Proposed Univariate Run Sum X And Multivariate Run Sum Hotelling’s x2 Control Charts With Variable Sampling Intervals
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Date
2016-10
Authors
Xinying, Chew
Journal Title
Journal ISSN
Volume Title
Publisher
Universiti Sains Malaysia
Abstract
Control charts are probably the most useful statistical process control (SPC)
problem solving tools and are commonly used to monitor process performance and to
detect process shifts in service and manufacturing industries so that changes that
adversely affect process quality can be detected as early as possible. Traditional
control charts for process monitoring are based on taking samples from the process at
fixed sampling intervals. Recently, numerous researches focus on the use of variable
sampling intervals (VSIs), where the lengths of the sampling intervals are varied
according to the process quality. A short sampling interval is used when the process
quality indicates a possible out-of-control situation while a long sampling interval is
used, otherwise. Results show that incorporating the VSI schemes into traditional
fixed sampling interval (FSI) charts enhance the performances of the traditional FSI
charts. In view of this, the univariate and multivariate run sum charts incorporating
the VSI scheme are proposed in this study. These two new charts are called the
univariate VSI run sum X chart and the multivariate VSI run sum Hotelling’s 2
chart, respectively. The procedure of implementation of the proposed charts is
discussed in this thesis. An optimization technique is developed to compute the
optimal scores and parameters of the proposed charts. The zero and steady state
performances of the proposed univariate VSI run sum X chart and multivariate VSI
run sum Hotelling’s 2 chart are measured using the Markov chain approach.
Illustrative examples using real datasets from manufacturing processes are presented
to demonstrate the application and implementation of the proposed charts. The VSI
approach enhances the sensitivity and efficiency of the basic charts while retaining
their simplicity of implementation. Both the proposed univariate VSI run sum X
chart and multivariate VSI run sum Hotelling’s 2 chart perform generally well
compared with other charts under comparison. Adding more regions and scores to
the proposed charts can further enhance the sensitivity and efficiency of the charts.
Description
Keywords
Control charts are probably the most useful , to monitor process performance