• International Journal of Technology (IJTech)
  • Vol 12, No 2 (2021)

Robust Synthetic Control Charting

Robust Synthetic Control Charting

Title: Robust Synthetic Control Charting
Ayu Abdul Rahman, Sharipah Soaad Syed-Yahaya, Abdu Mohammed Ali Atta

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Cite this article as:
Rahman, A.A., Syed-Yahaya, S.S., Atta, A.M.A., 2021. Robust Synthetic Control Charting. International Journal of Technology. Volume 12(2), pp. 349-359

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Ayu Abdul Rahman Department of Mathematics and Statistics, School of Quantitative Sciences, Universiti Utara Malaysia, 06010 UUM, Sintok, Kedah, Malaysia
Sharipah Soaad Syed-Yahaya Department of Mathematics and Statistics, School of Quantitative Sciences, Universiti Utara Malaysia, 06010 UUM, Sintok, Kedah, Malaysia
Abdu Mohammed Ali Atta Department of Mathematics, Statistics and Physics, College of Arts and Sciences, Qatar University, P.O. Box 2713-Doha
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Abstract
Robust Synthetic Control Charting

The proposal of synthetic charting is based on the normality assumption. This assumption, however, is hard to attain in practice. Therefore, it is important to examine how the chart would response under some types of non-normal data. The focus of this article is to monitor location shifts using a synthetic chart and to validate its performance under the g-and-h distributions. This study shows that the effect of non-normality on the standard synthetic chart is not trivial, especially when the underlying distributions are heavy-tailed. With these types of distribution, Phase II monitoring of location using median-based estimators is advisable. In doing so, the synthetic chart is more robust to departure in the normality assumption with little effect on its out-of-control performance. This paper shows how the synthetic parameters should be attained to reflect the use of the modified one-step M-estimator (MOM) in its Winsorized version, and the median for Phase II. The assessment is based on the average run length and supported by the extra quadratic loss function. Finally, the practical application of the proposed synthetic charts is illustrated using real data.

Average run length; Extra quadratic loss; Robust estimators; Shewhart chart; Synthetic chart

Introduction

Competition in the manufacturing sector involves delivering high-quality products or services quickly at a low cost (Baby and Jebadurai, 2018). Undeniably, cost and quality are among key factors in the development of manufacturing strategies (Nurcahyo et al., 2019). To achieve such a feat, lean production is usually advocated. Lean production typically involves the use of quality tools such as control charts, flowcharts and fish bone diagrams, aiming to reduce or eliminate waste that occur during the production process. Today, the lean concept has been extended considerably into various fields beyond manufacturing (Driouach et al., 2019). As such, the use of quality tools, especially the control chart, is vital.

Application of the standard control chart, which typically relies upon the normality assumption, is favorable in many areas of the statistical process monitoring (SPM), since the tool can offer fast detection of special cause(s) in the process. Subsequently, corrective action may be undertaken to preserve process quality. One of the many variable control charts introduced in the literature is the synthetic chart for process mean, by Wu and Spedding (2000). Its use in practice is justified based on its moderate robustness to non-normality for a large sample size n, i.e., n  6 (Calzada and Scariano, 2001). Nonetheless, there is a concern for unacceptably high false alarm rates from the synthetic chart based on the sample mean if data distribution is strongly skewed or very heavy-tailed, which brings us to the current discussion.

       Under non-normality, it is better to use robust statistics instead of the sample mean to monitor changes in the data (Rocke, 1989). This way, outliers in the subgroups do not cause a signal to occur and, as such, the chart only responds to genuine shifts in the process. Existing work on the design and implementation of synthetic charts, as based on the median estimator, is noted in the literature. See, for example, Hu et al. (2018) and Tran et al. (2019). It is not clear how this robust chart performance is impacted under severe non-normality, but it seems that making use of the robust estimator with the synthetic control structure would lead to better quality tools, as changes in the process can be detected efficiently.

Notably, there is an increasing frequency of coverage on works associated with control charts in the quality technology field, reflecting the relevancy of this quality tool in real application (Jensen et al., 2018). Unfortunately, as reviewed by Bono et al. (2017), real data usually defy the assumption of normality. Thus, it is important to address the robustness (to non-normality) issue and to evaluate the existing and any newly proposed synthetic charts with severe deviation from normality. To fill this gap, we investigate the performance of the synthetic chart that is based on four different estimators, including the aforementioned median estimator, in monitoring the process location of Phase II samples upon violation of the normality assumption. In the next section, we give the details regarding the selected Phase II estimators before explaining the synthetic charting structure.

Conclusion

Robustification in this study is intended to lead to a synthetic chart, the IC ARL of which is not sensitive to the non-normal data or the particular values of design parameters, kS and LS, but which will detect location shifts reliably. We identify MOM as best fit for the synthetic chart. This way, researchers in many application domains will not be constrained by the normality assumption, but may instead work with the original data without having to worry about the shape of the distributions. While this paper concentrated on the performance of the synthetic chart based on the assumption of known process parameters, we believe that the findings can be easily extended to the estimated parameters case, which will be considered in our future work. 

       The decision of what shift for which to design rarely gets attention in the literature, and even more rarely under non-normal cases. The three design shifts employed in this study provide valuable information for further implementation and for the designing of synthetic charts in practice. Generally, the synthetic charts designed for a small shift ( ) exhibit lack of IC robustness, and therefore can be misleading in the detection of OC status. However, for a large sample size (n = 9), the synthetic MOM and WMOM charts are better at controlling the ARL(0), which leads to the best charts (in terms of in-control robustness) across the distributional shapes. Moreover, the results confirm that these synthetic median-based charts (including the use of the usual median estimator) perform reliably and quickly if designed for a medium-sized ( ) or a large shift ( ). For OC processes, the data of which follow heavy-tailed distributions, these charts offer quickly declining ARLs, suggesting not much loss in responsiveness to genuine shifts in the process.

Acknowledgement

    The authors would like to acknowledge the work that has led to this paper, which is supported by Universiti Utara Malaysia, Fundamental Research Grant Scheme (S/0 Code 13578) of the Ministry of Higher Education, Malaysia.

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