Quality Control Analytics at Toyota
Answer in Excel, see templete below:.
As part of the process for improving the quality of their cars, The car engineers have identified a potential improvement in 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 fit can be loose, but if it does happen to get to large, it can cause the acelerator to bind and create a problem for the driver.
Let's assume that, as a first step to improving the process, a sample of 40 washers coming from the machine that produces the washers was taken and the thickness measured in millimeters. The following table has the measurements from the sample:
1.9 2.0 1.9 1.8 2.2 1.7 2.0 1.9 1.7 1.8
1.8 2.2 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 2.0 1.8 1.7 1.9 1.9
2.1 2.0 2.4 1.7 2.2 2.0 1.6 2.0 2.1 2.2
Questions
1. If the specification is such that no washer should begreater 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 specifi cation, wherethe upper thickness limit is 2.4 and the lower thick-ness limit is 1.4, what fraction of the output is expected to be out of tolerance?
3 What is the Cpk 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 current 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?