Optimum Multi-Objective Ramp-Stress Accelerated Life Test with Stress Upper Bound for Burr Type-XII Distribution

Srivastava, Preeti Wanti; Mittal, Neha

doi:10.1109/tr.2012.2221011

Cited by 15 publications

(9 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Under the progressive type II censoring, Abdel-Hamid [21] studied the maximum likelihood estimation method and provided a Fisher information matrix to implement reliability inferences for BurrXII distributions under the constant-partially accelerated life testing. Srivastava and Mittal [22] proposed optimal designs for BurrXII distributions through using a multi-objective ramp-stress ALT method. Zhao et al [23] proposed a simple constant-stress ALT to collect type I progressively hybrid censored samples from BurrXII distribution and obtained the maximum likelihood estimators of the model parameters via using numerical methods.…”

Section: Historical Review and Literature Reviewmentioning

confidence: 99%

Accelerated Life Test Method for the Doubly Truncated Burr Type XII Distribution

et al. 2020

View full text Add to dashboard Cite

The Burr type XII (BurrXII) distribution is very flexible for modeling and has earned much attention in the past few decades. In this study, the maximum likelihood estimation method and two Bayesian estimation procedures are investigated based on constant-stress accelerated life test (ALT) samples, which are obtained from the doubly truncated three-parameter BurrXII distribution. Because computational difficulty occurs for maximum likelihood estimation method, two Bayesian procedures are suggested to estimate model parameters and lifetime quantiles under the normal use condition. A Markov Chain Monte Carlo approach using the Metropolis–Hastings algorithm via Gibbs sampling is built to obtain Bayes estimators of the model parameters and to construct credible intervals. The proposed Bayesian estimation procedures are simple for practical use, and the obtained Bayes estimates are reliable for evaluating the reliability of lifetime products based on ALT samples. Monte Carlo simulations were conducted to evaluate the performance of these two Bayesian estimation procedures. Simulation results show that the second Bayesian estimation procedure outperforms the first Bayesian estimation procedure in terms of bias and mean squared error when users do not have sufficient knowledge to set up hyperparameters in the prior distributions. Finally, a numerical example about oil-well pumps is used for illustration.

show abstract

Section: Historical Review and Literature Reviewmentioning

confidence: 99%

Accelerated Life Test Method for the Doubly Truncated Burr Type XII Distribution

et al. 2020

View full text Add to dashboard Cite

show abstract

“…Zhu and Elsayed [12] developed an optimal model for exponential distribution with time censored and progressive stress based on the cumulative exposure model. Srivastava and Mittal [13] developed the model of the optimum multi-objective PSALT with a stress upper bound for a Burr type-XII distribution under time censoring. These studies have demonstrated that the design of the optimum test plan can contribute to improving the life estimation accuracy, but the improvement degree is not obvious.…”

Section: Introductionmentioning

confidence: 99%

Novel Accelerating Life Test Method and Its Application by Combining Constant Stress and Progressive Stress

Chen

Yang

Qian

et al. 2018

Chin. J. Mech. Eng.

View full text Add to dashboard Cite

Constant stress accelerated life tests (ALTs) can be applied to obtain a high estimation accuracy of reliability measurements, but these are time-consuming tests. Progressive stress ALTs can yield failures more quickly but cannot guarantee the estimation accuracy of reliability measurements. In this paper, a progressive-constant combination stress ALT is proposed to combine the merits of both tests. The optimal plan, in which the design variables are the initial progressive stress level, the progressive stress ramp rate, the sample allocation proportion of the progressive stress and the constant stress level, is determined using the principle of minimizing the asymptotic variance of the maximum likelihood estimator of the natural log reliable life for the connectors. A comparison between the optimal PCCSALT plan and the CSALT plan with the same sample size and estimation accuracy shows that the test time is reduced by 13.59% by applying the PCCSALT.

show abstract

“…Since then, the BTXII distribution has received considerable attention in reliability studies and failure time modeling due to its flexibility in shape. Various aspects and properties of the BTXII distribution with regard to other applications have been studied by many authors, including AL-Hussaini and Ali Mousa [18], Wingo [19], [20], Wang and Keats [21], Moore and Papadopoulos [22], Chen and Yeh [23], Tsai and Chiang [24], Lio et al [25], Lio and Tsai [26], Panahi and Sayyareh [27], and Srivastava and Mittal [28]. Connections of the BTXII distribution with various other distributions have been studied by Tadikamalla [29].…”

Section: Introductionmentioning

confidence: 99%

“…Tadikamalla [29] mentioned that the BTXII distribution can be used to fit almost any given unimodal data because it contains two shape parameters. Srivastava and Mittal [28] proposed optimal planning methods for the multi-objective ramp-stress accelerated life test for the BTXII distribution, and determined the ramp rate by the proposed optimal test plan to minimize the weighted sum of the asymptotic variances of the MLE of percentile lifetimes at the design constant stress. Srivastava and Mittal [28] indicated that the BTXII distribution has a non-monotone hazard function, and can accommodate many shapes of hazard functions.…”

Section: Introductionmentioning

confidence: 99%

“…Srivastava and Mittal [28] proposed optimal planning methods for the multi-objective ramp-stress accelerated life test for the BTXII distribution, and determined the ramp rate by the proposed optimal test plan to minimize the weighted sum of the asymptotic variances of the MLE of percentile lifetimes at the design constant stress. Srivastava and Mittal [28] indicated that the BTXII distribution has a non-monotone hazard function, and can accommodate many shapes of hazard functions. The tails make the BTXII distribution more effective for modeling failures that occur with less frequency than some of the models based on exponential tails.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Reliability Inference on Composite Dynamic Systems Based on Burr Type-XII Distribution

et al. 2015

View full text Add to dashboard Cite

Failure of a component in a composite dynamic system often induces a higher load on surviving components, and increases the hazard rate. Statistical inferential procedures on composite dynamic systems are developed here based on a Burr type-XII distribution with a power-trend hazard rate function. Point estimates of the Burr type-XII parameters, and interval estimates of the baseline survival function are obtained based on the maximum-likelihood estimates, and the Fisher information matrix. A test procedure is presented for examining the relationship between the hazard rate function and the number of failed components. The performance of the proposed method is then evaluated by means of an extensive Monte Carlo simulation study. An example is finally presented for illustrative purpose.Index Terms-Generalized likelihood ratio test, log-likelihood function, observed Fisher information, sequential order statistics.

show abstract

Optimum Multi-Objective Ramp-Stress Accelerated Life Test with Stress Upper Bound for Burr Type-XII Distribution

Cited by 15 publications

References 24 publications

Accelerated Life Test Method for the Doubly Truncated Burr Type XII Distribution

Accelerated Life Test Method for the Doubly Truncated Burr Type XII Distribution

Novel Accelerating Life Test Method and Its Application by Combining Constant Stress and Progressive Stress

Reliability Inference on Composite Dynamic Systems Based on Burr Type-XII Distribution

Contact Info

Product

Resources

About