Development of a New MEWMA – Wilcoxon Sign Rank Chart for Detection of Change in Mean Parameter
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Abstract
A nonparametric chart has been accepted and implemented for real world problems, especially, when the distribution of the population is unknown and the parameter could not be estimated. The nonparametric chart can overcome those limitations and it is user-friendly. Consequently, the objective of this research is to develop a new modified exponentially weighted moving average (MEWMA) chart based on Sign Rank statistics, namely MEWMA-SR, and to compare the performance of change detection with the EWMA and MEWMA charts and nonparametric EWMA based on the Sign (EWMA-Sign) and the Sign Rank (EWMA-SR), and MEWMA-Sign charts. The efficiency measurement of charts is commonly performed by average run length (ARL) divided into two states; in control ARL (ARL0) and out of control ARL (ARL1). The numerical results were carried out by Monte Carlo simulation with 105 replication and the best performance of the chart is considered by the minimum value of ARL1. The proposed chart outperforms when a subgroup is small and a magnitude of changes is moderate for Laplace, otherwise the EWMA-SR is superior to small changes. When the observations are from lognormal the MEWMA-SR performs better than EMWA-SR and other charts for moderate to large changes for all sizes of subgroups. Furthermore, the proposed chart is applied to real data set as the S&P 500 index and shows the best performance in detecting a change.
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