Improving the synthetic coefficient of variation chart by incorporating side sensitivity

Lee, PingYin (2024) Improving the synthetic coefficient of variation chart by incorporating side sensitivity. Doctoral thesis, Sunway University.

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Abstract

The control chart is recognized as a crucial technique in Statistical Process Control. However, due to inconsistencies in the mean and/or standard deviation of some processes, traditional control charts monitoring the mean or standard deviation become inappropriate in such situations. Therefore, monitoring the coefficient of variation is selected as an alternative and it has been implemented in numerous industries, for example, in human and public sciences, environmental research, agricultural sciences, engineering, technology, finance and education. The synthetic chart that monitors the coefficient of variation, namely the synthetic-y chart, is a widely used control chart. Unlike the Shewhart-y chart, the synthetic-y chart does not immediately signal an out-of-control condition when a sample coefficient of variation(yˆ) appears in the non-conforming region, i.e. the region below the lower control limit (LCL) or the region above the upper control limit (UCL). Instead, it waits until a second sample coefficient of variation to appear in the non-conforming region, and if these successive points are close to each other, it generates an out-of-control signal. In the existing literature, the synthetic-y chart performs better than the Shewhart-y chart at the same rate of false alarms, as waiting for the second sample coefficient of variation to appear in the non-conforming region allows for the adoption of tighter control limits without increasing the false alarm rate. However, the existing synthetic-y chart treats all points falling below the LCL or above the UCL as non-conforming samples. A side-sensitive synthetic-y chart is proposed in this thesis in order to monitor the coefficient of variation, where the non-conforming samples must appear in the same non-conforming region, for instance, either both samples must fall in the region above the UCL or both must fall in the region below the LCL, resulting in faster detection of out-of-control conditions. Markov chains are applied to compute various performance measures, for example, the Average Run Length (ARL), Standard Deviation of the Run Length (SDRL) and Expected Average Run Length (EARL). In order to evaluate the performance of the proposed chart accurately due to run lengths that may be skewed, the analysis of the entire run length distribution was conducted, together with the Median Run Length (MRL) and Expected Median Run Length (EMRL). Algorithms to obtain optimal chart parameters are also formulated. Based on the results obtained which had been validated using simulations, the proposed side-sensitive synthetic-y chart outperformed the Shewhart-y chart, the EWMA-y2 chart and the existing synthetic-y chart without the side sensitivity feature for most cases and displayed a significant improvement. For instance, when n=5, t=1.3 and yo = 0.05, the values of the ARL1 and MRL1 for the proposed chart were 10.18 and 4, respectively, whereas the values of the ARL1 and MRL1 were 30.61 and 14, respectively, for the Shewhart-y chart, 11.80 and 9, respectively, for the EWMA-y2 chart, and 16.38 and 5, respectively, for the existing synthetic-y chart. The proposed chart was further implemented on actual industrial data and compared with the same existing coefficient of variation charts, showed better efficiency in detecting out-of-control conditions.

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