Methodological insights for industrial quality control management: The impact of various estimators of the standard deviation on the process capability index

Statistical quality control (SQC) is used by companies and industries for many reasons. For example, the process capability of machines is an important aspect of SQC, which consists in evaluating the ability of a production process to perform with the required specifications. In other words, the process capability measures the ability of a process of producing acceptable products according to the established specifications. The most common indicator used to measure the process capability is the process capability index, which depends on the process standard deviation. In practice, the standard deviation is unknown, and the process capability index is thus estimated by using an estimator of the process standard deviation. In this paper, we describe the most common estimators of the process standard deviation, and define the corresponding estimators of the process capability index. A bound for the bias ratio of the various estimators is obtained. Monte Carlo simulation studies are carried out to analyze the empirical performance of the various estimators of the process capability index. Empirical results indicate that biases can be obtained, specially in the presence of small samples. We also observe that the estimators of the process capability index based on sample ranges are less accurate than the alternative estimators.