A Bayesian model for the joint optimization of quality and maintenance decisions

We develop a model for the economic design of a Bayesian control chart for monitoring a process mean. The process may randomly suffer failures that result in a non-operating state, and thus call for an immediate corrective maintenance action, as well as assignable causes that shift the process mean to an undesirable level. Quality shifts, apart from poorer quality outcome and higher operational cost, also result in higher failure rate. Consequently, their removal, besides improving the outcome quality and reducing the quality-related cost, is also a preventive maintenance action since it reduces the probability of a failure. The proposed Bayesian model allows the determination of the design parameters that minimize the total expected quality and maintenance cost per time unit. The effectiveness of the proposed model is evaluated through the comparison of its expected cost against the optimum expected cost of the simpler variable-parameter Shewhart chart.