As part of the process for improving the quality of their cars,Toyota engineers have identified a potential improvement to theprocess that makes a washer that is used in the acceleratorassembly. The tolerances on the thickness of the washer are fairlylarge since the fit can be loose, but if it does happen to get toolarge, it can cause the accelerator to bind and create a potentialproblem for the driver. (Note: This part of the case hasbeen fabricated for teaching purposes and none of these data wereobtained from Toyota.)

   Let’s assume that as a first step to improvingthe process, a sample of 40 washers coming from the machine thatproduces the washers was taken and the thickness measured inmillimeters. The following table has the measurements from thesample:

2.1	2.2	1.9	1.8	2.1	1.6	1.8	1.6	2.1	2.4
2.2	2.1	2.1	1.8	1.7	1.9	1.9	2.1	2.1	2.4
1.7	1.9	1.8	2.2	1.7	2.0	1.9	2.2	2.0	1.6
2.0	2.1	2.0	1.8	2.1	1.9	1.7	1.8	1.8	2.2

  

Use the appropriate Excel function to compute normaldistribution probabilities in Parts a, b, e and f.

a. If the specification is such that no washershould be greater than 2.4 millimeters, assuming that thethicknesses are distributed normally, what percentage of output isexpected to be greater than this thickness? (Round youranswer to 2 decimal places.)

Percentage of output            %

b. What if there is an upper and lowerspecification, where the upper thickness limit is 2.4 and the lowerthickness limit 1.4, what percentage of output is expected to beout of tolerance? (Round your answer to 2 decimalplaces.)

Percentage of the output            %

c. What is the C_pk for the process?(Round your answer to 4 decimal places.)

C_pk           

d. What would be the C_pk for theprocess if it were centered (assume the process standard deviationis the same)? (Round your answer to 3 decimalplaces.)

C_pk           

e. What percentage of output would be expectedto be out of tolerance if the process were centered? (Roundyour answer to 2 decimal places.)

Percentage of output            %

f. If the process could be improved so that thestandard deviation was only about 0.1 millimeters, what would bethe best that could be expected with the processes relative tofraction defective?

The process to be centered at           (Clickto select)1.92.41.4

g. Setup X-bar and Range control charts for thecurrent process. Assume the operators will take samples of 10washers at a time. (Round your answer to 3 decimalplaces.)

	X-bar chart	Range chart
Upper control limit
Lower control limit