An easy and low cost option for economic statistical process control using Excel

Abstract

In this paper, a user-friendly, Excel program is developed to search for the optimal values of the parameters in minimizing the total cost function in both economic and economic statistical designs of theX-control chart. Two assumptions are considered in the development and use of the economic or economic statistical models. These assumptions are potentially critical. It is assumed that the time between process shifts can be modelled by means of the exponential distribution. It is further assumed that there is only one assignable cause. Based on these assumptions, economic or economic statistical models are derived using a total cost function per unit time as proposed by a unified approach. In this approach the relationship between the three-control chart parameters as well as the three types of costs are expressed in the total cost function. The optimal parameters are usually obtained by the minimization of the expected total cost per unit time. Nevertheless, few practitioners have tried to optimize the design of theirX-control charts. One reason for this is that the cost models and their associated optimization techniques are often too complex and difficult for practitioners to understand and apply. Therefore, a user-friendly Excel program has been developed in this paper and the numerical examples illustrated are executed on this program. The optimization procedure is easy-to-use, easy-to-understand, and easy-to-access. Moreover, and not least important, it is a low cost option unlike previous approaches which can be found in expensive software packages only. The results and the execution times of all numerical examples show that our optimization procedure using Excel is accurate and efficient.