Abstract

Variable sample size and sampling interval (VSSI)  control charts have been shown superior to standard Shewhart (SS)  control charts for detection of a small or moderate shift in process mean. However, they might utilize more resources by a more frequent sampling rate and a large sample size to improve its performance. Recently, some economic models were used to express the long-run cost per hour of operating the VSSI  control charts and gain insight into the way to design the charts. The usual assumption for the models is the normality of the underlying data or measurements. However, this assumption may not be true in practice. In this paper, an economic design of the VSSI  control charts for skewed non-normal data is conducted by using the Markov chain approach and genetic algorithms. Two types of VSSI  charts are considered and compared with the SS  charts over several numerical examples: the symmetric control limits and asymmetric control limits. Moreover, effects of non-normality on the performance of the VSSI  charts with respect to the costs of operating the charts are studied. It is shown that the reduction in cost can be achieved by using the VSSI  charts instead of the SS  charts. However, an increase on the skewness coefficient results in a decrease on the cost savings. In addition, the asymmetric control limits is a better choice with respect to the costs and the false alarm rate.

Key words: Skewed non-normal, control chart, genetic algorithms, economic design.