Designs of X¯&S control charts with optimal manpower deployment

This article proposes an algorithm for deploying manpower (equipped with adequate measuring instrument) to an X¯&S   control chart scheme so that the resultant control chart (referred to as X¯&S   M-chart) minimizes the expected total cost incurred in the implementation of the Statistical Process Control (SPC). The design algorithm of the X¯&S   M-chart does not only optimize the deployed manpower, but also determine the sample size, sampling interval and control limits of the X¯ and S   charts in an optimal manner. Unlike the economic chart designs, most input specifications required by the design of an X¯&S   M-chart can be easily determined by the practitioners. The results of a numerical study, as well as from an example, show that the X¯&S   M-chart can reduce the total cost by more than 50 percent, on average, compared to the conventional X¯&S   control charts. It is also found that, in most SPC schemes, the allocated amount of manpower is far less than needed and, consequently, the total cost can be significantly reduced if some managerial arrangement can be made to increase SPC manpower. Some useful guidelines are also provided to aid users in deciding the appropriate amount of manpower for a particular application. Even though the design algorithm is discussed in detail only for the X¯&S chart, the general idea can be extended to many other charts such as the joint CUSUM charts and joint EWMA charts for detecting mean and variance shifts.