Modified EWMA Control Chart for Skewed Distributions and Contaminated Processes

  • Thanyaporn Noiplab
  • Tidadeaw Mayureesawan
Keywords: EWMA control chart, modified EWMA control chart, skewed distribution, contaminated data, average run length

Abstract

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 (gif.latex?n=5), low levels of gif.latex?\kappa&space;_{3}, gif.latex?(\kappa&space;_{3}=1) and gif.latex?\delta are low gif.latex?(\delta&space;=0.10,&space;0.2 in all levels of gif.latex?\lambda. The MEWMA control chart is the better than other charts for moderate levels of  gif.latex?\delta gif.latex?(\delta&space;=&space;0.50) on all levels of gif.latex?\kappa&space;_{3},&space;\lamb  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 gif.latex?(n=5) and gif.latex?\delta are low gif.latex?(\delta&space;=&space;0.10,&sp in all values of  gif.latex?\kappa&space;_{3}  and gif.latex?\lambda. If the sample sizes are moderate and large gif.latex?(n&space;=&space;10,&space;20), the MWSD-EWMA control chart is better than other charts for very low level of gif.latex?\delta gif.latex?(\delta&space;=&space;0.10) in all values of gif.latex?\kappa&space;_{3}  and  gif.latex?\lambda. For lognormal distribution, we found that the results as well as the Weibull distribution in all levels of gif.latex?\kappa&space;_{3},&space;\lamb and gif.latex?n.  Finally, all charts are similar performances for all values of gif.latex?\kappa&space;_{3},&space;\lamb and gif.latex?n when high levels of gif.latex?\delta  in all skewed distribution processes.

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Published
2018-12-27
Section
Articles