Failure Inference and Optimization for Step Stress Model Based on Bivariate Wiener Model

In this paper, we consider the situation under a life test, in which the failure time of the test units are not related deterministically to an observable stochastic time varying covariate. In such a case, the joint distribution of failure time and a marker value would be useful for modeling the step stress life test. The problem of accelerating such an experiment is considered as the main aim of this paper. We present a step stress accelerated model based on a bivariate Wiener process with one component as the latent (unobservable) degradation process, which determines the failure times and the other as a marker process, the degradation values of which are recorded at times of failure. Parametric inference based on the proposed model is discussed and the optimization procedure for obtaining the optimal time for changing the stress level is presented. The optimization criterion is to minimize the approximate variance of the maximum likelihood estimator of a percentile of the products' lifetime distribution

Accelerated Life Testing Of Subsea Equipment Under Hydrostatic Pressure

Accelerated Life Testing (ALT) is an effective method of demonstrating and improving product reliability in applications where the products are expected to perform for a long period of time. ALT accelerates a given failure mode by testing at amplified stress level(s) in excess of operational limits. Statistical analysis (parameter estimation) is then performed on the data, based on an acceleration model to make life predictions at use level. The acceleration model thus forms the basis of accelerated life testing methodology. Well established accelerated models such as the Arrhenius model and the Inverse Power Law (IPL) model exist for key stresses such as temperature and voltage. But there are other stresses like subsea pressure, where there is no clear model of choice. This research proposes a pressure-life (acceleration) model for the first time for life prediction under subsea pressure for key mechanical/physical failure mechanisms. Three independent accelerated tests were conducted and their results analyzed to identify the best model for the pressure-life relationship. The testing included material tests in standard coupons to investigate the effect of subsea pressure on key physical, mechanical, and electrical properties. Tests were also conducted at the component level on critical components that function as a pressure barrier. By comparing the likelihood values of multiple reasonable candidate models for the individual tests, the exponential model was identified as a good model for the pressure-life relationship. In addition to consistently providing good fit among the three tests, the exponential model was also consistent with field data (validation with over 10 years of field data) and demonstrated several characteristics that enable robust life predictions in a variety iv of scenarios. In addition the research also used the process of Bayesian analysis to incorporate prior information from field and test data to bolster the results and increase the confidence in the predictions from the proposed model

Simulation-based Bayesian optimal ALT designs for model discrimination

Accelerated life test (ALT) planning in Bayesian framework is studied in this paper with a focus of differentiating competing acceleration models, when there is uncertainty as to whether the relationship between log mean life and the stress variable is linear or exhibits some curvature. The proposed criterion is based on the Hellinger distance measure between predictive distributions. The optimal stress-factor setup and unit allocation are determined at three stress levels subject to test-lab equipment and test-duration constraints. Optimal designs are validated by their recovery rates, where the true, data-generating, model is selected under the DIC (Deviance Information Criterion) model selection rule, and by comparing their performance with other test plans. Results show that the proposed optimal design method has the advantage of substantially increasing a test plan׳s ability to distinguish among competing ALT models, thus providing better guidance as to which model is appropriate for the follow-on testing phase in the experiment.NOTICE: this is the author's version of a work that was accepted for publication in RELIABILITY ENGINEERING & SYSTEM SAFETY. Changes resulting from the publishing process, such as editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in RELIABILITY ENGINEERING & SYSTEM SAFETY, 134, 1-9. DOI: 10.1016/j.ress.2014.10.00

Data Analysis and Experimental Design for Accelerated Life Testing with Heterogeneous Group Effects

abstract: In accelerated life tests (ALTs), complete randomization is hardly achievable because of economic and engineering constraints. Typical experimental protocols such as subsampling or random blocks in ALTs result in a grouped structure, which leads to correlated lifetime observations. In this dissertation, generalized linear mixed model (GLMM) approach is proposed to analyze ALT data and find the optimal ALT design with the consideration of heterogeneous group effects. Two types of ALTs are demonstrated for data analysis. First, constant-stress ALT (CSALT) data with Weibull failure time distribution is modeled by GLMM. The marginal likelihood of observations is approximated by the quadrature rule; and the maximum likelihood (ML) estimation method is applied in iterative fashion to estimate unknown parameters including the variance component of random effect. Secondly, step-stress ALT (SSALT) data with random group effects is analyzed in similar manner but with an assumption of exponentially distributed failure time in each stress step. Two parameter estimation methods, from the frequentist’s and Bayesian points of view, are applied; and they are compared with other traditional models through simulation study and real example of the heterogeneous SSALT data. The proposed random effect model shows superiority in terms of reducing bias and variance in the estimation of life-stress relationship. The GLMM approach is particularly useful for the optimal experimental design of ALT while taking the random group effects into account. In specific, planning ALTs under nested design structure with random test chamber effects are studied. A greedy two-phased approach shows that different test chamber assignments to stress conditions substantially impact on the estimation of unknown parameters. Then, the D-optimal test plan with two test chambers is constructed by applying the quasi-likelihood approach. Lastly, the optimal ALT planning is expanded for the case of multiple sources of random effects so that the crossed design structure is also considered, along with the nested structure.Dissertation/ThesisDoctoral Dissertation Industrial Engineering 201