Analysis of Burr Type-XII Distribution Under Step Stress Partially Accelerated Life Tests with Type-I and Adaptive Type-II Progressively Hybrid Censoring Schemes

Nassar, Mazen; Nassr, Said G.; Dey, Sanku

doi:10.1007/s40745-017-0101-8

Cited by 17 publications

(9 citation statements)

References 29 publications

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“…The MLEs and Bayesian estimators and credible intervals of the Weibull parameters were obtained to analyze the competing risks model in the PALTs under progressively type-I hybrid censoring [18]. Nassar et al [19] analyzed performances of the estimators in the SS-PALTs under type-I and type-II progressive hybrid censoring. Soloman et al [20] concentrated on the estimation of inverse Weibull parameters under progressive type-II censoring.…”

Section: Related Workmentioning

confidence: 99%

Planning of Partially Accelerated Degradation Test with Two Stress Variables for Practical Lifetime Estimation

et al. 2018

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The reliability information for novel products and specimens available for various tests is limited during the development stage. In many real cases, the results of general tests under use and the maximum stress levels for checking performance and design are not utilized to obtain reliability information. To solve these problems, this paper proposes a practical partially accelerated degradation test (PADT) plans with two stress variables using a two-phase strategy. In addition, a sample scenario is introduced to demonstrate the feasibility of the proposed procedure. In the first phase, the ratios of the specimens used and the maximum stress levels for each variable are determined to estimate the parameters of an accelerated model based on the D-optimality criteria. To estimate the lifetime information and check the curvature effects of the accelerated model, practical PADT plans are developed in the second phase with three stress levels for each variable, which are based on the compromise concept. In this phase, the ratios for all test points and the middle-stress levels for two variables are determined. This information is used to minimize the asymptotic variance of the maximum likelihood estimator for the q-th quantile of the lifetime distribution under the use conditions. Thus, more accurate lifetime information and model validity can be obtained when using practical PADT plans. Finally, the statistical efficiency of the proposed test plan is demonstrated in a sample scenario.

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Section: Related Workmentioning

confidence: 99%

Planning of Partially Accelerated Degradation Test with Two Stress Variables for Practical Lifetime Estimation

et al. 2018

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“…The acceleration model is then used to extrapolate the reliability performance to the normal use conditions. Where these different types of methods met a lot of researchers and for more details, you can look at the researches [4][5][6][7][8][9][10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Analysis Simple Step Stress Model under Competing Extension Weibull Failure Distribution Based on Progressive Type-II Censoring

Abdelfattah¹,

El-Sherpieny²,

Khalil³

2023

MMEP

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Accelerated life testing (ALT), a procedure utilized in reliability analysis, allows testing units to be subject to increasingly elevated grades of stress during an experiment.Stepstress tests are a subclass of accelerated tests in which the stress levels rise consecutively at prearranged cycles, consequently, the researcher might find out results more swiftly than in ordinary working settings about the parameter of the lifetime distribution. Moreover, there are frequently multiple fatal causes for a test element's failure, for instance, technical or electric. These causes are recognized as "competing risks". The purpose of the analysis is to assess simple step stress accelerated life testing (SS-ALT) with competing Risks originating from the extension of Weibull distribution by applying a progressive Type-II censoring scheme. In this case, under the assumption of a cumulative exposure model, the authors successfully obtained the Bayes estimates (BEs) and maximum likelihood estimators (MLEs) of the undetermined average parameters of the various causes. For Bayesian computations, the squared error loss functions are considered. Additionally, the estimators' asymptotic variance-covariance matrix was created. Additionally, credible intervals and asymptotic confidence intervals (CIs) are provided. For a large sample size, the CIs of the unidentified parameters are developed. A numerical study is also involved to exhibit the accuracy and variability of various estimators for several sample sizes. An example is being used to exemplify the inference method that's also considered here. This study concludes that the mean lengths of credible intervals and asymptotic confidence intervals get shorter as the number of failures rises. The credible interval technique is suggested, nevertheless.

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“…Assuming the TRV model, Zhang et al [17] discussed the MLEs of the unknown parameters for the extended Weibull distribution. Ismail et al [18,19] investigated the MLEs of the parameters of the Weibull and Burr Type-XII distributions, respectively, and compared the results based on two different PrHC schemes. Mahmoud et al [20][21][22] deals with SSPALT based on an adaptive type PrHC scheme to obtain estimates of parameters using MLEs and Bayesian estimates (BEs) of generalized Pareto, two-parameter exponentiated Weibull and Lindley distributions, respectively.…”

Section: Introductionmentioning

confidence: 99%

Parameter Estimation Based on Censored Data under Partially Accelerated Life Testing for Hybrid Systems due to Unknown Failure Causes

Kamal¹

2022

Computer Modeling in Engineering &Amp; Sciences

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In general, simple subsystems like series or parallel are integrated to produce a complex hybrid system. The reliability of a system is determined by the reliability of its constituent components. It is often extremely difficult or impossible to get specific information about the component that caused the system to fail. Unknown failure causes are instances in which the actual cause of system failure is unknown. On the other side, thanks to current advanced technology based on computers, automation, and simulation, products have become incredibly dependable and trustworthy, and as a result, obtaining failure data for testing such exceptionally reliable items have become a very costly and time-consuming procedure. Therefore, because of its capacity to produce rapid and adequate failure data in a short period of time, accelerated life testing (ALT) is the most utilized approach in the field of product reliability and life testing. Based on progressively hybrid censored (PrHC) data from a three-component parallel series hybrid system that failed to owe to unknown causes, this paper investigates a challenging problem of parameter estimation and reliability assessment under a step stress partially accelerated life-test (SSPALT). Failures of components are considered to follow a power linear hazard rate (PLHR), which can be used when the failure rate displays linear, decreasing, increasing or bathtub failure patterns. The Tempered random variable (TRV) model is considered to reflect the effect of the high stress level used to induce early failure data. The maximum likelihood estimation (MLE) approach is used to estimate the parameters of the PLHR distribution and the acceleration factor. A variance covariance matrix (VCM) is then obtained to construct the approximate confidence intervals (ACIs). In addition, studentized bootstrap confidence intervals (ST-B CIs) are also constructed and compared with ACIs in terms of their respective interval lengths (ILs). Moreover, a simulation study is conducted to demonstrate the performance of the estimation procedures and the methodology discussed in this paper. Finally, real failure data from the air conditioning systems of an airplane is used to illustrate further the performance of the suggested estimation technique.

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Analysis of Burr Type-XII Distribution Under Step Stress Partially Accelerated Life Tests with Type-I and Adaptive Type-II Progressively Hybrid Censoring Schemes

Cited by 17 publications

References 29 publications

Planning of Partially Accelerated Degradation Test with Two Stress Variables for Practical Lifetime Estimation

Planning of Partially Accelerated Degradation Test with Two Stress Variables for Practical Lifetime Estimation

Analysis Simple Step Stress Model under Competing Extension Weibull Failure Distribution Based on Progressive Type-II Censoring

Parameter Estimation Based on Censored Data under Partially Accelerated Life Testing for Hybrid Systems due to Unknown Failure Causes

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