EWMA Charts for the Weibull Shape Parameter

Pascual, Francis G.

doi:10.1080/00224065.2010.11917836

Cited by 53 publications

(39 citation statements)

References 17 publications

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“…Among the monitoring schemes for Weibull processes proposed in literature, Pascual (2010), Pascual andNguyen (2011), Pascual andZhang (2011) and Pascual and Li (2012) proposed some control charts to check for the stability of the Weibull shape parameter . β Table 3.…”

Section: Stability Check Of the Shape Parametermentioning

confidence: 99%

A Semi‐empirical Bayesian Chart to Monitor Weibull Percentiles

Erto

Pallotta

Mastrangelo

2014

Scandinavian J Statistics

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This paper develops a Bayesian control chart for the percentiles of the Weibull distribution, when both its in-control and out-of-control parameters are unknown. The Bayesian approach enhances parameter estimates for small sample sizes that occur when monitoring rare events as in high-reliability applications or genetic mutations. The chart monitors the parameters of the Weibull distribution directly, instead of transforming the data as most Weibull-based charts do in order to comply with their normality assumption. The chart uses the whole accumulated knowledge resulting from the likelihood of the current sample combined with the information given by both the initial prior knowledge and all the past samples. The chart is adapting since its control limits change (e.g. narrow) during the Phase I. An example is presented and good Average Run Length properties are demonstrated. In addition, the paper gives insights into the nature of monitoring Weibull processes by highlighting the relationship between distribution and process parameters.

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Section: Stability Check Of the Shape Parametermentioning

confidence: 99%

A Semi‐empirical Bayesian Chart to Monitor Weibull Percentiles

Erto

Pallotta

Mastrangelo

2014

Scandinavian J Statistics

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“…For instance, Pascual [12] proposed EWMA control charts for monitoring the Weibull shape parameter. These charts are based on the sample range of the logarithms of the Weibull data and an unbiased estimator of 1/β.…”

Section: Related Workmentioning

confidence: 99%

Moving range EWMA control charts for monitoring the Weibull shape parameter

Akhundjanov

Pascual

2014

Journal of Statistical Computation and Simulation

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In this article, we propose an exponentially weighted moving average (EWMA) control chart for the shape parameter β of Weibull processes. The chart is based on a moving range when a single measurement is taken per sampling period. We consider both one-sided (lower-sided and upper-sided) and two-sided control charts. We perform simulations to estimate control limits that achieve a specified average run length (ARL) when the process is in control. The control limits we derive are ARL unbiased in that they result in ARL that is shorter than the stable-process ARL when β has shifted. We also perform simulations to determine Phase I sample size requirements if control limits are based on an estimate of β. We compare the ARL performance of the proposed chart to that of the moving range chart proposed in the literature.

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“…Chen and Cheng investigated the effect of non‐normality on the control limits of the

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chart. Pascual presented the EWMA control chart for monitoring the Weibull shape parameter. Pascual and Zhang proposed the MR control chart by taking the natural logarithm of the Weibull distribution and then setting control limits based on the range value of random samples from the resulting smallest extreme population for monitoring the Weibull shape parameter.…”

Section: Introductionmentioning

confidence: 99%

MaxEWMA Control Chart for a Weibull Process with Individual Measurements

Wang

2016

Qual. Reliab. Engng. Int.

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To monitor a Weibull process with individual measurements, some methods such as power transformation, inverse erf function, and Box-Cox transformation have been used to transform the Weibull data to a normal distribution. In this study, we conduct a simulation study to compare their performances in terms of the bias and mean square errors. A practical guide is recommended. Additionally, we present the maximum exponentially weighted moving average chart based on the transformation method to monitor a Weibull process with individual measurements. We compare the average run lengths of the proposed chart and the combined individual and moving range charts under the three cases including mean changes, sigma changes, and both mean and sigma changes. It is shown that the proposed control chart outperforms the combined individual and moving range charts for all three cases. Moreover, two examples are used to illustrate the applicability of the proposed control chart.

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EWMA Charts for the Weibull Shape Parameter

Cited by 53 publications

References 17 publications

A Semi‐empirical Bayesian Chart to Monitor Weibull Percentiles

A Semi‐empirical Bayesian Chart to Monitor Weibull Percentiles

Moving range EWMA control charts for monitoring the Weibull shape parameter

MaxEWMA Control Chart for a Weibull Process with Individual Measurements

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