Bayesian EWMA control charts based on Exponential and transformed Exponential distributions

Abstract

In this paper, we proposed the Bayesian exponentially weighted moving average (EWMA) control charts for mean under the nonnormal life time distributions. We used the time between events data which follow the Exponential distribution and proposed the Bayesian EWMA control charts for Exponential distribution and transformed Exponential distributions into Inverse Rayleigh and Weibull distributions. In order to develop the control charts, we used a uniform prior under five different symmetric and asymmetric loss functions (LFs), namely, squared error loss function (SELF), precautionary loss function (PLF), general entropy loss function (GELF), entropy loss function (ELF), and weighted balance loss function (WBLF). The average run length (ARL) and the standard deviation of run length (SDRL) are used to check the performance of the proposed Bayesian EWMA control charts for Exponential and transformed Exponential distributions. An extensive simulation study is conducted to evaluate the proposed Bayesian EWMA control chart for nonnormal distributions. It is observed from the results that the proposed control chart with the Weibull distribution produces the best results among the considered distributions under different LFs. A real data example is presented for implementation purposes.