TY - JOUR
T1 - The performance of the double sampling X̄ chart with estimated parameters for skewed distributions
AU - Teoh, Wei Lin
AU - Yeong, Wai Chung
AU - Khoo, Michael B. C.
AU - Teh, Sin Yin
PY - 2016
Y1 - 2016
N2 - 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.
AB - 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.
UR - http://www.universitypublications.net/ajs/0501/html/P6RS162.xml
M3 - Article
SN - 2165-6282
VL - 5
SP - 237
EP - 251
JO - Academic Journal of Science
JF - Academic Journal of Science
IS - 1
ER -