Derivation of the Limits for Control Chart Using the Median Absolute Deviation for Monitoring Non-Normal Process
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Date
2012
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Abstract
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. In practice, the normality
assumption was often violated by real-life data, therefore, the use of the Shewhart X-bar and S control charts on real-life data might lead to misplacement of control limits. There were many alternatives in the
literature to handle the nonnormality 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 processes. 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 the non-normal process than for the normal process.
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Keywords
Median Absolute Deviation (MAD), Non-normal, Control limits interval, Process variability