Complete Example 13.2: Process Control Chart Design, located in Chapter 13 of the textbook using the Excel spreadsheet, “Process Control Chart Design.” Answer questions 1-8 from Case: Quality Manageme
C a s e 1-8 : Quality Management—To y o t a
Quality Control Analytics at Toyota
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 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
Q u e s t i o n s
1 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?
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 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?
EXAMPLE 13.2: Process Control Chart Design
An insurance company wants to design a control chart to monitor whether insurance claim forms are being completed correctly. The company intends to use the chart to see if improvements in the design of the form are effective. To start the process, the company collected data on the number of incorrectly completed claim forms over the past 10 days. The insurance company processes thousands of these forms each day, and due to the high cost of inspecting each form, only a small representative sample was collected each day. 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 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.
To construct the control chart, first calculate the overall fraction defective from all samples. This sets the centerline for the control chart.
Next calculate the sample standard deviation:
Finally, calculate the upper and lower process control limits. A z-value of 3 gives 99.7 percent
confidence that the process is within these limits.
