Tables for Obtaining Weibull Confidence Bounds and Tolerance Bounds Based on Best Linear Invariant Estimates of Parameters of the Extreme-Value Distribution

Mann, Nancy R.; Fertig, Kenneth W.

doi:10.1080/00401706.1973.10489013

Cited by 89 publications

(21 citation statements)

References 14 publications

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“…An Example and Numerical Study 3.1. An Example Mann and Fertig (1973) gave failure times of airplane components taken during the early development of the F-100 fighter aircraft. The data represent failure times in hours of components aboard the aircraft.…”

Section: The Sampling Plansmentioning

confidence: 99%

Bayesian sampling plans with interval censoring

Tsai

2015

2015 IEEE International Conference on Industrial Engineering and Engineering Management (IEEM)

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AbstractsThis paper employs Bayesian approach to establish acceptance sampling plans for life tests with interval censoring. Assume that interval data have a multinomial distribution, and the interval probabilities are random and vary from lot to lot according to a conjugate prior of Dirichlet distribution. A Bayes risk is defined with a suitable loss function and a predictive distribution. Optimal Bayesian sampling plans are determined by minimizing the Bayes risk per lot. An example is used and some optimal Bayesian sampling plans with three equally-spaced intervals are tabulated for illustration. Sensitivity analysis are conducted to evaluate the influence of the parameter of prior distribution, the cost per sampled item and the cost per used unit time on the proposed Bayesian sampling plans.Keywords: reliability, Dirichlet distribution, life test plan, loss function IntroductionAcceptance sampling is one aspect of quality assurance in the applications of quality control. When quality characteristic is the lifetime of item, acceptance sampling plans are developed for lifetime data. Due to saving test time and cost, engineers would like to infer life information of components based on incomplete data through censoring tests, for instance type I censoring test, type II censoring test or hybrid censoring test. Among these censoring tests, type I censoring test is popular in practice because the termination time is known in advance. However, practitioners might only count the failure numbers at some fixed times and did not measure the exact lifetimes during a censoring test for the purpose of administrative convenience. We call such a censoring test as interval censoring test and the collected failure numbers are the interval censoring data or the grouped data.In practice, an interval censoring test is easier to operate than conducting a type I censoring test, but the interval censoring data contain less information than that contained in type I censoring data. Some acceptance sampling plans have been developed with interval censoring data, see, for example, Ehrenfeld (1962), Kendell and Anderson (1971), Seo and Yum (1993), Chen and Mi (1998), Lu and Tsai (2009a, Tsai (2009b), andLin (2010).In acceptance sampling studies, many acceptance sampling schemes have been investigated in the literatures. Among these, the decision theory approach is particularly attractive, more precise and scientific to develop sampling plans based on the economic consideration. The Bayesian methods arise naturally when prior information is available for planning and estimation.

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Section: The Sampling Plansmentioning

confidence: 99%

Bayesian sampling plans with interval censoring

Tsai

2015

2015 IEEE International Conference on Industrial Engineering and Engineering Management (IEEM)

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“…In this section, we will consider a real data set given by Mann and Fertig [28]. This data set is also studied by Prakash and Singh [29] from a Bayesian perspective.…”

Section: Illustrative Examplementioning

confidence: 99%

Statistical inference for the burr type III distribution under type II censored data

ÇANKAYA¹

2017

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

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Abstract. In this study, estimation and prediction problems for the Burr type III distribution under type II censored data are considered. Maximum likelihood and maximum product spacing estimation methods are used to estimate model parameters. EM algorithm is employed to obtain maximum likelihood estimates. Unobserved future order statistics are predicted with best unbiased prediction method. A simulation study is carried out to exhibit performance of the estimation methods. Further, a numerical example is presented to illustrate the usefulness of the Burr III distribution.

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“…The censoring time was set at c = α(− log p) 1/β Figure 2. Relative quantile discrepancies plot, H 0 : β = 1, type II censoring, (n, r) = (20,15 Table 6 show that the usual likelihood ratio test has reliable small sample behavior, with little room left for improvement. The adjusted tests display slightly superior behavior.…”

Section: Type I Censored Datamentioning

confidence: 99%

Adjusted profile likelihoods for the weibull shape parameter

Ferrari

Silva

Cribari‐Neto

2007

Journal of Statistical Computation and Simulation

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Abstract. This paper presents several different adjusted profile likelihoods for the Weibull shape parameter. These adjustments aim at reducing the impact of the nuisance parameter on the likelihood-based inference regarding the parameter of interest. Both point estimation and hypothesis testing are considered. We also show that the ratio between the estimators and the shape parameter are pivotal quantities and that the size properties of the usual and adjusted profile likelihood ratio tests depend neither on the scale parameter nor on the value of the shape parameter set at the null hypothesis. The numerical results suggest that the adjustment obtained by Yang and Xie (2003) outperforms not only the profile likelihood inference but also inference based on competing adjusted profile likelihoods.

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Tables for Obtaining Weibull Confidence Bounds and Tolerance Bounds Based on Best Linear Invariant Estimates of Parameters of the Extreme-Value Distribution

Cited by 89 publications

References 14 publications

Bayesian sampling plans with interval censoring

Bayesian sampling plans with interval censoring

Statistical inference for the burr type III distribution under type II censored data

Adjusted profile likelihoods for the weibull shape parameter

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