In quality improvement, it’s common to talk about the "voice of the process" (intrinsic variation in the outputs of an in-control process) and the "voice of the customer" (specification limits that express the range of output values customers will not be unhappy with). A capability analysis compares these two "voices," and summarizes the result via the well-known capability indices C_{p} and C_{pk}. These indices are both defined so that larger values correspond to better overall performance. C_{p} compares the process variation to the width of the spec window, and C_{pk} is a measure of how well this variation is centered on the target value (mid-way between the spec limits).

When calculating process capability from a normal fit to your data, the Capability Animation feature (available in JMP via *Analysis > Quality > Capability *or *Analysis > Distribution > Capability Analysis*) allows you to assess the relationship between C_{pk} and a proposed shift in the mean or a change in the specification limits.

For example, in Figure 1 we see a normal fit to output from a process that has a standard deviation of 3.51, and for which there is a lower spec limit (LSL) of 70 and an upper spec limit (USL) of 100. Figure 1 also shows the effect of shifting the original mean (72.8, in gray) to a new, higher value (78.12, in blue) that is closer to the target. So if we were (somehow . . . ) able improve the centering of the process in this way, we could expect the C_{pk} value to increase from 0.27 to 0.77. Note that in this case, the process variation is assumed to be unchanged, so the value of C_{p} is unchanged also.

My colleague William Zhou and I developed an add-in that extends this built-in Capability Animation to include the option of exploring how changes in the process variation may affect both C_{pk} and C_{p}. This add-in is now available in the JMP File Exchange.

You can install the add-in by double clicking on it, and then use it by selecting *Add-Ins > Capability Animation*. Figure 2 illustrates that reducing the standard deviation of the process from 3.51 to 1.96 (without shifting the mean) increases the C_{pk} from 0.27 to 0.48 and Cp from 1.42 to 2.54.

This new add-in allows you to perform what-if analysis to determine how any changes to the process mean, process standard deviation or specification limits are likely to impact the values of C_{pk} and C_{p}. This can help you to focus your process improvement efforts in the best way, either by re-engineering the process itself, or by renegotiating requirements with customers to get new spec limits.

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