Control Charts For Monitoring The Weibull Shape Parameter Based On Type‐II Censored Sample

Guo, Baining; Wang, Bingxing

doi:10.1002/qre.1473

Cited by 59 publications

(59 citation statements)

References 27 publications

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“…Analogous results for type II censored data with n = 5 and r = 4 are given in 20. Note that we indicate values of 1/ρ because the authors of 12 defined their ρ as the reciprocal of ours and to show that our results for the range and T(β S ) charts are similar to those in 12 . We have the following observations:…”

Section: Comparisons With Other Chartssupporting

confidence: 85%

“…12 On the basis of the results obtained, the range based is not recommended for relatively larger sample sizes because its ARL tend to me longer than those of theσ and T(β S ) charts. The proposed scheme 1σ chart performs as well as the T(β S ) chart, but interpretation of OOC signals is simpler and more direct with theσ chart simply because an unbiased estimator of the parameter of interest σ = 1/β is used as the monitoring statistic.…”

Section: Discussionmentioning

confidence: 97%

“…We also demonstrate that the proposed methods are at least as good and have simpler and more direct interpretations than the method in. 12 …”

Section: Introductionmentioning

confidence: 97%

See 2 more Smart Citations

Monitoring the Weibull Shape Parameter with Type II Censored Data

Chan

Han

Pascual

2014

Qual. Reliab. Engng. Int.

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In this article, we introduce a method for monitoring the Weibull shape parameter β with type II (failure) censored data. The control limits depend on the sample size, the number of censored observations, the target average run length, and the stable value of β. The method assumes that the scale parameter α is constant during each sampling period, which is true under rational subgrouping. The proposed method utilizes the relationship between Weibull and smallest extreme value distribution. We propose an unbiased estimator of σ = 1/β as the monitoring statistic. We derive the control limits for one-sided and two-sided charts for several stable process average run lengths. We discuss two schemes, namely, the control-limits-only scheme and the control-limits-with-warning-lines scheme. The stable process average run length performance of the proposed charts is studied and compared with those of other charts for monitoring β under similar assumptions.

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Section: Comparisons With Other Chartssupporting

confidence: 85%

Section: Discussionmentioning

confidence: 97%

See 1 more Smart Citation

Monitoring the Weibull Shape Parameter with Type II Censored Data

Chan

Han

Pascual

2014

Qual. Reliab. Engng. Int.

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“…Recently, Aslam and Jun introduced a truncated life test scheme in the area of control charts for the Weibull distribution and Pareto distribution of second kind distribution. More details about the control charts for the Weibull processes when data are type II censored can be seen in other studies …”

Section: Introductionmentioning

confidence: 99%

A new variable control chart under failure‐censored reliability tests for Weibull distribution

Khan

Aslam

Raza

2018

Quality & Reliability Eng

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In this paper, we propose a new variable control chart under type II or failure‐censored reliability tests by assuming that the lifetime of a part follows the Weibull distribution with fixed and stable shape parameter. The purpose is to monitor the mean and the variance of a Weibull process. In fact, the mean and the variance are related to the scale parameter. The necessary measures are given to calculate the average run length (ARL) for in‐control and shifted processes. The tables of ARLs are presented for various shift constants and specified parameters. A simulation study is given to show the performance of the proposed control chart. The efficiency of the proposed control chart is compared with a control chart based on the conditional expected value under type II censoring. An example is also given for the illustration purpose.

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“…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.…”

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

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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.

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Control Charts For Monitoring The Weibull Shape Parameter Based On Type‐II Censored Sample

Cited by 59 publications

References 27 publications

Monitoring the Weibull Shape Parameter with Type II Censored Data

Monitoring the Weibull Shape Parameter with Type II Censored Data

A new variable control chart under failure‐censored reliability tests for Weibull distribution

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

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