Tan, Eng Keng
(2020)
Side Sensitive Group Runs Double
Sampling Chart For Detecting Mean
Shifts.
Masters thesis, Universiti Sains Malaysia.
Abstract
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.
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