00409 75b3cae4b2bbdff72a1af31d491239

413

Process Capability: Engineering and Statistical Issues

_ USL - LSL ^pn~ 6t

where t² = ct² + (|A-r)² is the mean squared deviation about the process target. A primary difference between C_p and centers on a and x. While

a² is the mean squared deviation about the process mean, x² is the mean squared deviation about the process' target.

We again notę that the parameters employed for characterizing the process are not known. Next, we will discuss the impact of estimating process parameters on the calculation and interpretation of the process capability indices.

Statistical Summary

The October 1992 issue of the Journal of Quality Technology was devoted to statistical issues regarding process capability indices. The articles in that issue discuss the variability, biases and other distributional properties of estimates of process capability indices, as well as confidence intervals on process capability indices and the relationships between process capability indices and loss functions. The lead article by Rodriguez (1992) provides a summary of the entire issue.

To make use of those statistical results, several fairly strong assumptions are required. These assumptions are needed, for example, to draw inferences about the process, determine reasonable sample sizes and to interpret the process capability indices as intended. The required assumptions are:

•process stability: The process is in a State of statistical control, no special causes are present, the process does not drift nor oscillate, etc. •representative samples:    The obtained samples are representative of the

population. Random sampling is important in this regard.

•normality: The underlying process distribution is normal. This is needed to draw statistical inferences, construct confidence intervals, etc.

•independence: The observations are independent of each other. For example, consecutive observations from the process must not be correlated, either positively or negatively. Also notę that this precludes situations where batching is present.

One exception that should be noted is that the bootstrapping method discussed in Franklin and Wasserman (1992) does not necessarily reąuire normality to