Conditional Control Charts for Monitoring the Weibull Shape Parameter under Progressively Type II Censored Data

Haghighi, Firoozeh; Castagliola, Philippe

doi:10.1002/qre.1659

Cited by 8 publications

(3 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Pascual and Li [43], Guo and Wang [19] and Chan et al [10] developed different methods for monitoring the Weibull shape parameter when available samples are type II censored. Haghighi and Castagliola [20] proposed the monitoring of the Weibull shape parameter under progressively type II censored data. Haghighi et al [21] proposed the monitoring of Weibull quantiles under type II censoring.…”

Section: Monitoring Lifetimesmentioning

confidence: 99%

Monitoring the parameter vector of regression models with time-to-event response in phase II processes

Panza

Vargas

2017

Journal of Statistical Computation and Simulation

View full text Add to dashboard Cite

Palabras clave: Censuramiento, distribución de valor extremo, distribución Weibull, modelo de regresión, monitoreo de perfiles, razón de verosimilitudes, tiempos de vida. Abbreviations and conventions In the following table, there are listed some abbreviations and conventions used throughout this document. Short expression Extended expression ARL Average run length ARL 0 In-control average run length ARL 1 Out-of-control average run length CL Central line CU SU M Cumulative sum EV RM Extreme value regression model (or models) EW M A Exponentially weighted moving average GLM Generalized linear model LRT Likelihood ratio test LCL Lower control limit M EW M A Multivariate exponentially weighted moving average M LE Maximum likelihood estimator pdf Probability density function SP C Statistical process control U CL Upper control limit W RM Weibull regression model (or models) EV (a; b) The extreme value distribution with parameter vector (a; b) EV (0; 1) The standardized extreme value distribution N (a; b) The normal distribution with parameter vector (a; b) N (0; 1) The standard normal distribution W (a; b) The Weibull distribution with parameter vector (a; b) χ 2 p The chi-square distributions with p degrees of freedom X ∼ D(A) The random variable X follows a known distribution D with parameter vector A Aknowledgements The author expresses his gratitude to all those who have contributed to the development and successful completion of this work. The author would especially like to thank: • Professor J.A.Vargas, advisor of the thesis, for giving the opportunity to work in Staistical Quality Control, • The members of the jury evaluating this work for their comments and contributions that greatly enriched the final version of the thesis manuscript, • The reviewers of the articles and communications in specialized events that are products of this research work, • The executive staff of the Department of Statistics, professors in charge of doctoral courses and activities, coworkers and classmates for the support provided, • Mother and sisters.

show abstract

Section: Monitoring Lifetimesmentioning

confidence: 99%

Monitoring the parameter vector of regression models with time-to-event response in phase II processes

Panza

Vargas

2017

Journal of Statistical Computation and Simulation

View full text Add to dashboard Cite

show abstract

“…For a Weibull process under Type‐II censoring, Pascual and Li, Guo and Wang, and Chan et al proposed different methods for monitoring the Weibull shape parameter. Haghighi and Castagliola presented conditional control charts for monitoring Weibull shape parameter under progressively Type II censoring. Huang and Pascual presented 2 control schemes including 1‐of‐1 and 2‐of‐2 runs rules for monitoring the Weibull percentiles with known shape parameter when data are censored at the first observation.…”

Section: Introductionmentioning

confidence: 99%

New control charts for monitoring the Weibull percentiles under complete data and Type‐II censoring

Wang

Bizuneh

Cheng

2017

Quality & Reliability Eng

View full text Add to dashboard Cite

In this paper, we propose 3 new control charts for monitoring the lower Weibull percentiles under complete data and Type‐II censoring. In transforming the Weibull distribution to the smallest extreme value distribution, Pascaul et al (2017) presented an exponentially weighted moving average (EWMA) control chart, hereafter referred to as EWMA‐SEV‐Q, based on a pivotal quantity conditioned on ancillary statistics. We extended their concept to construct a cumulative sum (CUSUM) control chart denoted by CUSUM‐SEV‐Q. We provide more insights of the statistical properties of the monitoring statistic. Additionally, in transforming a Weibull distribution to a standard normal distribution, we propose EWMA and CUSUM control charts, denoted as EWMA‐YP and CUSUM‐YP, respectively, based on a pivotal quantity for monitoring the Weibull percentiles with complete data. With complete data, the EWMA‐YP and CUSUM‐YP control charts perform better than the EWMA‐SEV‐Q and CUSUM‐SEV‐Q control charts in terms of average run length. In Type‐II censoring, the EWMA‐SEV‐Q chart is slightly better than the CUSUM‐SEV‐Q chart in terms of average run length. Two numerical examples are used to illustrate the applications of the proposed control charts.

show abstract

“…With transforming the Weibull data to an exponential distribution, Guo and Wang 14 developed the one-sided and two-sided control charts based on a new monitoring statistic for type 2 censored data. Haghighi and Castagliola 15 generalized the control charts proposed by Guo and Wang 14 for the progressively type 2 censored data.…”

Section: Introductionmentioning

confidence: 99%

An exponentially weighted moving average chart based on likelihood‐ratio test for monitoring Weibull mean and variance with subgroups

Wang

Cheng

2017

Quality & Reliability Eng

View full text Add to dashboard Cite

Monitoring changes in the Weibull mean and variance simultaneously is of interest in quality control. The mean and variance of a Weibull process are determined by its shape and scale parameters. Most studies are focused on monitoring the Weibull scale parameter with fixed shape parameter or the Weibull shape parameter with fixed scale parameter. In this paper, we propose an exponentially weighted moving average chart based on the likelihood‐ratio test and an inverse error function called ELR chart to monitor changes in the Weibull mean and variance simultaneously. The simulation approach is used to derive the average run length. We compare our proposed chart with other existing control charts for 3 cases, including scale parameter changes with fixed shape parameter, shape parameter changes with fixed scale parameter, and both parameters changes. The results show that the ELR chart outperforms the other control charts in terms of average run length in most cases. Two numerical examples are used to illustrate the applications of the proposed control chart.

show abstract

Conditional Control Charts for Monitoring the Weibull Shape Parameter under Progressively Type II Censored Data

Abstract: International audienc

Cited by 8 publications

References 20 publications

Monitoring the parameter vector of regression models with time-to-event response in phase II processes

Monitoring the parameter vector of regression models with time-to-event response in phase II processes

New control charts for monitoring the Weibull percentiles under complete data and Type‐II censoring

An exponentially weighted moving average chart based on likelihood‐ratio test for monitoring Weibull mean and variance with subgroups

Contact Info

Product

Resources

About