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# Process Capability Index

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1. Aspen Plastics produces plastic bottles to customer order. The quality inspector randomly selects four bottles from the bottle machine and measures the outside diameter of the bottle neck, a critical quality dimension that determines whether the bottle cap will fit properly. The dimensions (in.) from the last six samples are:

Sample 1 | 2 | 3 | 4
1 | 0.594 | 0.622 | 0.598 | 0.590
2 | 0.587 | 0.611 | 0.597 | 0.613
3 | 0.571 | 0.580 | 0.595 | 0.602
4 | 0.610 | 0.615 | 0.585 | 0.578
5 | 0.580 | 0.624 | 0.618 | 0.614
6 | 0.585 | 0.593 | 0.607 | 0.569

a. Assume that only these six samples are sufficient, and use the data to determine control limits for an R- and an x-bar chart.

b. Suppose that the specification for the bottle neck diameter is 0.600 in ± 0.050 and the population standard deviation is 0.013 in. What is the Process Capability Index? The Process Capability Ratio?

##### Solution Summary

Answers are on the attached Excel spreadsheet, along with detailed explanations. Excel functions are used to find the grand average and ranges. Also in Excel, a chart is made along with calculating Process Capability Index Cp.

##### Solution Preview

Student,

a. Since we are told to "use the data to determine control limits for an R- and an x-bar chart", we have to average the measurements of each of the six samples and find the range of each of the six. This is at the top of columns F and I, respectively. We then find the separate control limits based on three anti-biasing constants in cells A12 thru A14 and resulting in the limits at the top of columns G-H and J-K, respectively. I am using commonly ...

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