Use-level lifetime distribution estimation under dependent right censored test data

Accelerated life testing (ALT) is a practice for estimating unit reliability at normal use conditions using failure data obtained under more severe test conditions. We focus on life tests where a potential critical unit failure at X2 (unit lifetime) may be avoided by a degraded failure at some random time X1. Degraded and critical failures are linked through the degradation process,hence the situation under consideration is that of dependent competing risks. We apply the general result that if the copula C(.; .) of (X1; X2) is known, competing risks data uniquely determine the marginal distributions at each stress level. Interest here (and in life testing studies in general) is in unit lifetime. Accordingly, our target of estimation is to extrapolate a use-level lifetime distribution from which important reliability measures such as mean lifetime, warranty period among others are derived. The paper is based in part on a PhD thesis by Hove (2014)

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

Accelerated degradation tests planning with competing failure modes

Accelerated degradation tests (ADT) have been widely used to assess the reliability of products with long lifetime. For many products, environmental stress not only accelerates their degradation rate but also elevates the probability of traumatic shocks. When random traumatic shocks occur during an ADT, it is possible that the degradation measurements cannot be taken afterward, which brings challenges to reliability assessment. In this paper, we propose an ADT optimization approach for products suffering from both degradation failures and random shock failures. The degradation path is modeled by a Wiener process. Under various stress levels, the arrival process of random shocks is assumed to follow a nonhomogeneous Poisson process. Parameters of acceleration models for both failure modes need to be estimated from the ADT. Three common optimality criteria based on the Fisher information are considered and compared to optimize the ADT plan under a given number of test units and a predetermined test duration. Optimal two- and three-level optimal ADT plans are obtained by numerical methods. We use the general equivalence theorems to verify the global optimality of ADT plans. A numerical example is presented to illustrate the proposed methods. The result shows that the optimal ADT plans in the presence of random shocks differ significantly from the traditional ADT plans. Sensitivity analysis is carried out to study the robustness of optimal ADT plans with respect to the changes in planning input

Contributions to accelerated reliability testing

A thesis submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Doctor of Philosophy. Johannesburg, December 2014.Industrial units cannot operate without failure forever. When the operation of a unit deviates from industrial standards, it is considered to have failed. The time from the moment a unit enters service until it fails is its lifetime. Within reliability and often in life data analysis in general, lifetime is the event of interest. For highly reliable units, accelerated life testing is required to obtain lifetime data quickly. Accelerated tests where failure is not instantaneous, but the end point of an underlying degradation process are considered. Failure during testing occurs when the performance of the unit falls to some specified threshold value such that the unit fails to meet industrial specifications though it has some residual functionality (degraded failure) or decreases to a critical failure level so that the unit cannot perform its function to any degree (critical failure). This problem formulation satisfies the random signs property, a notable competing risks formulation originally developed in maintenance studies but extended to accelerated testing here. Since degraded and critical failures are linked through the degradation process, the open problem of modelling dependent competing risks is discussed. A copula model is assumed and expert opinion is used to estimate the copula. Observed occurrences of degraded and critical failure times are interpreted as times when the degradation process first crosses failure thresholds and are therefore postulated to be distributed as inverse Gaussian. Based on the estimated copula, a use-level unit lifetime distribution is extrapolated from test data. Reliability metrics from the extrapolated use-level unit lifetime distribution are found to differ slightly with respect to different degrees of stochastic dependence between the risks. Consequently, a degree of dependence between the risks that is believed to be realistic to admit is considered an important factor when estimating the use-level unit lifetime distribution from test data. Keywords: Lifetime; Accelerated testing; Competing risks; Copula; First passage time

Reliability Estimation of Rotary Lip Seal in Aircraft Utility System Based on Time-Varying Dependence Degradation Model and Its Experimental Validation

With several attractive properties, rotary lip seals are widely used in aircraft utility system, and their reliability estimation has drawn more and more attention. This work proposes a reliability estimation approach based on time-varying dependence analysis. The dependence between the two performance indicators of rotary lip seals, namely leakage rate and friction torque, is modeled by time-varying copula function with polynomial to denote the time-varying parameters, and an efficient copula selection approach is utilized to select the optimal copula function. Parameter estimation is carried out based on a Bayesian method and the reliability during the whole lifetime is calculated based on a Monte Carlo method. Degradation test for rotary lip seal is conducted and the proposed model is validated by test data. The optimal copula function and optimal order of polynomial are determined based on test data. Results show that this model is effective in estimating the reliability of rotary lip seals and can achieve a better goodness of fit

Optimal Design for Accelerated-Stress Acceptance Test Based on Wiener Process

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Modeling Reliability Growth in Accelerated Stress Testing

Qualitative accelerated test methods improve system reliability by identifying and removing initial design flaws. However, schedule and cost constraints often preclude sufficient testing to generate a meaningful reliability estimate from the data obtained in these tests. In this dissertation a modified accelerated life test is proposed to assess the likelihood of attaining a reliability requirement based on tests of early system prototypes. Assuming each prototype contains an unknown number of independent competing failure modes whose respective times to occurrence are governed by a distinct Weibull law, the observed failure data from this qualitative test are shown to follow a poly-Weibull distribution. However, using an agent-based Monte Carlo simulation, it is shown that for typical products subjected to qualitative testing, the failure observations result from a homogenous subset of the total number of latent failure modes and the failure data can be adequately modeled with a Weibull distribution. Thus, the projected system reliability after implementing corrective action to remove one or more failure modes can be estimated using established quantitative accelerated test data analysis methods. Our results suggest that a significant cost and time savings may be realized using the proposed method to signal the need to reassess a product’s design or reallocate test resources to avoid unnecessary maintenance or redesigns. Further, the proposed approach allows a significant reduction in the test time and sample size required to estimate the risk of meeting a reliability requirement over current quantitative accelerated life test techniques. Additional contributions include a numerical and analytical procedure for obtaining the maximum likelihood parameter estimates and observed Fisher information matrix components for the generalized poly-Weibull distribution. Using this procedure, we show that the poly-Weibull distribution outperforms the best-fit modified Weibull alternatives in the literature with respect to their fit of reference data sets for which the hazard rate functions are non-monotone