Summary: Process capability and process performance index studies are to assess a process relative to specification criteria. Quantification of this measurement is often reported using various indices. One such index, namely \(C_p\), is considered in this paper. The equations for process capability indices are basically very simple; however, they are very sensitive to the input value for standard deviation, as it is not known. Unfortunately there can be difference of opinions on how to determine standard deviation for a given situation. Thus the basic problem is to estimate the standard deviation and thereby estimating the process capability index.
This paper provides a Bayes estimator for the process capability index \(C_p\) when an a priori or guessed interval of standard deviation is available. To express the belief of the experimenter, an improper prior distribution is considered. The squared error loss function has been used to assess goodness of the suggested estimator. The Bayes estimator thus obtained has been compared theoretically and empirically with the minimum mean squared error estimator.