Optimal Designs Of Univariate And Multivariate Synthetic Control Charts Based On Median Run Length
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Date
2012-05
Authors
Wong, Voon Hee
Journal Title
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Publisher
Universiti Sains Malaysia
Abstract
Univariate and multivariate control charts are usually optimally designed using average run length (ARL) as a sole measure of the charts’ performances. It is well known that the shape of the run length distribution for the univariate and multivariate charts changes from highly skewed when the process is in-control to approximately symmetric for large process shifts. Therefore, the median run length (MRL) is a more meaningful interpretation of the in-control and out-of-control performances of the charts and provides additional information not given by the average run length (ARL). This thesis proposes optimal design procedures for the univariate and multivariate synthetic charts, based on MRL, using the Markov chain approach for the zero and steady state processes. The univariate synthetic chart consists of an integration of the X sub-chart and the conforming run length (CRL) sub-chart while the multivariate synthetic chart consists of a combination of the Hotelling’s 2T sub-chart and the CRL sub-chart. Mathematica programs are written to compute the optimal parameters of the univariate and multivariate synthetic charts, based on desired in-control MRLs (0MRLs), for the zero and steady state processes. The MRL performance of the univariate synthetic chart is compared with that of the exponentially weighted moving average (EWMA) and Shewhart X charts, while the MRL performance of the multivariate synthetic chart is compared with that of the multivariate EWMA (MEWMA) and Hotelling’s 2Tcharts. Two examples, each for the univariate and multivariate synthetic charts are given to show how the proposed optimal design procedures, based on MRL, are used in a real situation.
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Keywords
Optimal designs of univariate and multivariate synthetic , control charts based on median run length