A Proposed Single Ewma Chart Combining The X And R Charts For A Joint Monitoring Of The Process Mean And Variance
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Date
2008-05
Authors
Kah Wai, Yeong
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Abstract
In manufacturing industries, two control charts are usually used to monitor the process
mean and the process variance separately. In the last 15 years, numerous single charts
are proposed to enable the use of only one single chart to jointly monitor both the
·process mean and variance for the purpose of efficiency improvement and resource
optimization. Most approaches are based on transforming the sample mean and the
sample variance statistics into two statistics, each having a standard scale, followed by
either plotting them on the same chart or combining them into a single statistic, which
serves as the plotting statistic to represent the process mean and the process variance.
Using the sample range instead of the sample variance in the monitoring of the process
variance, for small sample sizes, say n ~ 10, provides advantages, such as in reducing
computation work, time, cost and error as well as enabling easier detection of outliers in
the initial data sample. This thesis considers the transformation of the sample mean and
the sample range statistics into two different random variables which follow the same
standard normal distribution. From these two standard normal random variables, two
corresponding exponentially weighted moving average (EWMA) statistics are
computed which are then combined into a single statistic to form the plotting statistic of
the proposed chart, that will be named as the single EWMA X- R chart. From the
simulation conducted, it is found that the single EWMA X - R chart is effective in
detecting both increases and decreases in the mean and/or variance.
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Keywords
Mathematics , General