Apollo Drones Inc. manufactures small aerial drones for a variety of applications. Although they source some...

 

Transcribed Image Text:

Apollo Drones Inc. manufactures small aerial drones for a variety of applications. Although they source some of the parts, the frame for the body of the drone is manufactured in-house and must meet strict quality control guidelines. One of the measures that is particularly important is the total weight of the body frame. Quality control is based on statistical properties of sampling to make inferences about the process of interest. The company would like you to apply the analytic and problem-solving skills you recently developed in a statistics and data analytics course to provide guidance on the best parameters for the manufacturing process and to design a testing protocol to ensure quality standards are maintained. In particular, the company would like you to analyze data for a new small drone it has developed for which the body frame should weigh no more than 0.6 pounds. The company has begun an initial production run, manufacturing 5 units per week, and provides you with data from the first eight weeks. It would like you to determine whether the current average frame weight is acceptable, or whether it should be reduced, and what sample size of manufactured drones should be tested each day for quality control for a 95% confidence interval to have a margin of error no greater than 0.02. The company can reduce the average frame weight for the manufacturing process by up to 0.05 pounds per unit by machining out some of the metal of the frame, but the company estimates that each 0.01 lb. reduction in weight will cost an additional $3 per unit to manufacture. The company cannot adjust the standard deviation of the manufacturing process. Each drone frame that weighs more than 0.6 pounds and that goes into a final product for a customer will cost the company a total of $325 since the company will need to provide a free replacement drone to the customer under the product warranty. Assume the company plans to manufacture 100 units per day. 1. What is the point estimate of the ean frame weight for the manufacturi process? In other words, based on the sample, what is the point estimate of the population mean for the process? 2. What is the point estimate of the standard deviation of the frame weight for the manufacturing process? 3. Assume the frame weight follows a normal distribution. Given the current mean and standard deviation of the manufacturing process, what proportion of drone frames will weigh more than 0.6 pounds? 4. If 100 drones are manufactured per day at the current average frame weight, what is the expected cost per day using the proportion calculated in #3 and assuming that every drone manufactured goes into final products for customers? 5. What is the expected cost per day if the average frame weight is reduced by 0.01? 0.02? 0.03? 0.04? 0.05? Part 2: Determine what sample size of manufactured drones should be tested each day for quality control once final production begins. 6. What are the upper and lower bounds of an approximate 95% confidence interval on the average frame weight using the current average frame weight and a sample size of 5? 7. What are the upper and lower bounds of an approximate 95% confidence interval on the average frame weight using the recommended average frame weight and a sample size of 5? 8. If the company would like the margin of error (one half the total width of the confidence interval) to be no greater than 0.02 pounds, what sample size should be used? Part 3: Final recommendation 9. What is the role of assignable cause variation in quality control? Write a short explanation of what assignable cause variation is and its relationship to quality control. (This information is in the quality control video that accompanies this assignment.) 10. In 3-6 sentences, explain and justify your final recommendation to the company for the average frame weight and the quality control sample size. Within the recommendation, include a description of any other factors that you believe the company should consider, including whether any additional study is necessary or what follow-up analysis might be necessary. Apollo Drones Inc. manufactures small aerial drones for a variety of applications. Although they source some of the parts, the frame for the body of the drone is manufactured in-house and must meet strict quality control guidelines. One of the measures that is particularly important is the total weight of the body frame. Quality control is based on statistical properties of sampling to make inferences about the process of interest. The company would like you to apply the analytic and problem-solving skills you recently developed in a statistics and data analytics course to provide guidance on the best parameters for the manufacturing process and to design a testing protocol to ensure quality standards are maintained. In particular, the company would like you to analyze data for a new small drone it has developed for which the body frame should weigh no more than 0.6 pounds. The company has begun an initial production run, manufacturing 5 units per week, and provides you with data from the first eight weeks. It would like you to determine whether the current average frame weight is acceptable, or whether it should be reduced, and what sample size of manufactured drones should be tested each day for quality control for a 95% confidence interval to have a margin of error no greater than 0.02. The company can reduce the average frame weight for the manufacturing process by up to 0.05 pounds per unit by machining out some of the metal of the frame, but the company estimates that each 0.01 lb. reduction in weight will cost an additional $3 per unit to manufacture. The company cannot adjust the standard deviation of the manufacturing process. Each drone frame that weighs more than 0.6 pounds and that goes into a final product for a customer will cost the company a total of $325 since the company will need to provide a free replacement drone to the customer under the product warranty. Assume the company plans to manufacture 100 units per day. 1. What is the point estimate of the ean frame weight for the manufacturi process? In other words, based on the sample, what is the point estimate of the population mean for the process? 2. What is the point estimate of the standard deviation of the frame weight for the manufacturing process? 3. Assume the frame weight follows a normal distribution. Given the current mean and standard deviation of the manufacturing process, what proportion of drone frames will weigh more than 0.6 pounds? 4. If 100 drones are manufactured per day at the current average frame weight, what is the expected cost per day using the proportion calculated in #3 and assuming that every drone manufactured goes into final products for customers? 5. What is the expected cost per day if the average frame weight is reduced by 0.01? 0.02? 0.03? 0.04? 0.05? Part 2: Determine what sample size of manufactured drones should be tested each day for quality control once final production begins. 6. What are the upper and lower bounds of an approximate 95% confidence interval on the average frame weight using the current average frame weight and a sample size of 5? 7. What are the upper and lower bounds of an approximate 95% confidence interval on the average frame weight using the recommended average frame weight and a sample size of 5? 8. If the company would like the margin of error (one half the total width of the confidence interval) to be no greater than 0.02 pounds, what sample size should be used? Part 3: Final recommendation 9. What is the role of assignable cause variation in quality control? Write a short explanation of what assignable cause variation is and its relationship to quality control. (This information is in the quality control video that accompanies this assignment.) 10. In 3-6 sentences, explain and justify your final recommendation to the company for the average frame weight and the quality control sample size. Within the recommendation, include a description of any other factors that you believe the company should consider, including whether any additional study is necessary or what follow-up analysis might be necessary.

Answer rating: 100% (QA)

1 The point estimate of the mean frame weight for the manufacturing process is 0 612 2 The point est... View the full answer