3. The probability density function for mechanical component is given by: fT(t) = 1/(b-a) when t <=a<=b = 0; elsewhere Determine: • Cumulative distribution of the failures (5 points) • Reliability of the components (5 points) • Hazard rate for the components (5 points) • Mean, standard deviation of the failure distribution and reliability of components at the end of 2 years, when c=0.0025 (5 points) • Plot the probability density function, probability time distribution function, Reliability function and Hard Rate function for the given distribution when a=6000 and b=12000 (5 points)

## 3. The probability density function for mechanical component is given by: fT(t) = 1/(b-a) when t <=a<=b = 0; elsewhere Determine: • Cumulative distribution of the failures (5 points) • Reliability of the components (5 points) • Hazard rate for the components (5 points) • Mean, standard deviation of the failure distribution and reliability of components at the end of 2 years, when c=0.0025 (5 points) • Plot the probability density function, probability time distribution function, Reliability function and Hard Rate function for the given distribution when a=6000 and b=12000 (5 points)

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A novel on the Amazon.com website has the following ratings, in number of stars, from reviewers: Number of Stars Frequency 1 7 2 4 3 20 4 9 5 10 What is the mean of this distribution? A) 2.57 B) 3.22 C) 3.76 D) 3.85

## A novel on the Amazon.com website has the following ratings, in number of stars, from reviewers: Number of Stars Frequency 1 7 2 4 3 20 4 9 5 10 What is the mean of this distribution? A) 2.57 B) 3.22 C) 3.76 D) 3.85

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8. value: 10.00 points The following frequency distribution reports the number of frequent flier miles, reported in thousands, for employees of Brumley Statistical Consulting Inc., during the first quarter of 2013. Frequent Flier Miles (000) Number of Employees 0 up to 4 5 4 up to 8 13 8 up to 12 22 12 up to 16 7 16 up to 20 4 ________________________________________ ________________________________________ Total 51 ________________________________________________________________________________ ________________________________________________________________________________ ________________________________________ a. How many employees were studied? Number of employees b. What is the midpoint of the first class? (Round your answer to 1 decimal place.) Midpoint d. A frequency polygon is to be drawn. What are the coordinates of the plot for the second class? , References eBook & 9. value: 10.00 points The following cumulative frequency polygon shows the hourly wages of a sample of certified welders in the Atlanta, Georgia, area. a. How many welders were studied? Number of welders b. What is the class interval? Class interval c. About how many welders earn less than \$26 per hour? Number of welders d. About 80% of the welders make less than what amount? Amount e. Twenty of the welders studied made less than what amount? Amount f. What percent of the welders make less than \$23 per hour? Percent of welders 10. value: 10.00 points The following is the number of minutes to commute from home to work for a group of 25 automobile executives. 28 25 45 37 41 19 32 25 17 23 23 28 36 31 25 20 32 25 32 43 35 42 38 32 28 a. How many classes would you recommend? Number of classes b. What class interval would you suggest? (Round up your answer to the next whole number.) Class interval c. Organize the data and plot a frequency distribution on a piece of paper. Comment on the shape of the frequency distribution.

## 8. value: 10.00 points The following frequency distribution reports the number of frequent flier miles, reported in thousands, for employees of Brumley Statistical Consulting Inc., during the first quarter of 2013. Frequent Flier Miles (000) Number of Employees 0 up to 4 5 4 up to 8 13 8 up to 12 22 12 up to 16 7 16 up to 20 4 ________________________________________ ________________________________________ Total 51 ________________________________________________________________________________ ________________________________________________________________________________ ________________________________________ a. How many employees were studied? Number of employees b. What is the midpoint of the first class? (Round your answer to 1 decimal place.) Midpoint d. A frequency polygon is to be drawn. What are the coordinates of the plot for the second class? , References eBook & 9. value: 10.00 points The following cumulative frequency polygon shows the hourly wages of a sample of certified welders in the Atlanta, Georgia, area. a. How many welders were studied? Number of welders b. What is the class interval? Class interval c. About how many welders earn less than \$26 per hour? Number of welders d. About 80% of the welders make less than what amount? Amount e. Twenty of the welders studied made less than what amount? Amount f. What percent of the welders make less than \$23 per hour? Percent of welders 10. value: 10.00 points The following is the number of minutes to commute from home to work for a group of 25 automobile executives. 28 25 45 37 41 19 32 25 17 23 23 28 36 31 25 20 32 25 32 43 35 42 38 32 28 a. How many classes would you recommend? Number of classes b. What class interval would you suggest? (Round up your answer to the next whole number.) Class interval c. Organize the data and plot a frequency distribution on a piece of paper. Comment on the shape of the frequency distribution.

Due to an unequal distribution of fuel in the wing tanks, the centers of gravity for the airplane fuselage A and wing B and C are located as shown.

## Due to an unequal distribution of fuel in the wing tanks, the centers of gravity for the airplane fuselage A and wing B and C are located as shown.

plot three diagram for (graphical of exponential distribution) (graphical of normal distribution) (graphical of lognormal distribution) The question about: In study of a new insecticide, 20 insects are exposed. Survival times in seconds are 3,5,6,7,8,9,10,10,12,15,15,18,19,20,22,25,28,30,40,60. Use the plotting position formula (i-.5/n) and test fit using graphical methods for lognormal, exponential and normal distribution

## plot three diagram for (graphical of exponential distribution) (graphical of normal distribution) (graphical of lognormal distribution) The question about: In study of a new insecticide, 20 insects are exposed. Survival times in seconds are 3,5,6,7,8,9,10,10,12,15,15,18,19,20,22,25,28,30,40,60. Use the plotting position formula (i-.5/n) and test fit using graphical methods for lognormal, exponential and normal distribution

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INEN 415 Simulation Lab 6 Fall 2015 Due Date: November 24th, 2015 (Submit via Blackboard) Description A small pizza delivery outlet in a busy metro area opens only for the lunch and dinner hours; for lunch from 11AM to 4PM and for dinner from 6PM to 11PM. Orders for single pizzas (no other orders are accepted) arrive with an inter-arrival time that is exponentially distributed with a mean of 3.25 minutes. (Need to create a rate table, see lab 5) The inside operations are handled by an OrderTaker, two IronChef, and an OvenMeister named Cruz. The outlet has one oven with a capacity of five pizzas. Two drivers driving Mustangs handle the deliveries. Timmy takes orders (for order-taking assume a triangular distribution with parameters 1, 2, 3 minutes). The IronChefs make the pizza including adding of toppings (assume a triangular distribution with parameters 2, 2.5, 3 minutes). When the pizza is made (but not cooked), the IronChefs places it in a Load Area in front of the oven. Cruz picks up the pizza from the Load Area and places the pizza in the oven (assume a triangular distribution with parameters 10, 15, 20 seconds) (Cruz is a worker) The cook time in the oven requires 15 minutes (fixed), and does not require any supervision; a buzzer alerts Cruz whenever any pizza has completed its oven time. When the pizza has cooked in the oven, Cruz takes the pizzas out of the oven (assume a triangular distribution with parameters 10, 15, 20 seconds). He carries the pizza to the Box Area. Where Cruz boxes the pizza (assume a triangular distribution with parameters 30, 45, 60 seconds) and leaves it in an area for the delivery people, who can transport a maximum of 5 pizzas (Triangular 10,20,30). Note: Cruz moves between Load Area, Oven, and Box Area. Assume travel times are negligible. Drivers take the pizza to the sink. Run model for 16 hours to ensure all pizzas are made. Simulate operations for one day using two scenarios: 1. The data as given above. 2. Inter-arrival rate decreases to 3 minutes.   Deliverable(s) I. Objectives a. Clearly define the objective(s) of the project. II. System Description / Modeling Approach a. Describe the model (personnel, processes, etc.) III. Input Data Requirements a. Describe the data collected to be used in the model. IV. Simulation Model a. Simulation Model (Screen shot of SIMIO model) V. Results / Conclusions Compare the following statististics for the two scenarios in a table. 1. Number of pizzas delivered. 2. Utilization of the all three personnel types. 3. Time in System for an order. VI. Discussion a. Based on the data provided, will the system have issues? b. As the IE professional, suggest possible changes to the system and clearly explain why such changes may improve the process. Tutorials/Simbits 1. Workers using work schedule (Simbit) 2. Single Vehicle Usage (Simbit) 3. Check on YouTube, they have many videos that can help!

## INEN 415 Simulation Lab 6 Fall 2015 Due Date: November 24th, 2015 (Submit via Blackboard) Description A small pizza delivery outlet in a busy metro area opens only for the lunch and dinner hours; for lunch from 11AM to 4PM and for dinner from 6PM to 11PM. Orders for single pizzas (no other orders are accepted) arrive with an inter-arrival time that is exponentially distributed with a mean of 3.25 minutes. (Need to create a rate table, see lab 5) The inside operations are handled by an OrderTaker, two IronChef, and an OvenMeister named Cruz. The outlet has one oven with a capacity of five pizzas. Two drivers driving Mustangs handle the deliveries. Timmy takes orders (for order-taking assume a triangular distribution with parameters 1, 2, 3 minutes). The IronChefs make the pizza including adding of toppings (assume a triangular distribution with parameters 2, 2.5, 3 minutes). When the pizza is made (but not cooked), the IronChefs places it in a Load Area in front of the oven. Cruz picks up the pizza from the Load Area and places the pizza in the oven (assume a triangular distribution with parameters 10, 15, 20 seconds) (Cruz is a worker) The cook time in the oven requires 15 minutes (fixed), and does not require any supervision; a buzzer alerts Cruz whenever any pizza has completed its oven time. When the pizza has cooked in the oven, Cruz takes the pizzas out of the oven (assume a triangular distribution with parameters 10, 15, 20 seconds). He carries the pizza to the Box Area. Where Cruz boxes the pizza (assume a triangular distribution with parameters 30, 45, 60 seconds) and leaves it in an area for the delivery people, who can transport a maximum of 5 pizzas (Triangular 10,20,30). Note: Cruz moves between Load Area, Oven, and Box Area. Assume travel times are negligible. Drivers take the pizza to the sink. Run model for 16 hours to ensure all pizzas are made. Simulate operations for one day using two scenarios: 1. The data as given above. 2. Inter-arrival rate decreases to 3 minutes.   Deliverable(s) I. Objectives a. Clearly define the objective(s) of the project. II. System Description / Modeling Approach a. Describe the model (personnel, processes, etc.) III. Input Data Requirements a. Describe the data collected to be used in the model. IV. Simulation Model a. Simulation Model (Screen shot of SIMIO model) V. Results / Conclusions Compare the following statististics for the two scenarios in a table. 1. Number of pizzas delivered. 2. Utilization of the all three personnel types. 3. Time in System for an order. VI. Discussion a. Based on the data provided, will the system have issues? b. As the IE professional, suggest possible changes to the system and clearly explain why such changes may improve the process. Tutorials/Simbits 1. Workers using work schedule (Simbit) 2. Single Vehicle Usage (Simbit) 3. Check on YouTube, they have many videos that can help!

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