Chapter 5 – Part 1

1. Chapter 5 – Part 1 Solutions to SHW

2. What do we mean by a process that is consistently on target? USL LSL Target Amount of Toner Process is consistently on target if the distribution is tightly clustered around the target, or, equivalently, if the variance around the target is small.

3. USL LSL Target Mean 2. What do we mean by a process that is consistently on target? Amount of Toner Process is consistently off target if the distribution is off target but tightly clustered—or has a small variance—around its mean.

4. What do we mean by a process that is haphazardly on target? USL LSL Target Process is haphazardly on target if the distribution is on target but exhibits a great deal of variation around The target.

5. Refer to Jane and Sam in the notes to Chapter 5, Part 1. Draw the distribution of two machines, one behaving like Jane and the other like Sam. Which machine is easier to fix? How would you fix it? Target Jane (Machine B) Sam (Machine A)

6. Problem 4 - Continued • Easier to adjust mean to target than to reduce variance. • Machine A: reduce variance • Machine B: adjust mean to target

7. How does better quality increase productivity? • As quality improves, rework and scrap decrease • This results in fewer inputs being used to produce a units of output. • Also, more good units are produced the first time. • Since better quality means high output of good units and fewer inputs, productivity—output divided by inputs—increases.

8. Problem 6 • Find the loss function LSL = 0.6 USL = 1.6 Target = (USL+ LSL)/2 =(1.6+.6)/2 = 1.1 USL = Target + a 1.6 = 1.1 + a a=0.5

9. Problem 6

10. Problem 6 • If X= 1.3, • If the company ships a brake pad with a thickness of 1.3 inches, the company will impose a loss of $1.92 on the customer. The loss is due to the thickness being 0.2 inches off target.

11. Problem 6 • Expected loss The company imposes, on average, a loss of $36 on its customers from shipping off target units. (Note that some units will have a loss Greater than $36 but other units will a loss of less than $36. The average of the losses of all units shipped will be $36.)

12. Problem 7 • Ashi Newspapers on April 17, 1979 reported that: Identical sets were assembled by Sony in a plant in Japan and in a plant in the U.S. with same design, and the same parts. • U.S. customers preferred TV’s assembled in Japan to those assembled in U.S., because of better color. • The U. S. plant performed 100% inspection. As a result, none of the sets assembled in U.S. were out of specs. • However, Japan shipped all set “as is” without inspection.

13. Problem 7 • The result was that 0.0027% of sets assembled in Japan were out-of-spec, and thus defective. • The color density (the quality characteristic of interest, X) of sets produced in Japan was normally distributed, while the color density of the sets produced in the U.S. had a uniform distribution. The specification limits are 10 and 20. • The distributions at each plant are shown below.

14. Japan-built sets: .3% out of limits US-built sets: 100% within limit Problem 7 Color Density Distribution y 10 15 20

15. Problem 7

16. Solution to 7a –Tokyo • Defect rate = .003. Split between two tails • beyond spec limits = .0015 in each tail. LSL USL .0015 .0015 10 15 20

17. Use Appendix B, p. 652 to find z. Since the tail area above USL is .0015 and Appendix B gives the area between 0 and z, we Look up the area between 0 and z, which is .5000 -.0015 =.4985 Table area =.4985 .0015 .0015 LSL USL z = 2.965 0 From Appendix B, the z value is z = 2.96 or 2.97, so split z to get 2.965. See next slide.

18. z Table (Text, p. 652)

19. Solution to 7a -Tokyo Use formula for z to solve for standard deviation:

20. Solution to 5a - Tokyo • Expected loss

21. Solution to 5a-Tokyo • On average, each TV set shipped from the Tokyo plant imposes a loss $0.69 on the customer.

22. Solution to 5a – U.S. Plant

23. Solution to 5b • Why is the expected loss less at the plant that is producing a higher percentage of out of spec sets—the Tokyo plant?

24. Solution to 5b • E(Loss -Tokyo) =$.69 • E(Loss - U.S.) =$2.00 • The reason why the expected loss is less at the Tokyo plant than at the U.S. plant is because the variance is smaller at the Tokyo plant, so there is less variability around the target. • The sets are therefore more consistently on target, even if 3 out of 1000 sets are out-of-spec.

25. Solution to 5b • At the U.S. plant, all sets are in spec. but they are haphazardly on target. • Since the U.S. distribution is uniform, the percentage of sets on target is the same as the percentage of set near either on of the spec. limits. • This means that the customer is just as likely to get a set that is on target as one that it on the lower or upper spec. limit.

26. Solution to 5b • Note that, although the U.S. plant is performing 100% inspection and is not producing any out-of-spec sets, it still has a higher expected loss. Why? • The reason is that mass inspection will not reduce the expected loss because it does not reduce the variance of color density. • To reduce variance, we must improve the process by, for example, using better parts and/or materials, better maintenance of tools and equipment, etc.