Distribution-free Phase II CUSUM control chart for joint monitoring of location and scale

Abstract

Mukherjee and Chakraborti1 proposed a single distribution-free (nonparametric) Shewhart-type chart based on the Lepage2 statistic for simultaneously monitoring both the location and the scale parameters of a continuous distribution when both of these parameters are unknown. In the present work, we consider a single distribution-free CUSUM chart, based on the Lepage2 statistic, referred to as the CUSUM-Lepage (denoted by CL) chart. The proposed chart is distribution-free (nonparametric) and therefore, the in control (denoted IC) properties of the chart remain invariant and known for all continuous distributions. Control limits are tabulated for implementation of the proposed chart in practice. The IC and out of control (denoted OOC) performance properties of the chart are investigated through simulation studies in terms of the average, the standard deviation, the median and some percentiles of the run length distribution. Detailed comparison with a competing Shewhart-type chart is presented. Several existing CUSUM charts are also considered in the performance comparison. The proposed CL chart is found to perform very well in the location-scale models. We also examine the effect of the choice of the reference value (k) of CUSUM chart on the performance of the CL chart. The proposed chart is illustrated with a real data set. Summary and conclusions are presented.