INVESTIGATING THE PERFORMANCE OF PROGRESSIVE MEAN CHART BASED ON MEDIAN RUN LENGTH

Author(s) : ZAMEER ABBAS

Abstract:

The run length distribution of progressive mean (PM) control charts is highly skewed when the process
is in-control or there is small shift in the process, so the interpretation based on average run length (ARL) may
not be suitable. Furthermore, skewness varies at different shifts which cause difficulty in its interpretation on
the basis of ARL. In the presence of skewness in run length, median run length (MRL) is the best approach
for interpretation and accuracy in monitoring the process. The discussion of run length on the base of MRL
is quite easy and readily understood. In this article, performance of PM control chart is evaluated in MRL
and it is compared with ARL at the same shifts. This article indicates that MRL is more versatile average for
understanding and explaining the distribution of run length because it is quick detector in case of small and moderate shift (highly and moderately skewed run length distribution) and gives good results in case of large shifts (symmetrical run length distribution). Along with standard deviation of run length (SDRL) is computed which is showing higher variability in process when shift is small but in case of moderate and large shifts smaller values of (SDRL). The performance of proposed control is compared with existing optimal EWMA control charts based on MRL and optimal CUSUM control charts based on MRL. The proposed control chart found to be more efficient than competitors.