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determine confidence intervals.

Some Statistical Methods for Checking Assumptions

Although every process capability index can be computed regardless of the underlying distribution, there are some common required assumptions. Process capability indices are useful in estimating futurę performance. Thus, it is essential to verify that the process is stable. Process stability is best checked by using fundamental control charting techniąues. We will not elaborate on this issue further here. The interested reader should consult some basie quality control texts for details.

The independence assumption is generally difficult to verify (Weisberg 1985) and the best diagnostics for detecting correlated observations is from a careful consideration of the process itself and of the sampling methods used. The Durbin-Watson test (see Dielman 1991, for example) can be used to detect first-order autocorrelation and is often an option in many statistical computing packages.

There are several common methods available to verify the assumption of normality. We will only mention three: histograms, normal probability plots and goodness-of-fit tests.

Histograms provide an appealing visual summary. While they are useful in disceming anomalies, selection of the data intervals or bins can significantly influence the conclusions one might draw. For verification of the form of a probability distribution, a probability plot is better. Normal and other probability plots provide better visual assessments about this assumption.

Like a histogram, the normal probability plot is an informal graphical procedurę for assessing normality, but it is a morę reliable techniąue. Special normal probability paper can be used to prepare the plots manually or Computer software can be used. Data from normal distributions tend to plot as straight lines on normal probability plots. Data from a skewed distribution tend to plot as a concave or convex curve, depending on the direction of the skew. Data from heavy-tailed or light-tailed distributions tend to plot as an S-shaped curve. See Figures 1-4 for prototypical or characteristic normal probability plots from Normal, Student's t, %² and uniform distributions.

An even morę complete evaluation of the underlying probability distribution can be accomplished through goodness-of-fit tests. Goodness-of-fit tests are formal hypothesis tests that can be used to test whether the underlying population is normal. Some Computer packages offer one or morę such tests. The recommended (Rodriguez 1992) tests are the Komogorov-Smimov,