A Simulation Study on the Average Run Length of the Moving Range Control Chart

AbstractThe moving range control chart is usually established to monitor the variability of the process characteristic for situations where the individuals control chart is applied. In the design of a control chart, the average run length (ARL) of the chart is usually used as an important indicator for evaluating control chart performance. In the present paper, the out-of-control ARL of the moving range chart is investigated using computer simulation. Three types of data are generated for study: normal and independent data, non-normal data, and autocorrelated data, such that the effects of non-normality and autocorrelation on the detection ability of the chart can be investigated. From the simulation results, we find that positive skewness coefficient present in the underlying distribution would produce a shorter out-of-control ARL than the normal data. Also, if we are able to know that the data are positively highly autocorrelated, then “span two” should be used for the operation of the moving range chart to keep the chart's detection ability.