Economic design of adaptive (X)over-bar control charts for skewed data

Recent studies have demonstrated the variable parameters (VP, i.e., variable sample sizes, sampling intervals, and/or action limit coefficients) (X) over bar charts have better performance than standard Shewhart (SS) (X) over bar control chart by statistical and economic criteria. The usual assumption for designing a control chart is that the data or measurements are normally distributed. However, this assumption may not be true for some processes. In the present paper, the economic design for the adaptive (X) over bar chart is developed when the process data follow a skewed distribution. An example is presented to illustrate the solution procedure. Based on the study, it is shown that the VP X chart is more effective than the other adaptive control charts. The sensitivity analysis on the input parameters and various population distributions are illustrated through a numerical example.