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A parameter free Bayesian adaptive EWMA mean chart under different loss functions

The adaptive exponentially weighted moving average (AEWMA) control chart is more sensitive than the exponentially weighted moving average (EWMA) control chart for the mean shifts. The EWMA control chart is used to monitor the small or moderate shifts, and the Shewhart control chart is used to monitor only large shifts in the process mean. The AEWMA control chart is useful to monitor the small to large mean shifts. We proposed a new parameter free Bayesian AEWMA mean chart under different loss functions (LFs). We used two different LFs as symmetric LF namely squared error loss function (SELF) and asymmetric LF namely Linex loss function (LLF) with both informative and non‐informative priors for posterior and posterior predictive distributions. The average run length (ARL) and the standard deviation of run length (SDRL) are used to measure the performance of the proposed parameter free Bayesian AEWMA control chart under different LFs. A Monte Carlo simulation study is used to evaluate the proposed control chart under different LFs. A real data example is used for implementation purposes.