Optimal design of Shewhart-Lepage type schemes and its application in monitoring service quality

We generalize popular distribution-free (nonparametric) Shewhart-Lepage scheme for simultaneously monitoring of location and scale parameters using an adaptive approach. This approach is known as percentile modifications of ranks (or adaptive Gastwirth score) in the statistical literature. This is a powerful tool to improve rank tests to detect a shift in the process. The adaptive Gastwirth score is not much familiar among quality control practitioners and therefore rarely used in practice. Nevertheless, such scores are very useful in detecting various types of shifts in the process characteristics. Considering its distinct advantages, we develop a new class of Shewhart-type adaptive Lepage-Gastwirth (ALG) scheme. We discuss optimal implementation strategies of the proposed scheme to achieve lower out-of-control (OOC) average run length (ARL) and false alarm rate (FAR). This scheme is typically designed to monitor service quality where the reference sample may be non-normal. Post signal follow-up procedures of the proposed Shewhart-type optimal ALG chart is discussed. We illustrate the use of optimal ALG charts with a recent data on Vancouver city call centre service quality monitoring.