Using CUSUM Control Schemes for Monitoring Quality Levels in Compound Poisson Production Environment: The Geometric Poisson Process

Chen, Ching-Wen; Randolph, Paul H.; Liou, Tong‐Miin

doi:10.1081/qen-200056448

Cited by 9 publications

(7 citation statements)

References 19 publications

(18 reference statements)

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“…The method-of-moments estimators are generally used to estimate λ 0 and ρ 0 from phase-I samples. We have the method-of-moment estimates (see Chen et al, 2005).…”

Section: The Geometric-poisson Ewma Chart When Parameters Are Unknownmentioning

confidence: 99%

“…According to Chen (2012), the density function of the geometric-Poisson compound distribution with parameters λ (rate) and ρ (dispersion) for any t > 0 is where λ > 0, 0 < ρ < 1. The expected value and variance of total defects in a fixed unit t = 1, are derived by Chen et al (2005) (1− ) 2 , respectively. Clearly, the variance of the geometric-Poisson distribution is greater than or equal to the mean.…”

Section: The Geometric-poisson Ewma Chart With Known Parametersmentioning

confidence: 99%

“…Chen, Randolph, and Liou (2005) developed CUSUM control charts based on the geometric-Poisson compound distribution. Chen (2012) proposed an exponentially weighted moving average (EWMA) control chart for monitoring the number of defects over time.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The properties of the geometric-Poisson exponentially weighted moving control chart with estimated parameters

2015

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The geometric-Poisson exponentially weighted moving average (EWMA) chart has been shown to be more effective than the Poisson EWMA chart in monitoring the number of defects in the production processes. In these applications, it is assumed that the process parameters are known or have been accurately estimated. However, in practice, the process parameters are rarely known and must be estimated from reference sample to construct the geometric-Poisson EWMA chart. The performance of the given chart, due to variability in the parameter estimation, might differ from known parameters' case. This article explored the effect of estimated parameters on the conditional and marginal performance of the geometric-Poisson EWMA chart. The run length characteristics are calculated using a Markov chain approach and the effect of estimation on the performance of the given chart is shown to be significant. Recommendations about the proposer choice of sample size, smoothing constant, and dispersion parameter are made. Results of this study highlight the practical implications of estimation error, and to offer advice to practitioners when constructing/analyzing a phase-I sample.

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“…The method-of-moments estimators are generally used to estimate λ 0 and ρ 0 from phase-I samples. We have the method-of-moment estimates (see Chen et al, 2005).…”

Section: The Geometric-poisson Ewma Chart When Parameters Are Unknownmentioning

confidence: 99%

Section: The Geometric-poisson Ewma Chart With Known Parametersmentioning

confidence: 99%

See 1 more Smart Citation

The properties of the geometric-Poisson exponentially weighted moving control chart with estimated parameters

2015

Self Cite

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“…Jiang et al developed a weighted CUSUM chart to monitor inhomogeneous Poisson processes and detect a range of shifts when the sample size is not constant over time. This control chart can be applied to different distributions as in the study performed by Chen et al …”

Section: Introductionmentioning

confidence: 99%

“…Jiang et al 9 developed a weighted CUSUM chart to monitor inhomogeneous Poisson processes and detect a range of shifts when the sample size is not constant over time. This control chart can be applied to different distributions as in the study performed by Chen et al 10 Borror et al 11 introduced an exponentially weighted moving average (EWMA) chart that considered a weighted average of past information in the case of Poisson data. They evaluated used Markov chain approximation; it outperformed the c-chart.…”

Section: Introductionmentioning

confidence: 99%

Attribute Control Charts with Optimal Limits

Ahangar

Chimka

2015

Qual. Reliab. Engng. Int.

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A new attribute control chart is presented to monitor processes that generate count data. The economic objective of the chart is to minimize the total cost of its errors, a linear function of errors Type I and II. The proposed chart can be applied to Poisson, geometric, and negative binomial assumptions. Control limits are calculated optimally, because they are based on exact probability distributions and used to detect defined directional shifts in a process. Some numerical results are provided, and expected costs of the new chart are compared with those of a one-sided c-chart. Other effects such as changing the cost structure are shown graphically.

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