INSTRUCTIONS: You will have 2 hours to complete the exam. There are 8 questions worth a total of 150 points. Not all questions have the same point value so gauge your time appropriately. Read the questions carefully and completely. Answer each question and show work in the space provided on the exam. Turn in the entire exam when you are done or when time is up. For essay questions, think before you write.

1. [15 pts] A supplier ships lot of 10,000 parts to a customer. The customer randomly samples 100 parts and tests them destructively, once tested the part is destroyed and cannot be tested again.
   • (a) [3] Is the customer sampling with or without replacement? Explain your choice briefly.

   • (b) [5] The customer will accept the lot if there are 5 or fewer defective parts in the random sample of 100. Assuming that there are 1000 defective parts in the lot, write out, in terms of a probability function, the probability that the customer accepts the lot. Do not attempt to calculate this probability.

   • (c) [5] If in a sample of 100, 4 defective parts are found, give an approximate 95%confidence interval on the number of defective parts in the lot.

   • (d) [2] Again assuming that there are 1000 defective parts in the lot, if 100 parts are removed and 4 are found to be defective, what is the chance that the next part chosen will be defective?

2. [25 pts] In a previous STAT 495 class, one team looked at the production of a plastic agitator for a washing machine. The part was made using gas-assisted injection molding. The critical quality characteristic measured was the weight of the agitator. The target weight was 0.515 with a lower specification limit of 0.505 and an upper specification limit of 0.525. Below is Minitab output on the process stability and capability for 50 subgroups of size 5. The estimate of process standard deviation is based on .

    

      
   • (a) [8] Comment on the process. Describe any trends and interpret appropriate summary statistics.

   • (b) [3] Upon further investigation it was discovered that subgroups 1-25 came from the first cavity of the injection mold and subgroups 26-50 came from the second cavity. Which of the Magnificent Seven tools would be most helpful for further examination of the process? Explain briefly.

   • (c) [8] Below is Minitab output on the process stability and capability for the second cavity. Again the estimate of process standard deviation is based on . Comment on the process. Describe any trends and interpret appropriate summary statistics.

      

        
   • (d) [6] Continuing with the examination of the second cavity, what is the value of the process potential, ? What does this tell you about the process?

3. [20 pts] Perhaps the major concept explored in STAT 495 is the idea of variation and how variation can be quantified. Pick two statistical techniques from this course and briefly discuss how the quantification of variation is central to the technique. Caution: Control charts count as only one technique. Use only the space below.

4. [30 pts] Plastic viscosity is an important characteristic of a lubricant used to reduce friction between a rotating shaft and the casing that surrounds it. Measurements of plastic viscosity were taken on two lubricants. Three batches of each lubricant were used in the tests, with four samples of fluid taken from each batch. Below are the data.

   

   • (a) [15] Complete the following analysis of variance table.

     

   • (b) [10] From the analysis of variance table in (a), compute variance components for the three sources of variation. Express these as a percentage. Which source is the largest contributer to the variation in the plastic viscosity measurements?

   • (c) [5] Is there more variability from batch to batch within a lubricant or from sample to sample within a batch? Justify your answer by referring to part (b) above.

5. [20 pts] Robert Adams (GM-Delphi, Warren) looked at the process of locating and drilling the rear adjuster floor support clearance holes in a vehicle for his STAT 495 project. The quality characteristic was the deviation from the nominal (target) distance. The target deviation was zero with tolerances of . The deviation was found to be stable and predictable over time using standard control charts. The following capability indices were then calculated.
   • (a) [4] Interpret the value of the process potential. What does this tell you about the process?

   • (b) [4] Interpret the difference between the value of the process potential and the process capability. What does this tell you about the process?

   • (c) [5] Assuming that individual deviations follow a normal distribution, approximately what percentage of deviations would you expect to see above the upper specification limit?

   • (d) [6] Assuming that the capability indices were calculated using and , what are the values of and ?

6. [10 pts] A supplier ships parts in lots of 1000. Your acceptance sampling scheme is to accept the lot if there are 0 or 1 defective parts in a random sample of 10, sampling with replacement.
   • (a) [6] If there are 25 defective parts in a lot, what is the chance that the lot is accepted?

   • (b) [4] Below is a table giving various different values for the number of defective parts and the corresponding probability of accepting such a lot based on the scheme described above. According to the table what is 91.4%upper bound on the number of defective parts in a lot?

     

7. [10 pts] Briefly, but completely, explain the difference between a study with enumerative purposes and one with analytic purposes. Use only the space below.

8. [20 pts] Throughout the semester we have looked at statistical tools and methods for building knowledge about products and processes. Quality improvement is a process. Construct a logical flow chart for the process of improving the quality of a manufacturing/service process. Hint: It may help to think about your team project for this course.