The economic design of (x)over-bar control charts with repair cost depending on detection delay

This study extends Duncan's [1] model to two different manufacturing process models in which the processes continue and discontinue in operations during the search for the assignable cause. A more realistic assumption considered in this paper is that the cost of repair and the net hourly out-of-control income are functions of detection delay. In the continuous model, detection delay is defined as the elapsed time from the time when the shift of the process occurs until it is identified by (x) over bar control charts and the assignable cause is eliminated. The discontinuous model defines detection delay as the time interval from the occurrence of the process shift to the completion of testing a set of samples and interpreting the results. An efficient procedure is developed to determine the optimal designs without using any approximation approach. Thus, the proposed procedure can obtain the truly optimal designs rather than those approximate designs determined by Duncan [1] and other subsequent researchers. This paper illustrates several numerical examples and makes some relevant comparisons. The results indicate that this optimal solution procedure is more accurate than that of Panagos et al. [2]. Also, detection delay is sensitive to the economic design of (x) over bar control charts. Copyright (C) 1996 Elsevier Science Ltd