On the Steady-State Performance of the Poisson Double GWMA Control Chart

Abstract

______________________________________________________________________Abstract: This article presents a control chart called "Poisson double GWMA" (PDGWMA) chart for monitoring Poisson-distributed processes. Using simulation, the steady-state average run length (SSARL) of PDGWMA chart is evaluated and compared with those of other control charts including Poisson EWMA, Poisson GWMA and Poisson double EWMA (PDEWMA). It is shown that this chart is always more sensitive than other control charts in detecting an out-of-control signal. The PDGWMA chart is a generalized model for which the PDEWMA chart is a special case and also is an effective control chart in situations where the quality deterioration (upward shift) and the quality improvement (downward shift) can be detected agilely, which is important to a modern advanced system.

Monitoring of time between events with a double generally weighted moving average control chart

“…Sheu and Hsieh 35 studied the DGWMA control chart for the normal distribution, and it was found more effective than the DEWMA and GWMA control charts in detecting moderate shifts of the process mean. Other studies about the DGWMA control charts are Tai et al, 36 Sheu et al, 37 Huang et al, 38 Chiu and Lu, 39 Chiu, 40 and Lu. 41 In this article, a one-sided DGWMA control chart with a time-varying control limit based on gamma distribution is proposed for monitoring the TBE and detecting a downward shift in a process.…”

“…Sheu and Hsieh studied the DGWMA control chart for the normal distribution, and it was found more effective than the DEWMA and GWMA control charts in detecting moderate shifts of the process mean. Other studies about the DGWMA control charts are Tai et al, Sheu et al, Huang et al, Chiu and Lu, Chiu, and Lu …”

Generally weighted moving average monitoring schemes: Overview and perspectives

“…Chiu and Sheu 35 studied the zero‐state performance of the DGWMA scheme, where it is shown that it is preferred for small downward shifts over the GWMA scheme with time‐varying limits or FIR feature. The corresponding steady‐state performance is discussed in Chiu and Lu, 72 where it is shown that it is preferred for downward shifts, while the GWMA scheme is more competitive for upward shifts.…”

Some theoretical comments regarding the run-length properties of the synthetic and runs-rules X¯ monitoring schemes – part 1: zero-state

“…It seems that only one mode is selected upfront and investigated. For example, the zero-state mode of the Poisson GWMA chart is investigated in Chiu and Sheu (2008), whereas the steady-state mode is only investigated seven years later in Chiu and Lu (2015). And it is a continuing trend where authors have a publication on one mode and, only later, publish the results on the other mode.…”