Mukherjee and Chakraborti1 proposed a single distribution-free (nonparametric) Shewhart-typechart based on the Lepage2 statistic for simultaneously monitoring both the location and the scaleparameters 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 theCUSUM-Lepage (denoted by CL) chart. The proposed chart is distribution-free (nonparametric) andtherefore, the in control (denoted IC) properties of the chart remain invariant and known for allcontinuous 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 throughsimulation studies in terms of the average, the standard deviation, the median and some percentiles of therun length distribution. Detailed comparison with a competing Shewhart-type chart is presented. Severalexisting CUSUM charts are also considered in the performance comparison. The proposed CL chart isfound to perform very well in the location-scale models. We also examine the effect of the choice of thereference value (k) of CUSUM chart on the performance of the CL chart. The proposed chart is illustratedwith a real data set. Summary and conclusions are presented.
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