A double exponentially weighted moving average control chart for monitoring COM‐Poisson attributes

Abstract

The Conway‐Maxwell‐Poisson (COM‐Poisson) distribution is a two‐parameter generalization of the Poisson distribution, which can be used for overdispersed or underdispersed count data and also contains the geometric and Bernoulli distributions as special cases. This article presents a double exponentially weighted moving average control chart with steady‐state control limits to monitor COM‐Poisson attributes (regarded as CMP‐DEWMA chart). The performance of the proposed control chart has been evaluated in terms of the average, the median, and the standard deviation of the run‐length distribution. The CMP‐DEWMA control chart is studied not only to detect shifts in each parameter individually but also in both parameters simultaneously. The design parameters of the proposed chart are provided, and through a simulation study, it is shown that the CMP‐DEWMA chart is more effective than the EWMA chart at detecting downward shifts of the process mean. Finally, a real data set is presented to demonstrate the application of the proposed chart.

A Double Generally Weighted Moving Average Chart for Monitoring the COM-Poisson Processes

“…Saghir and Lin [15] first generalized the attribute exponentially weighted moving average (EWMA) chart based on the COM-Poisson distribution, namely the GEWMA chart, to monitor count data. Recently, Alevizakos and Koukouvinos [20] proposed a double 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. In this study, we extend the GEWMA and CMP-DEWMA charts by adding design and adjustment parameters to enhance detection ability.…”

“…(t − j + 1)q t− j X j + q t (t − tq + 1)G 0 (14) In this case, the CMP-DGWMA chart is reduced to the CMP-DEWMA chart proposed by Alevizakos and Koukouvinos [20]. DG t becomes the statistic of the CMP-DEWMA chart, which uses the GEWMA(1 − q) weighted sequence twice, and is denoted by CMP − DEWMA(1 − q) for simplification.…”

“…For a clearer depiction, Figure 1 depicts the corresponding ARLs' curves of the CMP-DGWMA chart with q = 0.95 and α = 0.3, 0.5, 0.7, 0.9 and 1.0. In particular, when α = 1 and q = 1 − λ, the CMP-GWMA and CMP-DGWMA charts are reduced, to the GEWMA chart by Saghir and Lin [15], and the CMP-DEWMA chart by Alevizakos and Koukouvinos [20], respectively. (1).…”

A hybrid method based on P and P′ control chart for identifying hotspots

“…Tercero-Gómez et al 41 proposed a cumulative sum chart also known as CUSUM for monitoring of any location simultaneously that provides a powerful tool to detect every variation, even those that are minuscule, in the process of monitoring which can help to organize a suitable reaction from the people in charge of preventive measures. Alevizakos et al 42 proposed a double exponentially weighted moving average chart based on the Conway-Maxwell-Poisson distribution to monitor the data. The preference of this chart was to detect not only changes in each parameter, but also the cases that both parameters altered simultaneously.…”

Self‐information‐based weighted CUSUM charts for monitoring Poisson count data with varying sample sizes

“…To monitor the Poisson count data, some authors have proposed the CUSUM charts, 4,13 the EWMA charts 14–15 and the GLR charts, 11 as well as the classical c ‐ and u ‐ charts 3 . To take the under‐ or overdispersion into consideration, the COM‐Poisson distribution 16–17 or the BerG distribution 18 was applied to model the counting process and the EWMA, CUSUM or Shewhart control schemes were developed. Furthermore, to monitor the high‐yield processes characterized by a large number of zero counts under unknown shifts, the zero‐inflated Poisson distribution is applied to model the data, and the Wald statistic‐based chart 19 and the generally weighted moving average chart 20 were developed, respectively.…”