Side Sensitive Group Runs Double Sampling Chart For Detecting Mean Shifts - Tan, Eng Keng (2020)
In this thesis, a side sensitive group runs double sampling (SSGRDS) chart to detect shifts in the process mean is proposed. The SSGRDS chart is an improvement over the side sensitive group runs (SSGR) chart proposed by Gadre and Rattihalli in 2007 and the DS chart suggested by Daudin in 1992. The step-by-step implementation of the SSGRDS chart, as well as the performance measures of the chart, i.e. the average number of observations to signal (ANOS) and expected average number of observations to signal (EANOS) criteria are explained in the thesis. The zero state and steady state ANOS and EANOS formulae are derived using the Markov chain approach. Tables of optimal charting parameters n1, n2 , L, L1, L2 , L3  of the SSGRDS chart for different combinations of the in-control ANOS   0 ANOS , incontrol EANOS   0 EANOS and in-control average sample size   0 ASS are provided for practical reasons to facilitate the implementation of the chart. The optimization procedures in (i) minimizing the out-of-control ANOS value for a standardized size of the mean shift   opt  , based on different combinations of 0 ANOS and 0 ASS values, and (ii) minimizing the out-of-control EANOS value for a range of standardized sizes of the mean shifts   min max  , , based on different combinations of 0 EANOS and 0 ASS values, are provided. Optimization programs for all the charts are written in the ScicosLab, Mathematica and Matlab software. A real case study is used to show the implementation of the SSGRDS chart.