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

Abstract

<b>Problem statement:</b> 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. <b>Approach:</b> 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. <b>Results:</b> 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. <b>Conclusion:</b> 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

Modified Simple Robust Control Chart Based on Median Absolute Deviation

“…The evaluation parameters used in this study (the control limits interval and the average run length) show insiginificant difference for the S control charts when compared with the earlier results by Abu-shawiesh (2008) and Adekeye et al (2012). However, for theX control charts, there is considerable improvement as seen in the control limits interval and the average run length for all the data set considered in this study.…”

“…1, No. 2;2012 Control Limits Interval (CLI) and the Average Run Length (ARL) for theX and S control charts using the modified control limits and the control limits of Abu-Shawiesh (2008) and Adekeye et al (2012) are presented in Table 2. …”

“…If σ is known, then the derived control limits by Adekeye et al (2012) will be used. However, if σ is unknown, then the control limits will be derived from Equation (5).…”

“…1, No. 2;2012 consider situation when the standard value of sigma is unknown and we are interested in monitoring past data. Thus, we modify the control limits earlier presented by Abu-Shawiesh (2008) for the S-control chart and Adekeye et al (2012) for theX control chart.…”

Methodology for the Application of Nonparametric Control Charts into Practice

“…An overview of the advantages and disadvantages of the nonparametric control charts that were analyzed in this study is given in Table 1. Nonparametric control charts for monitoring position SSCC [4], NP-EWMA [5], NP-CUSUM [6] and PM [7] and NPCC for monitoring variability Mood [8,9] and MAD [10,11] have now been analyzed.…”