Modified Simple Robust Control Chart Based on Median Absolute Deviation

Abstract

The control limits derived for the Median Absolute Deviation  (MAD) based Standard deviation (S) control chart proposed by Abu-Shawiesh was for monitoring quality characteristics when a standard value of sigma (${\sigma}$) is known or given by the management/ engineers. When sigma (${\sigma}$) is unknown and we are interested in monitoring past/non-normal data, then there is the need to modify the simple robust control limits. In this paper, the control limits for the Shewhart $\bar{X}$ and S control chart based on median absolute deviation  were modified using the concept of three sigma (3${\sigma}$) limits. An evaluation performance tool was also developed to evaluate the efficiency of the modified control chart.  An algorithm implemented on S-Plus programming language was developed to compute the two evaluation parameters used in this study. The results show that the control limits interval and the average run length for the modified control charts is smaller than that of the existing control charts. Therefore, the modified control limits is more efficient than the existing control limits. It is recommended that the modified control limits be used when monitoring past/non-normal data or when there is no standard value of sigma specify by the process engineer/ management.