Abstracts

The Bayesian X control chart with ∊-contaminated priors: A robust performance

Nirpeksh Kumar

In this work, the control chart for monitoring the process mean is developed within the Bayesian framework, aiming to combine the prior beliefs with the evidence provided by the Phase I samples. However, one common criticism of the Bayesian method is its reliance on a single prior to represent the understanding of one or more individuals. It is now understood that no elicitation process can fully capture beliefs with a single prior without some degree of uncertainty. To address this, a more robust approach is employed using the ε- contamination class of priors which accounts for uncertainty in the elicitation process. A popular method to deal with this class is ML-II prior technique resulting in a single robust ML-II prior. The primary aim of the study is to construct control limits for chart using ML-II prior under a robust Bayesian framework, with the expectation it will be relatively insensitive to variations in priors within the ε-contamination class. The study suggests that the ML-II control limits provide confidence in the user by effectively addressing uncertainty in the prior distribution and utilizing both prior knowledge and observed evidence in constructing the limits, thus offering more reliable inference about the process status. It is found that the ML-II chart outperforms the frequentist chart in terms of average in-control and out-of-control performance metrics, particularly for appropriate choices of the base prior and when the subgroup size is small.