Life Test Model Research Articles

Likelihood and Bayesian estimations for step-stress life test model under Type-I censoring

This paper discusses likelihood and Bayesian estimations for partially accelerated step-stress life test model under Type-I censoring assuming Pareto distribution of the second kind. The posterior means and posterior variances are obtained under the squared error loss function using Lindleys approximation procedure. It has been observed that Lindley’s method usually provides posterior variances and mean square errors smaller than those of the maximum likelihood estimators. Furthermore, the highest posterior density credible intervals of the model parameters based on Gibbs sampling technique are computed. For illustration, simulation studies and an illustrative example based on a real data set are provided.

A Comprehensive Model for Assessing the Impact of Steel Cleanliness on Bearing Performance

Steel cleanliness as measured by nonmetallic inclusion content in steel plays a major role in affecting bearing durability. A high-fidelity virtual bearing life test model was developed to predict the impact of inclusions on bearing fatigue life. This model analyzes distributions of inclusion size, shape, orientation, and location, and computes stress alterations to bearing material due to inclusions and the resulting life reduction. Comparisons between model predictions and experimental test results were made, confirming the validity of the model. Parametric studies were conducted to explore the effects of inclusion counts, inclusion size distributions, and the effect of overall bearing size on bearing life. A regression equation was proposed based on simulation results, linking the bearing life reduction factor (LRF) to the accumulative inclusion length within the stressed volume under contact load.

Inference for constant-stress accelerated life test with Type-I progressively hybrid censored data from Burr-XII distribution

This paper proposes a simple constant-stress accelerated life test (ALT) model from Burr type XII distribution when the data are Type-I progressively hybrid censored. The maximum likelihood estimation (MLE) of the parameters is obtained through the numerical method for solving the likelihood equations. Approximate confidence interval (CI), based on normal approximation to the asymptotic distribution of MLE and percentile bootstrap CI is derived. Finally, a numerical example is introduced and then a Monte Carlo simulation study is carried out to illustrate the proposed method.

Bayesian Analysis for Accelerated Life Tests Using a Dirichlet Process Weibull Mixture Model

This study proposes a semiparametric Bayesian approach to accelerated life test (ALT). The proposed accelerated life test model assumes a log-linear lifetime-stress relationship, without making any assumption on the parametric form of the failure-time distribution. A Dirichlet process mixture model with a Weibull kernel is employed to model the failure-time distribution at a given stress level. A simulation-based model fitting algorithm that implements Gibbs sampling is developed to analyze right-censored ALT data, and to predict the failure-time distribution at the normal stress level. The proposed model and algorithm are applied to two practical examples related to the reliability of nanoelectronic devices. The results have demonstrated that the proposed methodology is capable of providing accurate prediction of the failure-time distribution at the normal stress level without assuming any restrictive parametric failure-time distribution.

Statistical Inference of Weibull Distribution under a Progressive Stress Partially Accelerated Life Testing Model

This paper considers a progressive stress partially accelerated life test model when the lifetime of a product under the use condition follows a Weibull distribution. It is assumed that the progressive stress is directly proportional to time. The maximum likelihood method is used to obtain the estimates of the model parameters. In addition, approximate confidence intervals for the parameters are constructed. A Monte Carlo simulation study is conducted to illustrate the theoretical results of the proposed model.

半导体激光器空间辐射应力加速寿命实验模型

半导体激光器空间辐射应力加速寿命实验模型

고압호스 조립체의 가속수명시험에 관한 연구

Hydraulic hose assemblies are used as piping components for construction machinery, automobile, aircraft, industrial machinery, machine tools, and machinery for ships. Then the reliability of hose assemblies is important because total hydraulic system, which used to deliver the fluid power () needed to flexibility in the piping system, is not operated if the hose assembly failed in the system. The data of the accelerated life test estimated through the shape parameter() resulting of the Weibull distribution analysis. This study has tried to reduce the test time resulting from varying impulse pressure range and the flexing diameter. Accelerated life test model for the test results was adopted the GLL(generalized log linear) and the accelerated indexes are identified as 6.64 for the pressure and 4.46 for flexing radius. Also, it found that shape parameter is 6.19, scale parameter() is , which were adopted the pressure 35 MPa and the flexing diameter R100 mm in the used condition.

An accelerated life test model for solid lubricated bearings based on dependence analysis and proportional hazard effect

Solid lubricated bearings are important mechanical components in space, and accelerated life tests (ALT) of them are widely conducted. ALT model is needed to give the lifetime of solid lubricated bearings with ALT data, and former accelerated life test models of solid lubricated models are mainly statistical models, while physical models can imply an understanding of the failure mechanism and are preferred whenever possible. This paper proposes a physical model, which is called copula dependent proportional hazards model. A solid lubricated bearing is considered as a system consisting of several dependent items and Clayton copula function is used to describe the dependence. Proportional hazard effect is also considered to build the model. An ALT of solid lubricated bearing is carried out and the results show that this model is effective.

Discriminating Between Generalized Exponential Distribution and Some Life Test Models Based on Population Quantiles

A test statistic based on population quantiles using sample order statistics is suggested. The quantiles of the test statistics are evaluated for generalized exponential distribution. Similar test statistic based on moments of sample order statistic is referred and the proposed test formula is compared with it. Between the pairs of the above models it is established that the test formula proposed by us is more effective and useful than the formula based on the moments of order statistics as developed by Sultan (2007).

An in vitro study of the effect of different restorative materials on the reliability of a veneering porcelain

Implant-supported, porcelain veneered restorations experience a greater rate of porcelain fracture than tooth-supported restorations. For completely edentulous patients, one approach to minimizing porcelain fracture is touse acrylic resin in the mandible, although its efficacy is unknown. The purpose of this study was to evaluate the reliability of a veneering porcelain fatigued with different restorative materials invitro. Fifty-nine veneering porcelain disk specimens were fabricated by layering veneering porcelain on nickel-chromium base metal alloy disks. Four groups of different indenter materials fatigued the porcelain specimens: group WC, tungsten carbide served as a control; group FC, pressed leucite glass ceramic; group NHC, nanohybrid composite resin denture tooth; and group AR, unfilled acrylic resin denture tooth. Porcelain specimens were randomly divided into 4 groups (n=14). A step-stress accelerated life-testing model was used. Use-level probability Weibull plots were generated, and the reliability of each group was estimated for a theoretical completion of 50 000 cycles at 150 N. Nanohybrid composite resin and unfilled acrylic resin denture tooth groups had higher reliability than tungsten carbide and leucite glass ceramic groups. No significant differences existed between the reliability of the tungsten carbide and leucite glass ceramic groups and the nanohybrid composite resin and acrylic resin denture tooth groups. Veneering porcelain disk specimens fatigued with the unfilled acrylic resin and nanohybrid composite resin denture tooth indenters exhibited higher reliability than the specimens fatigued with either the tungsten carbide or leucite glass ceramic indenters. All of the veneering porcelain disk specimens failed with the same mode of fracture, although thesurface posttest exhibited different fracture characteristics among specimens fatigued with the 4 different materials.

Inference for a step-stress partially accelerated life test model with an adaptive Type-II progressively hybrid censored data from Weibull distribution

In this paper, the maximum likelihood estimators of Weibull distribution parameters and the acceleration factor are discussed based on two different types of progressively hybrid censoring schemes under step-stress partially accelerated life test model. The performances of the estimators of the model parameters using the two progressively hybrid censoring schemes are evaluated and compared in terms of biases and mean squared errors through a Monte Carlo simulation study.

Likelihood inference for a step-stress partially accelerated life test model with Type-I progressively hybrid censored data from Weibull distribution

Recently, progressively hybrid censoring schemes have become quite popular in life testing and reliability studies. In this article, the point and interval maximum-likelihood estimations of Weibull distribution parameters and the acceleration factor are considered. The estimation process is performed under Type-I progressively hybrid censored data for a step-stress partially accelerated test model. The biases and mean square errors of the maximum-likelihood estimators are computed to assess their performances in the presence of censoring developed in this article through a Monte Carlo simulation study.

Methods for Estimating the 2-Parameter Weibull Distribution with Type-I Censored Data

This study is concerned with the two-parameter Weibull distribution which has and is still being used as a model in life testing and reliability engineering. We seek to find out whether Rank Regression Method can be a good alternative to that of the world publicised traditional method known as Maximum Likelihood for estimating two parameters of the Weibull distribution. The methods under consideration are: Maximum Likelihood Estimation, Least Square Estimation on Y and that of Least Square Estimation on X. These estimators are derived for Random Type-I censored samples. These methods were compared using Mean Square Error and Mean Percentage Error through simulation study with small, medium and large sample sizes in estimating the Weibull parameters under Type-I censored data. The observations that are made based on this study are that Maximum Likelihood Estimator stands out when estimating the scale parameter followed by Least Square Estimator on X but for the shape parameter Least Square Estimator on X performed better than Maximum Likelihood Estimator thereby making it a good alternative method to MLE.

Optimum Step Stress Accelerated Life Testing for Mukherjeeislam Failure Model

Step stress accelerated life testing model is presented to obtain the optimal hold time at which the stress level is changed. A Mukherjee-Islam Failure model is assumed for the failure time at any constant stress level and a cumulative exposure model is assumed. The scale parameter of the Mukherjee-Islam Failure model at constant stress levels is assumed to be a log-linear function of the stress level. The maximum likelihood function is given for the step stress accelerated life testing. Optimal SSALT plan is proposed by minimizing the Asymptotic Variance (AV) of the desired life reliability estimate. Fisher information matrix is obtained. An optimal test plan with the minimum asymptotic variance of reliability estimate at time τ is determined.

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

This paper deals with the formulation of optimum multi-objective ramp-stress accelerated life test (ALT) plans with stress upper bounds for the Burr type-XII distribution under type-I censoring. It is impractical to estimate only one objective parameter after conducting such costly ALT tests. Therefore, an optimum ramp-stress ALT plan with multiple estimating objectives has been designed. The Burr type-XII life distribution has been found appropriate in accelerated life testing models. The commonly used Weibull and exponential distributions are its limiting cases, and the log-logistic distribution is its particular case. The inverse power law, and a cumulative exposure model are assumed. The optimal test plan consists of determining the ramp rate by minimizing the weighted sum of the asymptotic variances of the maximum likelihood estimator of quantile lifetimes at design constant stress. The method developed has been illustrated using an example, and the effects of the pre estimates of design parameters were investigated. Comparative study has also been done to highlight the merits of the proposed model.

Bayesian prediction for type-II progressive-censored data from the Rayleigh distribution under progressive-stress model

The two-sample prediction is considered to derive Bayesian prediction bounds for future order statistics based on progressively type-II censored informative samples obtained from progressive-stress accelerated life testing models. The lifetime of an item under the use condition stress is assumed to follow the Rayleigh distribution with a scale parameter satisfying the inverse power law. The informative and future samples are assumed to be obtained from the same population. Explicit forms for prediction bounds of the first future order statistic are obtained in the case of one unknown parameter. When two parameters are unknown, a simulation study is performed and numerical computations are carried out, based on three different progressive-censoring schemes. The coverage probabilities and average interval lengths of the confidence intervals are computed via a Monte Carlo simulation.

A General Proportional Model and Modelling Procedure

This paper presents a unified representation for the Cox model and its extensions (e.g. proportional intensity model, proportional wear‐out model and accelerated life testing model) and calls it the general proportional model. A multi‐step procedure is proposed to sequentially determine the three parts of the model (i.e. baseline, covariate and stochastic parts). The basic idea of the proposed approach is to use an optimization method to estimate the ‘accelerated factor’ associated with each ‘stress’ (i.e. covariate) level. The estimated accelerated factors are fitted to an adequate model as a function of the stress level. The fitted accelerated factor model is used to transform the observed sample into an equivalent (or mixed) sample, which corresponds to a specified reference stress level. The main advantages of the proposed approach are that it makes the modelling process flexible and transparent, avoids making possibly unrealistic assumptions on the forms (or distribution family) of relevant functions (or random variable) and fully utilizes all the observations for modelling. The appropriateness and usefulness of the model and modelling approach are illustrated through a detailed analysis for two real‐world examples published in the literature. Copyright © 2012 John Wiley & Sons, Ltd.

A GLM approach to step-stress accelerated life testing with interval censoring

In this paper, we present a statistical inference procedure for the step-stress accelerated life testing (SSALT) model with Weibull failure time distribution and interval censoring via the formulation of generalized linear model (GLM). The likelihood function of an interval censored SSALT is in general too complicated to obtain analytical results. However, by transforming the failure time to an exponential distribution and using a binomial random variable for failure counts occurred in inspection intervals, a GLM formulation with a complementary log–log link function can be constructed. The estimations of the regression coefficients used for the Weibull scale parameter are obtained through the iterative weighted least square (IWLS) method, and the shape parameter is updated by a direct maximum likelihood (ML) estimation. The confidence intervals for these parameters are estimated through bootstrapping. The application of the proposed GLM approach is demonstrated by an industrial example.

Record values from a family of J-shaped distributions

A family of J-shaped distributions has applications in life testing modeling. In this paper we study record values from this family of distributions. Based on lower records, recurrence relations and bounds as well as expressions for moments and product moments of record values are obtained, the maximum likelihood estimator of the shape parameter is derived and shown to be consistent, sufficient, complete and UMVU estimator. In addition, an application in reliability is given.

Bayesian Parameter Estimation with Prior Weighting in ALT Model

This paper provides an overview of the application of Bayesian inference to accelerated life testing (ALT) models for the concrete case of estimation by Maximum of Aposteriori (MAP) method in the case of constant stress levels. It studies the Bayesian inference over the accelerated life model as presented in [9]. It suites, integrates and generalizes the particular cases presented in [12] and [13]. Towards the end, weighting of the prior information according to data is integrated. The paper also illustrates an experimental example.