Abstract
Generalized exponentially weighted moving average (EWMA) and double EWMA (DEWMA) charts based on the Conway–Maxwell–Poisson (CMP or COM-Poisson) distribution, also known as the GEWMA and CMP-DEWMA charts, are effectively used for monitoring the counts of non-conformities in a process. To further enhance their performance, this study utilizes design and adjustment parameters to develop generally weighted moving average (GWMA) and double GWMA charts, also known as the CMP-GWMA and CMP-DGWMA charts, to monitor COM-Poisson attributes. Numerical simulations indicate that the CMP-DGWMA chart outperforms its prototype CMP-DEWMA and CMP-GWMA charts in detecting small location and dispersion shifts, as well as both shifts together, in terms of average run lengths. Finally, an example is provided to demonstrate the efficiency of the proposed CMP-DGWMA chart and its counterparts.
Highlights
In a number of medicine and manufacturing industries, the quality attributes use counts of defects or non-conformities to indicate the production quality
Motivated by the features of the Poisson generally weighted moving average (PGWMA) chart, this study aims to improve the sensitivity of generalized EWMA (GEWMA) and CMP-double EWMA (DEWMA) charts, namely the CMP-generally weighted moving average (GWMA) and CMP-DGWMA charts, to effectively monitor COM-Poisson-distributed data
Alevizakos and Koukouvinos [20] proposed a double exponentially weighted moving average (EWMA) chart, namely the CMP-DEWMA chart, to monitor COM-Poisson attributes, and showed it to be more effective in detecting the downward shifts of process mean than the GEWMA chart
Summary
In a number of medicine and manufacturing industries, the quality attributes use counts of defects or non-conformities to indicate the production quality. The Shewhart c-chart is widely used as an attribute control chart to monitor production processes when the data may be modeled by a Poisson distribution. The Shewhart c-chart is insensitive to the detection of small to moderate process shifts. To overcome this limitation, Brook and Evans [1] developed the Poisson cumulative sum (PCUSUM) chart, for monitoring the location of a Poisson process. Lucas [2] provided the design structure and implementation procedures of the PCUSUM chart. White and Keats [3] and
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