Summary
Beaver Brothers, Inc. is conducting a study to assess the accuracy, and consistency of their 150-gram bar soap production line. They are interested in seeking; the reliability, average weight and range of each soap bar. By conducting this study Beaver Brothers, Inc. wants to see the consistency of their machines, dependability of their marketing tools and the level of assurance that they are promoting and supplying trustworthy products to their consumers.
Beaver Brother, Inc. achieves their wanted information by collecting 25 samples of 5 observations and recorded the data in a table. The task is to use these collected samples to create; means, graphs, and tables to present the data and draw conclusions about the production line.
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The greater the Cp and the closer the Cpk is to the Cp, indicates a higher level of working capacity. These values can be calculated using the Process Capability module on the POM software.
Parameter Value Results Value
Upper tolerance limit 170 Process capability index 0.08 The actual process capability is Cpk = -0.08
Lower tolerance limit 162 Upper one sided index 0.8392 The potential process capability is Cp = 0.4596
Mean (optional) 162.6959 Lower one sided index 0.08
Standard deviation 2.9012
Table 1 shows the factors used in finding out the actual results of; Cp, and Cpk from the initial study. With a suggested Cp of 1.33 to demonstrate that the production line is well centered, and working at a high rate, you can see that the initial results do not suggest this. The Cp is well below the recommended index at 0.4596, suggesting that the process needs to be altered to make improvements.
It is also visible that the Cpk (0.08) has a much less number in comparison to the Cp. This implies that this process is not working to its full potential. Consequently it is necessary that Beaver Brothers, Inc makes further improvements to create a more centered, higher potential productivity rate.
c) After improvements, and collecting more samples the results of the Cp and Cpk are as follows:
Parameter Value Results Value
Upper tolerance limit 170 Process capability
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Quality Associates, Inc. is a consulting firm that advises its clients about sampling and statistical procedures that can be used to control manufacturing processes. In one case, a client provided Quality Associates with a sample of 800 observations that were taken during a time when the client's process was operating satisfactorily. The sample standard deviation for these data was .21, hence, the population standard deviation was assumed to be .21. Quality Associates then suggested that random samples of size 30 be taken periodically to monitor the process on an ongoing basis. By analyzing the new samples, the client could quickly learn whether the process was operating satisfactorily. When the process was not operating
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