A Phase-II Nonparametric Cusum Chart with an Application to Exchange Rates Data

Abstract

Recently, Chowdhury et al. (2014a) proposed a single distribution-free Shewhart-type control chart based on the Cucconi (1968) test statistic for monitoring shift in the unknown location and scale parameters of a process distribution simultaneously. Several recent researches demonstrated that the CUSUM type charts perform better than the Shewhart-type charts under small and persistent shift. In the present work, we develop a phase II distribution-free CUSUM chart based on the Cucconi statistic, referred to as CUSUM-Cucconi (CC) chart. Nonparametric nature of the Cucconi statistic ensures that all the in control (IC) properties of the proposed chart remain invariant and known for all continuous process distributions. Control limits are tabulated for implementation of the chart. The IC and out of control (OOC) performance of the chart are thoroughly investigated in terms of the average, standard deviation, median and some percentiles of the corresponding run length distributions. A detailed comparison with the Shewhart-type Cucconi and Lepage charts as well as the CUSUM Lepage chart (as in Chowdhury et al. (2014b)) is presented. The proposed chart is illustrated with exchange rates data.