Optimal designs of the median run length based double sampling X chart for minimizing the average sample size.
Designs of the double sampling (DS) X chart are traditionally based on the average run length (ARL) criterion. However, the shape of the run length distribution changes with the process mean shifts, ranging from highly skewed when the process is in-control to almost symmetric when the mean shift is large. Therefore, we show that the ARL is a complicated performance measure and that the median run length (MRL) is a more meaningful measure to depend on. This is because the MRL provides an intuitive and a fair representation of the central tendency, especially for the rightly skewed run length distribution. Since the DS X chart can effectively reduce the sample size without reducing the statistical efficiency, this paper proposes two optimal designs of the MRL-based DS X chart, for minimizing (i) the in-control average sample size (ASS) and (ii) both the in-control and out-of-control ASSs. Comparisons with the optimal MRL-based EWMA X and Shewhart X charts demonstrate the superiority of the proposed optimal MRL-based DS X chart, as the latter requires a smaller sample size on the average while maintaining the same detection speed as the two former charts. An example involving the added potassium sorbate in a yoghurt manufacturing process is used to illustrate the effectiveness of the proposed MRL-based DS X chart in reducing the sample size needed.
Department of Physical and Mathematical Science, Faculty of Science, Universiti Tunku Abdul Rahman, Jalan Universiti, Bandar Barat, Kampar, Perak, Malaysia.
Wei Lin
WL
Teoh
Michael B C
MB
Khoo
Sin Yin
SY
Teh
D000465:Algorithms; D003611:Dairy Products / Q000032:analysis; D005503:Food Additives / Q000737:chemistry; D019649:Food Industry / Q000379:methods / Q000706:statistics & numerical data*; D006801:Humans; D015233:Models, Statistical; D011786:Quality Control; D018401:Sample Size; D012984:Software; D013011:Sorbic Acid / Q000737:chemistry
D005503:Food Additives; D013011:Sorbic Acid