Teoh, Wei Lin
(2013)
Optimal Designs Of The Double
Sampling X Chart Based On Parameter
Estimation.
PhD thesis, Universiti Sains Malaysia.
Abstract
Control charts, viewed as the most powerful and simplest tool in Statistical Process
Control (SPC), are widely used in manufacturing and service industries. The double
sampling (DS) X chart detects small to moderate process mean shifts effectively,
while reduces the sample size. The conventional application of the DS X chart is
usually investigated assuming that the process parameters are known. Nevertheless,
the process parameters are usually unknown in practical applications; thus, they are
estimated from an in-control Phase-I dataset. In this thesis, the effects of parameter
estimation on the DS X chart’s performance are examined. By taking into
consideration of the parameter estimation, the run length properties of the DS X
chart are derived. Since the shape and the skewness of the run length distribution
change with the magnitude of the process mean shift, the number of Phase-I samples
and sample size, the widely applicable performance measure, i.e. the average run
length (ARL) should not be used as a sole measure of a chart’s performance. For this
reason, the ARL, the standard deviation of the run length (SDRL), the median run
length (MRL), the percentiles of the run length distributions and the average sample
size (ASS) are recommended to effectively evaluate the proposed DS X chart with
estimated parameters.
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