Research Article Published online 5 April 2010 in Wiley Online Library (wileyonlinelibrary.com) DOI: 10.1002/qre.1101 A Bayesian Model for the Joint Optimization of Quality and Maintenance Decisions George Nenes a∗ † and Sofia Panagiotidou b 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. Copyright © 2010 John Wiley & Sons, Ltd. Keywords: Bayesian chart; corrective maintenance; cost minimization; preventive maintenance; quality control 1. Introduction O ver the last decades, researchers have allocated considerable effort on designing more and more effective tools for monitoring the quality of production processes. It has been almost eight decades since the pioneering work of Walter Shewhart 1 who first introduced the idea of a control chart, and more than five decades since Duncan 2 first designed an ¯ X control chart from an economic point of view. The continuous effort for providing increasingly effective tools has led to the development of more sophisticated, economically designed, control charts which can have adaptive design parameters like the Variable-parameter (Vp) Shewhart control charts of Costa and Rahim 3 and De Magalhaes et al. 4 . These schemes allow the design parameters of the chart to vary based on the latest observation. A more sophisticated control chart type is based on the Bayes theorem which is well known to lead to the optimum adaptive process control, taking into consideration all the accumulated information from the process. The origins of the Bayesian process control can be found in the first theoretical approach of Girshik and Rubin 5 . More recent Bayesian control charts are proposed by Tagaras 6 who introduces the one-sided Bayesian ¯ X control chart while at about the same time, a similar Bayesian p-chart for monitoring the fraction nonconforming of a process, is proposed by Calabrese 7 . Tagaras and Nikolaidis 8 compare various Bayesian charts from an economic viewpoint, whereas Nenes and Tagaras 9 and Tagaras and Nenes 10 develop two-sided Bayesian ¯ X control charts. In an effort to further improve the effectiveness of quality control tools, a number of models have recently been developed that combine typical statistical process control (SPC) with preventive maintenance (PM) procedures 11--14 . A more recent SPC-type model that can be very effective in cases where the probability of a process quality shift increases over time has been presented by Zhou and Zhu 15 . The common characteristic of all the aforementioned models is that they only consider quality deterioration mechanisms and consequently, they are designed from a pure SPC point of view. That is, their purpose is solely the monitoring and control of a process that may operate either under statistical control or under the effect of some assignable cause and they completely ignore the possibility of an equipment failure that brings the equipment to a non-operating state. However, in most real-life applications, the process is likely to suffer a failure as well; in those cases, preventive maintenance (PM) policies have been proved to contribute significantly to the improvement of the process’ economic and statistical effectiveness. Derman 16, 17 was among the first who studied various PM policies in production processes with both multiple operating states and a failure state. Derman’s models, however, focus on determining the optimum maintenance scheme, assuming that the actual operating state of the process is always known with accuracy. Nonetheless, in many production processes, the actual operating a Department of Mechanical Engineering, University of Western Macedonia, Bakola & Sialvera, 50100 Kozani, Greece c Department of Mechanical Engineering, Aristotle University of Thessaloniki, PO Box 461, 54124 Thessaloniki, Greece ∗ Correspondence to: George Nenes, Department of Mechanical Engineering, University of Western Macedonia, Bakola & Sialvera, 50100 Kozani, Greece. † E-mail: gnenes@uowm.gr Copyright © 2010 John Wiley & Sons, Ltd. Qual. Reliab. Engng. Int. 2011, 27 149--163 149