Theory for Optimum Accelerated Censored Life Tests for Weibull and Extreme Value Distributions

Nelson, Wayne; Meeker, William Q.

doi:10.1080/00401706.1978.10489643

Cited by 120 publications

(24 citation statements)

References 11 publications

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“…This dataset was presented in [11] on insulating fluids and it is related an accelerated test performed in order to determine the relationship between time (in minutes) to breakdown and voltage (in kilovolts). The authors assumed a regression structure based on the Weibull model and a common censoring time at L = 200 (type I censoring), i.e., time i ∼WEI(θ i , σ), where log θ i = X i β, i = 1, .…”

Section: Insulating Fluids Datasetmentioning

confidence: 99%

Skewness of Maximum Likelihood Estimators in the Weibull Censored Data

2019

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In this paper, we obtain a matrix formula of order n − 1 / 2 , where n is the sample size, for the skewness coefficient of the distribution of the maximum likelihood estimators in the Weibull censored data. The present result is a nice approach to verify if the assumption of the normality of the regression parameter distribution is satisfied. Also, the expression derived is simple, as one only has to define a few matrices. We conduct an extensive Monte Carlo study to illustrate the behavior of the skewness coefficient and we apply it in two real datasets.

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Section: Insulating Fluids Datasetmentioning

confidence: 99%

Skewness of Maximum Likelihood Estimators in the Weibull Censored Data

2019

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“…1. Note that, censored data (such as right censoring and interval censoring) are often encountered in ALT [36,37]. In this paper, we assume that all the specimens are tested until failure.…”

Section: Whenmentioning

confidence: 99%

Design of validation experiments for life prediction models

Mahadevan

2017

Reliability Engineering & System Safety

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This paper proposes a novel validation experiment design optimization (VEDO) method for the assurance of life prediction model, which is one of the key steps in guaranteeing the reliable design of products in meeting the target service life. Life testing data collected from experiments are important for the validation of time-dependent models. However, directly collecting life data for model validation at the operating stress level is usually time-consuming and expensive. In order to overcome this challenge, the accelerated life testing (ALT) method is employed in the proposed method to collect data for model validation. The connection between ALT and model validation is established first; then a VEDO model is developed using the prior information obtained from the computer simulation model. In the VEDO model, the information gain for model validation is maximized within the testing budget and available testing chamber constraints. The obtained optimal number of tests and testing stress levels are designed to maximize the confidence in the validation results. Various sources of uncertainty such as prediction uncertainty, uncertainty of prior information, and observation errors are included within the optimization process in order to improve the robustness of validation experiment design. A composite helicopter rotor hub component is used to demonstrate the effectiveness of the proposed VEDO method.

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“…Chernoff (1962) considers optimum plans for an exponential distribution data at design stress level. Nelson and Meeker (1978) provide optimum test plans to estimate percentiles of Weibull and smallest extreme-value distribution at a design stress. Nelson (1990) provides a number of guidelines for planning ALTs.…”

Section: Introductionmentioning

confidence: 99%

Design of Optimum Simple Step-Stress Accelerated Life Testing Plans

Elsayed

Zhang

2007

Recent Advances in Stochastic Operations Research

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Accelerated life testing (ALT) is widely conducted to obtain failure-time data in a much shorter time and to make inference about reliability at normal conditions. The accuracy of the reliability prediction is dependent on well-designed ALT plans. A stepstress ALT allows the test condition to change at a given time or upon the occurrence of a specified number of failures. In this paper, we propose a procedure to determine the parameters of the optimum simple step-stress testing plan so that the reliability prediction at normal conditions is accurately determined. We investigate efficient procedures to estimate most, if not all, of the ALT parameters under different operating conditions. The objective function is formulated as a nonlinear programming problem. The resultant optimum plan is demonstrated through numerical example and sensitivity analysis.

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Theory for Optimum Accelerated Censored Life Tests for Weibull and Extreme Value Distributions

Cited by 120 publications

References 11 publications

Skewness of Maximum Likelihood Estimators in the Weibull Censored Data

Skewness of Maximum Likelihood Estimators in the Weibull Censored Data

Design of validation experiments for life prediction models

Design of Optimum Simple Step-Stress Accelerated Life Testing Plans

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