Abstract
Recently, quality plays an important and necessary role in many products. The most important statistical tool for quality control in manufacturing is the statistical process control (SPC), so control charts are used widely. A control chart is called dynamic if at least one of the three chart parameters, namely, sample size, sampling interval, and locations of control limits, are allowed to change in progress. Because the improvement in computers, more and more researchers study dynamic charts, and find they normally perform better than the corresponding static charts. In this paper, we consider the sampling scheme for the cumulative sum control chart using a Bayesian approach in minimizing the average cost per unit time. It gives a dynamic system in which inspection frequency is allowed to vary according to the prior probability that the system will be out of control when producing the next item. We will show how to obtain the optimal solutions, in which one decides when to keep producing without inspection, when to keep producing with inspection, and when to stop the process by considering the trade-off between repair costs, inspection costs, and the quality cost. An example is given to illustrate the proposed procedure.