Case: Quality Management—Toyota
Quality Control Analytics at Toyota
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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 fi t 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. (Note: This part of the case has been fabricated for teaching purposes, and none of these data were obtained from Toyota.) 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
- If the specification is such that no washer should be greater than 2.4 millimeters, assuming that the thicknesses are distributed normally, what fraction of the output is expected to be greater than this thickness?
- 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?
- What is the Cpk for the process?
- What would be the Cpk for the process if it were centered between the specification limits (assume the process standard deviation is the same)?
- What percentage of output would be expected to be out of tolerance if the process were centered?
- Set up X – and range control charts for the current process. Assume the operators will take samples of 10 washers at a time.
- Plot the data on your control charts. Does the cur-rent process appear to be in control?
- 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?