Monitoring the coefficient of variation using a variable sample size EWMA chart. (December 2018)

• Record Type: Journal Article
• Authors: Muhammad, Anis Nabila Binti; Yeong, Wai Chung; Chong, Zhi Lin; Lim, Sok Li; Khoo, Michael Boon Chong
• Is Part Of: Computers & industrial engineering. Volume 126(2018)
• Page Start: 378
• Page End: 398
• Publication Date: 2018-12
• Subjects: Average sample size -- Coefficient of variation -- Expected average run length -- Exponentially Weighted Moving Average chart -- Markov chain -- Variable sample size; Engineering -- Data processing -- Periodicals; Industrial engineering -- Periodicals; 620.00285
• DOI: 10.1016/j.cie.2018.09.045
• Languages: English
• ISSNs: 0360-8352

Abstract

Highlights: This paper proposes the VSS EWMA- γ 2 chart. Derivation of the ARL, SDRL, ASS and EARL formulae of the proposed chart is shown. Optimization algorithms which minimizes the ARL 1 and EARL 1 values are shown. Performance comparison shows that the proposed chart outperforms existing CV chart. Implementation of the proposed chart is shown through an industrial example. Abstract: Control charts for monitoring the coefficient of variation (CV) have been receiving a lot of attention in the literature, with numerous more powerful and robust CV charts being proposed. CV charts are attracting attention due to their usefulness in monitoring processes with an inconsistent mean and a standard deviation which changes with the mean. These processes could not be monitored by conventional mean and/or standard deviation-type charts. One of the strategies to improve the performance of CV charts is by incorporating adaptive features, i.e. by varying the chart's parameters according to past sample information. Hence, this paper proposes a variable sample size (VSS) Exponentially Weighted Moving Average (EWMA) chart to monitor the CV squared ( γ 2 ), which is not available in the literature. The proposed chart allows different sample sizes to be adopted in the EWMA chart according to prior sample information. This paper shows the derivation of formulae to compute the average run length ( ARL ), average sample size ( ASS ) and expected average run length ( EARL ). Subsequently, an optimization algorithm to optimize the performance of the proposed chart is developed. Tables of optimal charting parameters are also provided. Next, the performance of the proposed chart is compared with five existing CV charts in the literature. The comparison shows that the proposed chart outperforms the five existing CV charts in almost all scenarios. Finally, this paper shows the implementation of the VSS EWMA- γ 2 chart on an actual industrial example.