As part of the process for improving the quality of their cars, Toyota engineers have identified a potential improvement to the process that makes a washer that is used in the accelerator assembly. The tolerances on the thickness of the washer are fairly large since the it can be loose, but if it does happen to get too large, it can cause the accelerator to bind and create a potential problem for the driver.

1 If the specification is such that no washer should be greater than 2.4 millimeters, assuming that the thick-nesses are distributed normally, what fraction of the output is expected to be greater than this thickness?

2 If there are an upper and lower specification, where the upper thickness limit is 2.4 and the lower thickness limit is 1.4, what fraction of the output is expected to be out of tolerance?

3 What is the C pk for the process?

4 What would be the Cpk for the process if it were centered between the specification limits ( assume the process standard deviation is the same)?

5 What percentage of output would be expected to be out of tolerance if the process were centered?

6 Set up X-and range control charts for the current process. Assume the operators will take samples of 10 washers at a time.

7 Plot the data on your control charts. Does the cur-rent process appear to be in control?

8 If the process could be improved so that the standard deviation were only about .10 millimeter, what would be the best that could be expected with the processes relative to fraction defective?