Process capability indices for Marshall–Olkin inverse log-logistic distribution

Abstract

Process capability analysis is a vital tool in quality management that enables organizations to evaluate and enhance their processes. Real-world data are mostly non-normal, they often deviate from the assumption of normality. The estimators of process capability indices (PCIs) for normal processes are not sufficient to characterize non-normal processes and can give misleading results. The Marshall-Olkin inverse log-logistic (MO-ILL) distribution is a flexible distribution that can effectively model data exhibiting positive skewness, asymmetry and heavy tails. In this paper, we derived the process capability indices (PCIs) based on the MO-ILL distribution when the process is assumed to be in a state of statistical control. Two PCIs based on MO-ILL mean and variance, and MO-ILL quantiles are proposed. The proposed PCIs were compared with the traditional PCIs and percentile-based PCIs using two real life data and data generated from MO-ILL distribution. Moreover, the effect of the sample size and parameters of the MO-ILL distribution on the PCI measures is also investigated. The results showed that PCIs values based on the proposed MO-ILL mean and variance, and MO-ILL quantiles are respectively lower and better than the traditional PCIs and percentile-based PCIs. This is an indication that MO-ILL distribution-based methods developed have narrow margin of error and are more appropriate in assessing the performance of a skewed process.