The performance of the double sampling  chart with estimated parameters for skewed distributions

Wei Lin Teoh, Wai Chung Yeong, Michael B. C. Khoo, Sin Yin Teh

Research output: Contribution to journalArticle

Abstract

The double sampling (DS) X chart is favourable among practitioners in the context of Statistical Process Control. However, in the construction of the DS Xbar chart, process parameters are rarely known and need to be estimated from the Phase-I historical dataset. The DS Xbar chart with estimated parameters is effective in detecting small and moderate mean shifts. Traditionally, the DS Xbar chart with estimated parameters is designed based on the assumption of a normal underlying distribution. In many real applications, the normality assumption may not be true. Therefore, this paper aims at investigating the performance of the DS Xbar chart with estimated parameters for skewed populations. The skewed distributions considered in this paper are the Weibull, lognormal and gamma distributions. By applying the Monte-Carlo-simulation approach, the performance of the DS Xbar chart, in terms of the average run length and the standard deviation of the run length, are studied for different levels of skewness and various magnitudes of mean shifts. The results reveal that the performance of the DS Xbar chart with known and estimated parameters is significantly affected by skewed distributions. Particularly, the DS Xbar chart with small number of Phase-I samples and sample size is seriously influenced by skewed distributions when the process mean is slightly out-of-control (small shift in the process mean). At least 80 Phase-I samples are required for the DS Xbar chart with estimated parameters to behave similarly to its known-parameter counterpart when the underlying distribution is not normal.
Original languageEnglish
Pages (from-to)237-251
JournalAcademic Journal of Science
Volume5
Issue number1
Publication statusPublished - 2016

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