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Pignatiello & Ramberg

by a single niunber. In situations where managers are responsible for many (and possibly hundreds) of processes, the use of process capability indices can appear to be an attractive and practical solution in that reporting a single-number process capability index for each process does facilitate a management-by-exception strategy. Probably the most common reason why manufacturers calculate process capability indices is that their customers have asked them to do so. In their quest to satisfy their customers' needs, the producers comply.

In practice, these ubiąuitous process capability indices are used far too casually. They are freąuently employed without any concerns for the fundamental statistical assumptions that are a prerequisite to their use and the associated data analyses that are necessary for the evaluation of these statistical assumptions. Even morę important is the apparent lack of a realization of the naturę and role of an appropriate data collection scheme that is required for the interpretation and use of these indices.

Ali too often, a relatively smali ‘lampie” of about 30 items is collected in some loosely specified manner from the process or from a historical data base of the process. Then summary statistics, including an estimate of the selected process capability index, are computed and reported. The interpretation of these statistics, when the process is not in statistical control, when the probability distribution underlying the process is not normal, or when the observations are not independent, is highly ąuestionable. These statistics do not indicate the capability of the process.

Conseąuently, common practices for obtaining an estimate of a process capability index are often so flawed that the reported numerical value can be meaningless. Even under ideał situations, each single-number summary is a gross oversimplification of a process' performance. One has to ąuestion any management strategy that directs managers' attentions by the extreme values of a set of calculated indices that, individually, may not be particularly meaningful. Although this practice may be better than nothing, the real issue is whether it is of any value.

Moreover, unfortunate situations can arise if one fails to recognize that a process capability index is a random ąuantity. For example, some customers use process capability indices as one basis for making purchasing decisions. If they do not recognize the random naturę of the calculated process capability index, it is very possible that they may be purchasing product from an incapable process or not purchasing from a very capable process. We discuss this issue below.

Clouding the issue further, a number of competing process capability indices have been advocated by various proponents. Several research articles have recently appeared in the literaturę, arguing in favor of one process