconds of “Don’t Walk Flashing” should a pedestrian sequence be active. Then after two seconds of ‘Red both directions’ plus “Don’t Walk” (‘a’ on) it should flash amber at 1Hz in both directions. In this state all pedestrian -5- signals will remain continuously showing “Don’t Walk” and no pedestrian call buttons will be registered. The design must also include an reset (active low), which will immediately place the lights on both roads in the Red state, plus all pedestrian signals showing “Don’t Walk” continuously, hold for two seconds, and then move to normal operations. You should use SW0 for the reset. For the purposes of testing and demonstrating this assignment, you should include a state clock speed modification option (i.e. x4); under “test switch” control (SW2). This will enable an option of viewing (and testing) the sequence changes more quickly. Finally, so that each design is unique, arrange for a selectable option (using SW1) where your student number is displayed on the 7-segment displays. Clearly when the student number is being displayed the traffic light status cannot be shown, although normal operations should continue in the background. That is, SW1 controls a multiplexer that selects between traffic light and student number data to be displayed. There is no need to include this section in your report, as it is not part of the Traffic Light Controller design. However, it is required for the demonstration. Design Specifications – Enhanced Design. Add additional features to enhance your design. 1. Implement the “Walk”/”Don’t Walk” on the LCD display. 2. Display a count of the current ‘seconds’ for a particular state in the sequence. i.e. count up the seconds in “green-red”, then “amber-red”, then “red-red”, then “red-green” etc. 3. Implement Green right turn arrows on the cross roads. Use the four slide switches (SW16, SW14, SW12 & SW10) for the right turn sensors. If a North or East direction road has an right turn sensors that is active prior to the intended green cycle of that road then an additional 6 seconds inserted into the sequence showing “Green Arrow” and “Green” in one direction with “Red” in the opposite direction (i.e. South or West). After the 6 seconds have elapsed the “Green Arrow” is switched off while the “Green” remains on with “Red” still showing in the opposite direction. After a further four seconds the “Red” in opposite direction changes to “green” and the sequence continues normally. Alternatively, the right turn arrow for South or East direction roads is inserted at the end of the green sequence, as follows. If a South or West has an active right turn sensor then at the end of the common “Green” time for that road then an additional ten seconds is added to the sequence to accommodate the “Green Arrow”. This consists of four seconds of “Amber” in the corresponding opposite direction, with “Green” still showing in the South or East direction, followed by “Red” in the opposite direction, and “Green Arrow” with “Green” still on for a further 6 seconds. The cycle then moves to “Amber” in the South or East direction with the “Green Arrow” off and “Red” showing in the opposite direction for four seconds. After that is the “All Red” state for two seconds and then the start of a new sequence. For the purposes of the demonstration HEX7 & HEX6 are North & South respectively, while HEX5 & HEX4 are East & West respectively. As an example the following is a heavy traffic sequence with right turns. Red All Roads 2 sec Green and Green Arrow On North Road (South Red) 6 sec Green North Road with Green Arrow off (South Red) 4 sec Green North & South Roads 24 sec -6- Amber North Road with Green South Road 4 sec Red North Road with Green South Road 2 sec Green and Green Arrow On South Road (North Red) 6 sec Amber with Green Arrow off South Road (North Red) 4 sec Red All Roads 2 sec Green and Green Arrow On East Road (West Red) 6 sec Green East Road with Green Arrow off (West Red) 4 sec Green East & West Roads 24 sec Amber East Road with Green West Road 4 sec Red East Road with Green West Road 2 sec Green and Green Arrow On West Road (East Red) 6 sec Amber with Green Arrow off West Road (East Red) 4 sec Red All Roads 2 sec Shown above is a diagram of a seven-segment display indicating how segment ‘c’ is used to indicate a green right turn arrow in a traffic light, in conjunction with ‘a’, ‘g’ and ‘d’ representing the red, yellow and green lights. Notes/Hints: (i) A pedestrian signal sequence will only occur if a pedestrian call button has been pressed (and hence registered); otherwise it will remain in the continuous “Don’t Walk” state. (ii) The decision to extend a traffic signal sequence from 14 to 24 seconds should be made between the 10 and 14 second mark (inclusive). i.e. read the traffic sensors between these times. (iii) It is recommended that you practice implementing some of the basic functions on the DE2 Board first and build on this before implementing the entire design. At the end of the day, a partially implemented prototype that works will be easier to demonstrate than an entire design that does not work at all. (iv) There are many different ways of describing timing circuits in VHDL, not all are synthesisable. (v) At this stage it may be safer to stick with the standard ieee libraries, while it is possible to set up your own libraries – great care needs to be exercised. a d e f g c b -7- (vi) If you use a package – keep it in your work library, download it to the same folder as your design files (for the Quartus II compiler) and compile it (using the Quartus II compiler) before compiling your vending machine design. (vii) MOST IMPORTANT – the Quartus II compiler does NOT like integers of different ranges being assigned to each other – even though this may compile and simulate correctly in ModelSim. For your assignment report YOU ARE REQUIRED TO SUBMIT THE FOLLOWING: (a) Block diagrams of your design, showing the hierarchy of the design and signals at each level. You can use HDL Designer or another drawing package if you wish. To assist the explanation of your design (e) it may be appropriate to embed these in the written text. (b) Printout(s) of your Traffic Light Controller design (inc. VHDL code). Key parts of the design graphics/code should be included in the main body of the report, along with the explanation of the design. With the complete design code included as an appendix. Reset Amber Flash Road 1 Lights Pedestrian Signals Pedestrian Call Buttons Display Student No. Traffic Sensors Test Road 2 Lights -8- (c) Printout(s) of your test bench (stimulus) file(s). Where key to the understanding of the testing methodology and simulation results these should included in the main body of the report. Otherwise, a complete set of testbench code must be included as an appendix. (d) Test data (i.e. annotated printouts of simulation results and summary of on board testing); <> (e) A concise (two – three pages writing) explanation of your design and your testing methodologies (i.e. how your circuit works, and why your test results demonstrate that it is functioning correctly), also include comments on any particular innovative ideas you have implemented in your design; (f) Include a summary of the FPGA resource usage of your completed design. Briefly comment on the general efficiency of your design, remember that, typically the smaller the design the lower the cost (as it may fit in a smaller/cheaper device), and the lower the power consumption. Are there any areas where you think the design could save some resources by being implemented differently? You are not required to make changes to the VHDL just brief comment(s). (Half page plus resource usage summary). Submission (by 2pm Monday, September 14):  Your complete report (including code) must be converted to an OCR compatible (i.e. searchable) PDF file and submitted to the Design Assignment drop box on the LMS site for this subject. No paper copies are required.  When you submit your assignment it will be checked automatically by the Turnitin software for similarity with past and present work, web sites, books etc. Any report with a high Turnitin similarity index will be scrutinised for potential plagiarism.  It is highly recommended that you submit a draft copy of your assignment report, to the draft Turnitin drop box (on LMS) and check the generated Turnitin report before finalising your submission. If you submit plagiarised work (that is work copied from others – including code) it will most likely be identified and your assignment deemed unsatisfactory! YOU WILL BE REQUIRED TO SUBMIT YOUR DESIGN CODE AND DEMONSTRATE YOUR DESIGN IN PRACTICAL CLASS SESSION IN THE WEEK PRIOR TO THE REPORT DUE DATE (i.e. September 9). Jim Whittington August 2015 -9- APPENDIX – Altera DE2 Board, Switch, LED, 7-Segment Display and Clock pins The following information is taken from the Altera DE2 Board Manual Signal Name FPGA Pin Description SW0 PIN_N25 Slide Switch[0] SW1 PIN_N26 Slide Switch[1] SW2 PIN_P25 Slide Switch[2] SW3 PIN_AE14 Slide Switch[3] SW4 PIN_AF14 Slide Switch[4] SW5 PIN_AD13 Slide Switch[5] SW6 PIN_AC13 Slide Switch[6] SW7 PIN_C13 Slide Switch[7] SW8 PIN_B13 Slide Switch[8] SW9 PIN_A13 Slide Switch[9] SW10 PIN_N1 Slide Switch[10] SW11 PIN_P1 Slide Switch[11] SW12 PIN_P2 Slide Switch[12] SW13 PIN_T7 Slide Switch[13] SW14 PIN_U3 Slide Switch[14] SW15 PIN_U4 Slide Switch[15] SW16 PIN_V1 Slide Switch[16] SW17 PIN_V2 Slide Switch[17] Table-1 Altera DE2 Board Slide Switch Pin Assignments Signal Name FPGA Pin Description KEY0 PIN_G26 Pushbutton[0] KEY1 PIN_N23 Pushbutton [1] KEY2 PIN_P23 Pushbutton [2] KEY3 PIN_W26 Pushbutton [3] Table-2 Altera DE2 Board Push Button Pin Assignments Signal Name FPGA Pin Description LEDR0 PIN_AE23 Red LED[0] LEDR1 PIN_AF23 Red LED[1] LEDR2 PIN_AB21 Red LED[2] LEDR3 PIN_AC22 Red LED[3] LEDR4 PIN_AD22 Red LED[4] LEDR5 PIN_AD23 Red LED[5] LEDR6 PIN_AD21 Red LED[6] LEDR7 PIN_AC21 Red LED[7] LEDR8 PIN_AA14 Red LED[8] LEDR9 PIN_Y13 Red LED[9] LEDR10 PIN_AA13 Red LED[10] LEDR11 PIN_AC14 Red LED[11] LEDR12 PIN_AD15 Red LED[12] -10- LEDR13 PIN_AE15 Red LED[13] LEDR14 PIN_AF13 Red LED[14] LEDR15 PIN_AE13 Red LED[15] LEDR16 PIN_AE12 Red LED[16] LEDR17 PIN_AD12 Red LED[17] LEDG0 PIN_AE22 Green LED[0] LEDG1 PIN_AF22 Green LED[1] LEDG2 PIN_W19 Green LED[2] LEDG3 PIN_V18 Green LED[3] LEDG4 PIN_U18 Green LED[4] LEDG5 PIN_U17 Green LED[5] LEDG6 PIN_AA20 Green LED[6] LEDG7 PIN_Y18 Green LED[7] LEDG8 PIN_Y12 Green LED[8] Table-3 Altera DE2 LED Pin Assignments Signal Name FPGA Pin Description HEX0[0] PIN_AF10 HEX0 Segment a HEX0[1] PIN_AB12 HEX0 Segment b HEX0[2] PIN_AC12 HEX0 Segment c HEX0[3] PIN_AD11 HEX0 Segment d HEX0[4] PIN_AE11 HEX0 Segment e HEX0[5] PIN_V14 HEX0 Segment f HEX0[6] PIN_V13 HEX0 Segment g HEX1 [0] PIN_V20 HEX1 Segment a HEX1 [1] PIN_V21 HEX1 Segment b HEX1 [2] PIN_W21 HEX1 Segment c HEX1 [3] PIN_Y22 HEX1 Segment d HEX1 [4] PIN_AA24 HEX1 Segment e HEX1 [5] PIN_AA23 HEX1 Segment f HEX1 [6] PIN_AB24 HEX1 Segment g HEX2 [0] PIN_AB23 HEX2 Segment a HEX2 [1] PIN_V22 HEX2 Segment b HEX2 [2] PIN_AC25 HEX2 Segment c HEX2 [3] PIN_AC26 HEX2 Segment d HEX2 [4] PIN_AB26 HEX2 Segment e HEX2 [5] PIN_AB25 HEX2 Segment f HEX2 [6] PIN_Y24 HEX2 Segment g HEX3 [0] PIN_Y23 HEX3 Segment a HEX3 [1] PIN_AA25 HEX3 Segment b HEX3 [2] PIN_AA26 HEX3 Segment c HEX3 [3] PIN_Y26 HEX3 Segment d HEX3 [4] PIN_Y25 HEX3 Segment e HEX3 [5] PIN_U22 HEX3 Segment f -11- HEX3 [6] PIN_W24 HEX3 Segment g HEX4 [0] PIN_U9 HEX4 Segment a HEX4 [1] PIN_U1 HEX4 Segment b HEX4 [2] PIN_U2 HEX4 Segment c HEX4 [3] PIN_T4 HEX4 Segment d HEX4 [4] PIN_R7 HEX4 Segment e HEX4 [5] PIN_R6 HEX4 Segment f HEX4 [6] PIN_T3 HEX4 Segment g HEX5 [0] PIN_T2 HEX5 Segment a HEX5 [1] PIN_P6 HEX5 Segment b HEX5 [2] PIN_P7 HEX5 Segment c HEX5 [3] PIN_T9 HEX5 Segment d HEX5 [4] PIN_R5 HEX5 Segment e HEX5 [5] PIN_R4 HEX5 Segment f HEX5 [6] PIN_R3 HEX5 Segment g HEX6 [0] PIN_R2 HEX6 Segment a HEX6 [1] PIN_P4 HEX6 Segment b HEX6 [2] PIN_P3 HEX6 Segment c HEX6 [3] PIN_M2 HEX6 Segment d HEX6 [4] PIN_M3 HEX6 Segment e HEX6 [5] PIN_M5 HEX6 Segment f HEX6 [6] PIN_M4 HEX6 Segment g HEX7 [0] PIN_L3 HEX7 Segment a HEX7 [1] PIN_L2 HEX7 Segment b HEX7 [2] PIN_L9 HEX7 Segment c HEX7 [3] PIN_L6 HEX7 Segment d HEX7 [4] PIN_L7 HEX7 Segment e HEX7 [5] PIN_P9 HEX7 Segment f HEX7 [6] PIN_N9 HEX7 Segment g Table-4 Altera DE2 Board 7-Segment Display Pin Assignments Signal Name FPGA Pin Description CLOCK_27 PIN_D13 27 MHz Clock CLOCK_50 PIN_N2 50 MHz Clock EXT_CLOCK PIN_P26 External Clock Input (SMA) Table-5 Altera DE2 Board Clock Pin Assignments

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Assignment 2 Conditional Probability, Bayes Theorem, and Random Variables Conditional Probability and Bayes’ Theorem Problems 1-14 from Problem Set on Conditional Probability and Bayes’ Theorem I am including all the question here so that there is no confusion. Q1. Pair of six sided dices are rolled and the outcome is noted: What is the sample space? What is the size of the sample space? Suppose all we are interested in is the sum of the two outcomes. What is the probability that the sum of the two is 6? 7? 8? (Note: This can be solved using both enumeration and conditional probability method). Here, it makes more sense to use the enumeration approach than conditional probability. It is, however, listed here to set the stage for Q5. What is the probability that the sum of the two is above 5 and the two numbers are equal? Express this question in terms of events A, B, and set operators. What is the probability that the sum of the two is above 5 or the two numbers are equal? Express this question in terms of events A, B, and set operators. Q2. If P(A)=0.4, P(B)=0.5 and P(A∩B)=0.3 What is the value of (a) P(A|B) and (b) P(B|A) Q3. At a fair, a vendor has 25 helium balloons on strings: 10 balloons are yellow, 8 are red, and 7 are green. A balloon is selected at random and sold. Given that the balloon sold is yellow, what is the probability that the next balloon selected at random is also yellow? Q4. A bowl contains seven blue chips and three red chips. Two chips are to be drawn at random and without replacement. What is the probability that the fist chip is a red chip and the second a blue? Express this question in terms of events A, B, and set operators and use conditional probability. Q5. Three six sided dices are rolled and the outcome is noted: What is the size of the sample space? What is the probability that the sum of the three numbers is 6? 13? 18? Solve using conditional probability How does the concept of conditional probability help? Q6. A grade school boy has 5 blue and four white marbles in his left pocket and four blue and five white marbles in his right pocket. If he transfers one marble at random from his left pocket to his right pocket, what is the probability of his then drawing a blue marble from his right pocket? Q7. In a certain factory, machine I, II, and III are all producing springs of the same length. Of their production, machines I, II, and III produce 2%, 1%, and 3% defective springs respectively. Of the total production of springs in the factory, machine I produces 35%, machine II produces 25%, and machine III produces 40%. If one spring is selected at random from the total springs produced in a day, what is the probability that it is defective? Given that the selected spring is defective, what is the probability that it was produced on machine III? Q8. Bowl B1 contains 2 white chips, bowl B2 contains 2 red chips, bowl B3 contains 2 white and 2 red chips, and Bowl B4 contains 3 white chips and 1 red chip. The probabilities of selecting bowl B1, B2, B3, and B4 are 1/2, 1/4, 1/8, and 1/8 respectively. A bowl is selected using these probabilities, and a chip is then drawn at random. Find P(W), the probability of drawing a white chip P(B1|W): the probability that bowl B1 was selected, given that a white chip was drawn. Q9. A pap smear is a screening procedure used to detect cervical cancer. For women with this cancer, there are about 16% false negative. For women without cervical cancer, there are about 19% false positive. In the US, there are about 8 women in 100,000 who have this cancer. What is the probability that a woman who has been tested positive actually has cervical cancer? Q10. There is a new diagnostic test for a disease that occurs in about 0.05% of the population. The test is not perfect but will detect a person with the disease 99% of the time. It will, however, say that a person without the disease has the disease about 3% of the time. A person is selected at random from the population and the test indicates that this person has the disease. What are the conditional probabilities that The person has the disease The person does not have the disease Q11. Consider two urns: the first contains two white and seven black balls, and the second contains five white and six black balls. We flip a fair coin and then draw a ball from the first urn or the second urn depending on whether the outcome was a head or a tails. What is the conditional probability that the outcome of the toss was heads given that a white ball was selected? Q12. In answering a question on a multiple-choice test a student either knows the answer or guesses. Let p be the probability that she knows the answer. Assume that a student who guesses at the answer will be correct with probability 1/m where m is the number of multiple choice alternatives. What is the conditional probability that a student knew the answer given that she answered it correctly? Q13. A laboratory blood test is 95% effective in detecting a certain disease when it is, in fact, present. However, the test also yields a “false positive” result for 1% of the healthy persons tested (i.e., if a healthy person is tested, then, with probability 0.01, the test result will imply that he has the disease.). If 0.5% of the population actually have the disease, what is the probability a person has the disease given that his test results are positive? Q14. An urn contains b black balls and r red balls. One of the balls is drawn at random, but when it is put back in the urn, c additional balls of the same color are put in it with it. Now suppose that we draw another ball. What is the probability that the first ball drawn was black given that the second ball drawn was red? Random Variables Q15. Suppose an experiment consists of tossing two six sided fair dice and observing the outcomes. What is the sample space? Let Y denote the sum of the two numbers that appear on the dice. Define Y to be a random variable. What are the values that the random variable Y can take? What does it mean if we say Y=7? What does it mean if I say that Y<7? Q16. Suppose an experiment consists of picking a sample of size n from a population of size N. Assume that n≪N. Also, assume that the population contains D defective parts and N-D non defective parts, where n<D≪N. What is the sample space? If we are interested in knowing the number (count) of defective parts in the sample space, describe how, the concept of a random variable could help. Define a random variable Y and describe what values the random variable Y can take? What does it mean if we say Y=5? Q17. Suppose an experiment consists of tossing two fair coins. Let Y denote the number of heads appearing. Define Y to be a random variable. What are the values that the random variable Y can take? What does it mean if we say Y=1? What are the probabilities associated with each outcome? What is the sum of the probabilities associated with all possible values that Y can take? Q18. A lot, consisting of 100 fuses, is inspected by the following procedure. Five fuses are chosen at random and tested: if all 5 fuses pass the inspection, the lot is accepted. Suppose that the lot contains 20 defective fuses. What is the probability of accepting the lot? Define the random variable, its purpose, and the formula/concept that you would use. Q19. In a small pond there are 50 fish, 10 of which have been tagged. If a fisherman’s catch consists of 7 fish, selected at random and without replacement. Give an example of a random variable that can be defined if we are interested in knowing the number of tagged fish that are caught? What is the probability that exactly 2 tagged fish are caught? Define the random variable, its purpose, and the formula/concept that you would use. Applied to Quality Control Q20. My manufacturing firm makes 100 cars every day out of which 10 are defective; the quality control inspector tests drives 5 different cars. Based on the sample, the quality control inspector will make a generalization about the whole batch of 100 cars that I have on that day. Let d denote the number of defective cars in the sample What are the values that d can take (given the information provided above)? What is the probability that the quality control inspector will conclude that: (a) 0% of the cars are defective- call this P(d=0); (b) 20% of the cars are defective- call this P(d=1); (c) 40% of the cars are defective- call this P(d=2); (d) 60% of the cars are defective- call this P(d=3),(e) 80% of the cars are defective- call this P(d=4), and (f) 100% of the cars are defective- call this P(d=5) What is P(d=0)+ P(d=1)+ P(d=2)+ P(d=3)+ P(d=4)+ P(d=5) Let’s assume that the quality control inspector has been doing the testing for a while (say for the past 1000 days). What is the average # of defective cars that he found? Q21. Assume that the quality control inspector is selecting 1 car at a time and the car that he tested is put back in the pool of possible cars that he can test (sample with replacement). Let d denote the number of defective cars in the sample (n) What are the values that d can take (given the information provided above)? What is the probability that the quality control inspector will conclude that: (a) 0% of the cars are defective, (b) 20% of the cars are defective, (c) 40% of the cars are defective, (d) 60% of the cars are defective, (e) 80% of the cars are defective, and (f) 100% of the cars are defective. Let’s call these P(d=0)….P(d=5) What is P(d=0)+ P(d=1)+ P(d=2)+ P(d=3)+ P(d=4)+ P(d=5) Let’s assume that the quality control inspector has been doing the testing for a while (say for the past 1000 days). What is the average # of defective cars that he found? Interesting Problems Q22. A closet contains n pairs of shoes. If 2r shoes are chosen at random (2r<n), what is the probability that there will be no matching pair in the sample? Q23. In a draft lottery containing the 366 days of the leap year, what is the probability that the first 180 days drawn (without replacement) are evenly distributed among the 12 months? What is the probability that the first 30 days drawn contain none from September? Q25. You and I play a coin-tossing game. If the coin falls heads I score one, if tails, you score one. In the beginning, the score is zero. What is the probability that after 2n throws our scores are equal? What is the probability that after 2n+1 throws my score is three more than yours?

Assignment 2 Conditional Probability, Bayes Theorem, and Random Variables Conditional Probability and Bayes’ Theorem Problems 1-14 from Problem Set on Conditional Probability and Bayes’ Theorem I am including all the question here so that there is no confusion. Q1. Pair of six sided dices are rolled and the outcome is noted: What is the sample space? What is the size of the sample space? Suppose all we are interested in is the sum of the two outcomes. What is the probability that the sum of the two is 6? 7? 8? (Note: This can be solved using both enumeration and conditional probability method). Here, it makes more sense to use the enumeration approach than conditional probability. It is, however, listed here to set the stage for Q5. What is the probability that the sum of the two is above 5 and the two numbers are equal? Express this question in terms of events A, B, and set operators. What is the probability that the sum of the two is above 5 or the two numbers are equal? Express this question in terms of events A, B, and set operators. Q2. If P(A)=0.4, P(B)=0.5 and P(A∩B)=0.3 What is the value of (a) P(A|B) and (b) P(B|A) Q3. At a fair, a vendor has 25 helium balloons on strings: 10 balloons are yellow, 8 are red, and 7 are green. A balloon is selected at random and sold. Given that the balloon sold is yellow, what is the probability that the next balloon selected at random is also yellow? Q4. A bowl contains seven blue chips and three red chips. Two chips are to be drawn at random and without replacement. What is the probability that the fist chip is a red chip and the second a blue? Express this question in terms of events A, B, and set operators and use conditional probability. Q5. Three six sided dices are rolled and the outcome is noted: What is the size of the sample space? What is the probability that the sum of the three numbers is 6? 13? 18? Solve using conditional probability How does the concept of conditional probability help? Q6. A grade school boy has 5 blue and four white marbles in his left pocket and four blue and five white marbles in his right pocket. If he transfers one marble at random from his left pocket to his right pocket, what is the probability of his then drawing a blue marble from his right pocket? Q7. In a certain factory, machine I, II, and III are all producing springs of the same length. Of their production, machines I, II, and III produce 2%, 1%, and 3% defective springs respectively. Of the total production of springs in the factory, machine I produces 35%, machine II produces 25%, and machine III produces 40%. If one spring is selected at random from the total springs produced in a day, what is the probability that it is defective? Given that the selected spring is defective, what is the probability that it was produced on machine III? Q8. Bowl B1 contains 2 white chips, bowl B2 contains 2 red chips, bowl B3 contains 2 white and 2 red chips, and Bowl B4 contains 3 white chips and 1 red chip. The probabilities of selecting bowl B1, B2, B3, and B4 are 1/2, 1/4, 1/8, and 1/8 respectively. A bowl is selected using these probabilities, and a chip is then drawn at random. Find P(W), the probability of drawing a white chip P(B1|W): the probability that bowl B1 was selected, given that a white chip was drawn. Q9. A pap smear is a screening procedure used to detect cervical cancer. For women with this cancer, there are about 16% false negative. For women without cervical cancer, there are about 19% false positive. In the US, there are about 8 women in 100,000 who have this cancer. What is the probability that a woman who has been tested positive actually has cervical cancer? Q10. There is a new diagnostic test for a disease that occurs in about 0.05% of the population. The test is not perfect but will detect a person with the disease 99% of the time. It will, however, say that a person without the disease has the disease about 3% of the time. A person is selected at random from the population and the test indicates that this person has the disease. What are the conditional probabilities that The person has the disease The person does not have the disease Q11. Consider two urns: the first contains two white and seven black balls, and the second contains five white and six black balls. We flip a fair coin and then draw a ball from the first urn or the second urn depending on whether the outcome was a head or a tails. What is the conditional probability that the outcome of the toss was heads given that a white ball was selected? Q12. In answering a question on a multiple-choice test a student either knows the answer or guesses. Let p be the probability that she knows the answer. Assume that a student who guesses at the answer will be correct with probability 1/m where m is the number of multiple choice alternatives. What is the conditional probability that a student knew the answer given that she answered it correctly? Q13. A laboratory blood test is 95% effective in detecting a certain disease when it is, in fact, present. However, the test also yields a “false positive” result for 1% of the healthy persons tested (i.e., if a healthy person is tested, then, with probability 0.01, the test result will imply that he has the disease.). If 0.5% of the population actually have the disease, what is the probability a person has the disease given that his test results are positive? Q14. An urn contains b black balls and r red balls. One of the balls is drawn at random, but when it is put back in the urn, c additional balls of the same color are put in it with it. Now suppose that we draw another ball. What is the probability that the first ball drawn was black given that the second ball drawn was red? Random Variables Q15. Suppose an experiment consists of tossing two six sided fair dice and observing the outcomes. What is the sample space? Let Y denote the sum of the two numbers that appear on the dice. Define Y to be a random variable. What are the values that the random variable Y can take? What does it mean if we say Y=7? What does it mean if I say that Y<7? Q16. Suppose an experiment consists of picking a sample of size n from a population of size N. Assume that n≪N. Also, assume that the population contains D defective parts and N-D non defective parts, where n

xposure Evaluation – Single substance, different exposure time, different concentrations: 3- A person is working in a factory producing. This person is exposure to different concentrations of Toluene with different exposures time. The results of a personal sampling in an 8-hour shift is shown here: Exposure Time Concentration 3 hr. 35 min 790 mg/m^3 43 min 27 ppm 3.70 hr. 800 mg/m^3 What is this worker’s time weighted average of exposure in mg/m^3? Is the company in compliance with the OSHA requirement? 6- Phenyl ether can be used in soap factories as fragrance. A worker is exposed to this material during 9-hour shift and the exposure information is given in the following table: Exposure Time Concentration 1 hr. 45 min 4×〖10〗^(-6 ) mg/〖cm〗^3 2 hr. 5 min 7×〖10〗^(-6 ) mg/〖cm〗^3 65 min 3×〖10〗^(-3 ) mg/L Remaining Time 7.5 mg/m^3 What is this worker’s time weighted average of exposure in mg/m^3? Is the company in compliance with the OSHA requirement? 7- One of the major ingredients of insect repellents is Naphthalene. Consider a situation in which a worker is exposed to this material. The exposure time and concentration is given in a table below: Exposure Time Concentration 275 min 12 ppm 40 min 5 ppm 165 min 10 ppm What is this worker’s time weighted average of exposure? Is the condition hazardous? Exposure Evaluation – Multiple substance, equal exposure time, constant concentrations: 1- A person is exposed to the vapors of Benzene and Ethyl alcohol. Tests show that the concentration of Benzene is 1 ppm and Ethyl alcohol is 450 ppm. What is the threshold limit value of the mix? Is this person at risk? 6- Several workers at a rubber and leather manufacturing company are exposed to vapors of Vinyl chloride, Toluene and Xylene with concentration of 0.2 ppm, 135 ppm 200 mg/m^3 respectively. What is the threshold limit value of the mix? Are the employees at risk? 7- Several workers exposed to vapors of Ammonia, Arsine, Chloroform and Acetone with concentration of 12 ppm, 0.04 mg/m^3, 15 ppm, and 570 mg/m^3 respectively. What is the threshold limit value of the mix? Are the employees at risk?

xposure Evaluation – Single substance, different exposure time, different concentrations: 3- A person is working in a factory producing. This person is exposure to different concentrations of Toluene with different exposures time. The results of a personal sampling in an 8-hour shift is shown here: Exposure Time Concentration 3 hr. 35 min 790 mg/m^3 43 min 27 ppm 3.70 hr. 800 mg/m^3 What is this worker’s time weighted average of exposure in mg/m^3? Is the company in compliance with the OSHA requirement? 6- Phenyl ether can be used in soap factories as fragrance. A worker is exposed to this material during 9-hour shift and the exposure information is given in the following table: Exposure Time Concentration 1 hr. 45 min 4×〖10〗^(-6 ) mg/〖cm〗^3 2 hr. 5 min 7×〖10〗^(-6 ) mg/〖cm〗^3 65 min 3×〖10〗^(-3 ) mg/L Remaining Time 7.5 mg/m^3 What is this worker’s time weighted average of exposure in mg/m^3? Is the company in compliance with the OSHA requirement? 7- One of the major ingredients of insect repellents is Naphthalene. Consider a situation in which a worker is exposed to this material. The exposure time and concentration is given in a table below: Exposure Time Concentration 275 min 12 ppm 40 min 5 ppm 165 min 10 ppm What is this worker’s time weighted average of exposure? Is the condition hazardous? Exposure Evaluation – Multiple substance, equal exposure time, constant concentrations: 1- A person is exposed to the vapors of Benzene and Ethyl alcohol. Tests show that the concentration of Benzene is 1 ppm and Ethyl alcohol is 450 ppm. What is the threshold limit value of the mix? Is this person at risk? 6- Several workers at a rubber and leather manufacturing company are exposed to vapors of Vinyl chloride, Toluene and Xylene with concentration of 0.2 ppm, 135 ppm 200 mg/m^3 respectively. What is the threshold limit value of the mix? Are the employees at risk? 7- Several workers exposed to vapors of Ammonia, Arsine, Chloroform and Acetone with concentration of 12 ppm, 0.04 mg/m^3, 15 ppm, and 570 mg/m^3 respectively. What is the threshold limit value of the mix? Are the employees at risk?

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Which statement regarding science technology is false? Select one: Science technology has brought about life-improving discoveries, such as antibiotics. Science technology helps us to understand the causes of cancer. Science technology is a basis for all ethical or moral decisions. Science technology may ease the feeding of the world population by producing new plant strains. Scientific experimentation may make use of a model instead of an actual subject.

Which statement regarding science technology is false? Select one: Science technology has brought about life-improving discoveries, such as antibiotics. Science technology helps us to understand the causes of cancer. Science technology is a basis for all ethical or moral decisions. Science technology may ease the feeding of the world population by producing new plant strains. Scientific experimentation may make use of a model instead of an actual subject.

Which statement regarding science technology is false? Select one: Science … Read More...