A Flexible and Generalized Exponentially Weighted Moving Average Control Chart for Count Data

Abstract

The Conway-Maxwell-Poisson distribution can be used to model under-dispersed or over-dispersed count data. This study proposes a flexible and generalized attribute exponentially weighted moving average (EWMA), namely GEWMA, control chart for monitoring count data. The proposed EWMA chart is based on the Conway-Maxwell-Poisson distribution. The performance of the proposed chart is evaluated in terms of run length (RL) characteristics such as average RL, median RL, and standard deviation of the RL distribution. The average RL of the proposed GEWMA chart is compared with Sellers chart. The sensitivity of the standard Poisson EWMA (PEWMA) chart is also studied and compared with the proposed GEWMA chart for under-dispersed or over-dispersed data. It has been observed that the PEWMA chart is very sensitive for under-dispersed or over-dispersed data while the proposed GEWMA is very robust. Finally, the generalization of the proposed chart to the Bernoulli EWMA, PEWMA, and geometric EWMA charts is also studied using someone simulated data sets.

A Control Chart for COM-Poisson Distribution Using Resampling and Exponentially Weighted Moving Average

“…In this paper, we will propose and design the COM–Poisson EWMA control chart using repetitive sampling. We expect that the proposed control chart will perform better than the control chat proposed by Saghir and Lin for the same values of the specified parameters. We will present the industrial application of the proposed plan.…”

“…This becomes the Poisson distribution when v = 1, the geometric distribution when v = 0, μ < 1 and Bernoulli distribution when v → ∞ with probability μ/(1 + μ). Note also that v < 1 shows data over‐dispersion and v > 1 indicates data under‐dispersion [see, Saghir and Lin] . The approximate values of mean and variance of the COM–Poisson distribution are given as …”

“…Gan worked on the modification of EWMA to monitor the mean of the Poisson distribution. He developed ceil, round and floor EWMA charts [see for details, Saghir and Lin] . Later on, Borror et al .…”

“…According to Saghir and Lin Poisson EWMA control charts are commonly used to monitor the number of nonconformities and are very sensitive for over‐spread and under‐spread because mean and variance are the same for the Poisson distribution. To overcome this issue, recently, Saghir and Lin proposed a control chart using the Conway–Maxwell (COM–Poisson) distribution and generalized EWMA (GEWMA).…”

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

“…Saghir et al extended the Sellers chart using the exact k ‐sigma limits and true probability limits. Saghir and Lin proposed an EWMA chart based on the COM‐Poisson distributon. Saghir and Lin proposed a Shewhart‐type control chart for multivariate attributes count data using the COM‐Poisson distribution.…”