Quality Management

1. (20 points) Brake systems are purchased in large lots. A brake system is conforming if it stops the car traveling at 50 mph within 45 feet. Design a sampling plan which has the following characteristics

α, producer’s risk = 0.03
β, consumer’s risk  = 0.11
“good” lot  has 0.04 proportion non-conforming
“bad” lot has 0.15 proportion non-conforming
Standard deviation of the population of brake systems’ stopping distance is 5 feet. (applies to all lots)
Steps: (support all of your calculations by drawing appropriate normal curves)

1. The mean stopping distance for good lots
2. The mean stopping distance for bad lots
3. Expression for finding the critical value
4. Find the sample size after finding Z value corresponding to producer’s and consumer’s risks, and applying the formula 10-24 on page 545.
5. the critical value (cutoff value) for sample average which directs that if a random sample of size n has an average stopping distance of less than or equal to the cutoff value, the lot is accepted and if it is more than the cutoff value the lot is rejected.
6. Verify that the critical value is the same when you calculate it from µ_g or from µ_b

2. (10 points) Consider a sampling plan with n = 30 and c = 1. If n is increased to 60, (other things remaining the same) what would happen to producer’s risk, consumer’s risk and AOQL? (Other things remaining the same.) Briefly explain why.

 
Producer’s risk:
 
Consumer’s risk:
 
AOQL:
 
 

3. (10 points) Prior probability for the proportion defectives produced by a newly designed robot is given below. Suppose that you had a chance to collect a random sample of 10 units produced by this robot and found 0 defective. What are the revised probabilities for the Robot being a 1%, 2% or 3% defective Robot?

4. (15 points) Number of dissatisfied customers of LFT Airlines during the past 12 weeks, (starting from 1-1-2020) is given in the table below using a sample size of 100. Use the data to set up an attribute control chart. Comment on whether there are assignable causes and how to use the chart going forward from April 1, 2020. Set the control limits such that α – risk is 0.05.
   1. Standard error is ______________
   2. UCL for the control chart of dissatisfied customers is ________
   3. LCL for the control chart of dissatisfied customers is ________
   4. Plot the control chart.

1. Revise the chart, assuming special causes for points outside the control limits, revise the chart and the revised LCL is __________
2. Revised UCL is _________

5. (15 points) Draw a standardized control chart for proportion defectives for the following problem with variable sample sizes. Comment on the performance of the billing department. Assuming out of control data are due to assignable causes, revise the chart and report on new control limits. Use graphs as appropriate.