Parameter Estimation and Performance of the -Chart for Attributes Data

Effects of parameter estimation are examined for the well-known p-chart for the fraction nonconforming based on attributes (binary) data. The exact run-length distribution of the chart is obtained for Phase II applications, when the fraction of nonconforming items, p, is unknown, by conditioning on the observed number of nonconformities in a set of reference data (from Phase I) used to estimate p. Numerical illustrations show that the actual performance of the chart can be substantially different from what one would nominally expect, in terms of the false alarm rate and/or the in-control average run-length. Moreover, the performance of the p-chart can be highly degraded in that an exceedingly large number of false alarms are observed, particularly when p is estimated, unless the number of reference observations is substantially large, much larger than what might be commonly used in practice. These results are useful in the study of the reliability of products or systems that involve binary data