Optimal Bayesian Control of the Proportion of Defectives in a Manufacturing Process

In this paper, we present a model and an algorithm for
the calculation of the optimal control limit, average cost, sample size,
and the sampling interval for an optimal Bayesian chart to control
the proportion of defective items produced using a semi-Markov
decision process approach. Traditional p-chart has been widely
used for controlling the proportion of defectives in various kinds
of production processes for many years. It is well known that
traditional non-Bayesian charts are not optimal, but very few optimal
Bayesian control charts have been developed in the literature, mostly
considering finite horizon. The objective of this paper is to develop
a fast computational algorithm to obtain the optimal parameters of a
Bayesian p-chart. The decision problem is formulated in the partially
observable framework and the developed algorithm is illustrated by
a numerical example.

Authors:

• Viliam Makis
• Farnoosh Naderkhani
• Leila Jafari

Keywords:

• Bayesian control chart
• semi-Markov decision process
• quality control
• partially observable process.

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