Distribution-free Phase II CUSUM Control Chart for Joint Monitoring of Location and Scale

A single distribution‐free (nonparametric) Shewhart‐type chart on the basis of the Lepage statistic is well known in literature 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 cumulative sum chart, on the basis of the Lepage statistic, referred to as the cumulative sum‐Lepage (CL) chart. The proposed chart is distribution‐free (nonparametric), and therefore, the in‐control 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 in‐control and out‐of‐control performance properties of the cumulative sum‐Lepage (CL) 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 cumulative sum 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) on the performance of the CL chart. The proposed chart is illustrated with a real data set. Summary and conclusions are presented.