Derivation of the Limits for Control Chart Using the Median Absolute Deviation for Monitoring Non-Normal Process
K. S. Adekeye and P. I. Azubuike
DOI : 10.3844/jmssp.2012.37.41
Journal of Mathematics and Statistics
Volume 8, Issue 1
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.
© 2012 K. S. Adekeye and P. I. Azubuike. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.