Approximate distribution of demerit statistic—A bounding approach

The traditional classical demerit control chart is used to plot the demerit statistic, a weighted sum of the number of defects in each category, on a control chart. The approximate normal method is usually used to obtain control limits though the distribution that depends on the values of the weights and the parameters of the Poisson distribution which may not always be normal. [Jones, L.A., Woodall, W.H., Conerly, M.D., 1999. Exact properties of demerit control charts. Journal of Quality Technology 31 (2), 207–216] used the characteristic function approach to determine the distribution of the demerit statistic. Unfortunately, the process that they used to determine the distribution needs complex integral evaluation via mathematical software packages or using the approximate truncated infinite series. Moreover, the characteristic function does not provide an accurate result easily. In this paper, a bounding approach is proposed to determine the approximate distribution of the demerit statistic. It is easy to implement and also the approximate error can be controlled to meet the desired accuracy. In addition, an example is demonstrated to illustrate the proposed method. The results indicate that the proposed approach is efficient and accurate. Finally, the performance among the approximate normal method, the characteristic function approach, and the proposed bounding approach are discussed.