Modified EWMA Control Chart for Skewed Distributions and Contaminated Processes
Keywords:
EWMA control chart, modified EWMA control chart, skewed distribution, contaminated data, average run lengthAbstract
In this paper, we proposed the variable control chart for monitoring process mean by modified the traditional Exponentially Weighted Moving Average (EWMA) control chart for skewed and contaminated processes. The proposed EWMA control charts are modified both of mean and standard deviation in the control limits of the traditional EWMA control chart based on three different heuristic methods, namely, the Modified Exponentially Weighted Moving Average (MEWMA) control chart, the Modified Weighted Standard Deviation Exponentially Weighted Moving Average (MWSD-EWMA) control chart, and the Modified Weighted Variance Exponentially Weighted Moving Average (MWV-EWMA) control chart. A comparison of the performance measures is the average run length (ARL) were compared with the traditional EWMA control chart in various situations via simulation. The results show that for Gamma distribution, the MWSD-EWMA control chart is performs well for small sample size (), low levels of
,
and
are low
in all levels of
. The MEWMA control chart is the better than other charts for moderate levels of
on all levels of
and relatively small differences with the MWV-EWMA control chart. When the process distribution is Weibull, the MWSD-EWMA control chart is performs well for small sample size
and
are low
in all values of
and
. If the sample sizes are moderate and large
, the MWSD-EWMA control chart is better than other charts for very low level of
in all values of
and
. For lognormal distribution, we found that the results as well as the Weibull distribution in all levels of
and
. Finally, all charts are similar performances for all values of
and
when high levels of
in all skewed distribution processes.
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