Derivation of the Limits for Control Chart Using the Median Absolute Deviation for Monitoring Non-Normal Process

Abstract

Problem statement: The Shewhart and S control charts, in the literature, were combined to evaluate the stability of a process. These charts were based on the fundamental assumption of normality of the quality characteristics under investigation. Approach: In practice, the normality assumption was often violated by real life data, therefore, use of the Shewhart and S control charts on real life data might leads to misplacement of control limits. There were many alternatives in the literature to handle non-normality of quality characteristics. The Median Absolute Deviation (MAD) claimed in the literature to be the best estimate when the data under consideration is non-normal. Thus in this study, we derived the control limits for the-control chart using the median absolute deviation for monitoring process stability when the quality characteristic under investigation was non-normal. Results: The derived control limits were compared with the control limits when the sample standard deviation was used as a measure of controlling the process variability using manufacturing process (real life) data. Furthermore, a simulation study was carried out to evaluate the performance of the proposed MAD based control charts on both normal and non-normal process. Conclusion: The obtained results show that the derived control limit is an improvement on the control limit of the Shewhart and that the MAD control charts performed better for non-normal process than for normal process.