Tampered Failure Rate Model Research Articles

이질적 부품 공급자를 고려한 부하분담시스템의 신뢰도 모형

Traditionally, system reliability is obtained in terms of the component reliability and the system structure under the assumption that the components are independent. In the load sharing system, components are dependent because the residual life of surviving components is affected at each component failure. Previous research has focused on evaluating reliability of a given load sharing system where components are provided from a single supplier. In this paper, we consider a problem of selecting components from several suppliers to maximize the system reliability. We first obtain system reliability in terms of reliability of each supplier using the tampered failure rate model to consider the effect of the operational load on the component reliability. We then show that the sensitivity of the component lifetime on the operational load plays an important role for selecting the component supplier that maximize the system reliability, only if there is redundant component. We believe that the result is useful for selecting the components to maximize the reliability of a load sharing system.

Inference for the Exponential Distribution under Generalized Progressively Hybrid Censored Data from Partially Accelerated Life Tests with a Time Transformation Function

In this article, the tampered failure rate model is used in partially accelerated life testing. A non-decreasing time function, often called a ‘‘time transformation function", is proposed to tamper the failure rate under design conditions. Different types of the proposed function, which have sufficient conditions in order to be accelerating functions, are investigated. A baseline failure rate of the exponential distribution is considered. Some point estimation methods, as well as approximate confidence intervals, for the parameters involved are discussed based on generalized progressively hybrid censored data. The determination of the optimal stress change time is discussed under two different criteria of optimality. A real dataset is employed to explain the theoretical outcomes discussed in this article. Finally, a Monte Carlo simulation study is carried out to examine the performance of the estimation methods and the optimality criteria.

Time and cost constrained optimal designs of multiple step stress tests under progressive censoring

Purpose The purpose of this paper is to consider the general k level step-stress accelerated life test with the Rayleigh lifetime distribution for units subjected to stress under progressive Type-I censoring. Design/methodology/approach The parameter of this distribution is assumed to be a log-linear function of the stress, and a tampered failure rate model holds. The progressive Type-I censoring reduces the cost of testing. Due to constrained resources in practice, the test design must be optimized carefully. A numerical study is conducted to illustrate the optimum test design based on several four optimality criteria under the constraint that the total experimental cost does not exceed a pre-specified budget. Findings This paper compares unconstrained and constrained optimal k level step-stress test. Based on the results of the simulation study, the cost constraint reduces cost and time of the test and it also, in the most cases, increases the efficiency of the test. Also, the T-optimal design is lowest cost and time for testing and it is found more optimal in both conditions. Originality/value In this paper, various optimization criteria for selecting the stress durations have been used, and these criteria are compared together. Also, because of affecting the stress durations on the experimental cost, the author optimize under the constraint that the total experimental cost does not exceed a pre-specified budget. The efficiency of the unconstrained test in comparison with constrained test is discussed.

Copula based constant-stress PALT using tampered failure rate model with dependent competing risks

PurposeAccelerated life tests (ALTs) are used to make timely assessments of the lifetime distribution of highly reliable materials and components. Life test under accelerated environmental conditions may be fully accelerated or partially accelerated. In fully accelerated life testing, all the test units are run at accelerated condition, while in partially accelerated life testing, they are both run at normal and accelerated conditions. The products can fail due to one of the several possible causes of failure which need not be independent. The purpose of this paper is to design constant-stress PALT with dependent competing causes of failure using the tampered failure rate model.Design/methodology/approachGumbel–Hougaard copula is used to model and measure the dependence between the life times of competing causes of failure. The use of the copula simplifies the model specification and gives a general class of distributions with the same dependent structure and arbitrary marginal distributions.FindingsThe optimal plan consists in finding optimum allocation of test units in different chambers by minimizing the reciprocal of the determinant of Fisher Information Matrix. The confidence interval for the estimated values of the design parameters has been obtained and sensitivity analysis carried out. The results of sensitivity analysis show that the plan is robust to small deviations from the true values of baseline parameters.Originality/valueThe model formulated can help reliability engineers obtain reliability estimates quickly of high reliability products that are likely to last for several years.

On Exact Inferential Results for a Simple Step-Stress Model Under a Time Constraint

In simple step-stress models based on exponential distributions, the distributions of the MLEs are commonly obtained using the moment generating function. In this paper, we propose an alternative method, the so-called expected value approach, introduced in Gorny (2017) to derive the exact distribution of the MLEs. Moreover, we discuss the benefits of this technique. Further, assuming uniformly distributed lifetimes, we show that the MLEs are also explicitly available and that their distributions are discrete for both the cumulative exposure and the tampered failure rate model. Additionally, we illustrate that confidence regions as well as confidence intervals can be established utilizing a connection to the multinomial distribution. The results are illustrated by an illustrative example as well as simulation results.

Joint modeling of linear degradation and failure time data with masked causes of failure under simple step-stress test

In this paper, we propose a method to model the relationship between degradation and failure time for a simple step-stress test where the underlying degradation path is linear and different causes of failure are possible. It is assumed that the intensity function depends only on the degradation value. No assumptions are made about the distribution of the failure times. A simple step-stress test is used to induce failure experimentally and a tampered failure rate model is proposed to describe the effect of the changing stress on the intensities. We assume that some of the products that fail during the test have a cause of failure that is only known to belong to a certain subset of all possible failures. This case is known as masking. In the presence of masking, the maximum likelihood estimates of the model parameters are obtained through the expectation–maximization algorithm by treating the causes of failure as missing values. The effect of incomplete information on the estimation of parameters is studied through a Monte-Carlo simulation. Finally, a real-world example is analysed to illustrate the application of the proposed methods.

Prediction of Generalized Order Statistics Based on Some Accelerated Data Using the Tampered Failure Rate Model

Prediction of Generalized Order Statistics Based on Some Accelerated Data Using the Tampered Failure Rate Model

Statistical inference for masked interval data with Weibull distribution under simple step-stress test and tampered failure rate model

In this article, we consider the planning of simple step-stress life test in the presence of competing risks with the possibility of masked causes of failure and interval censoring. It is assumed t...

Estimation of the extended Weibull parameters and acceleration factors in the step-stress accelerated life tests under an adaptive progressively hybrid censoring data

ABSTRACTBased on the tampered failure rate model under the adaptive Type-II progressively hybrid censoring data, we discuss the maximum likelihood estimators of the unknown parameters and acceleration factors in the general step-stress accelerated life tests in this paper. We also construct the exact and unique confidence interval for the extended Weibull shape parameter. In the numerical analysis, we describe the simulation procedures to obtain the adaptive Type-II progressively hybrid censoring data in the step-stress accelerated life tests and present an experimental data to illustrate the performance of the estimators.

Bayesian Inference for Step-Stress Partially Accelerated Competing Failure Model under Type II Progressive Censoring

This paper deals with the Bayesian inference on step-stress partially accelerated life tests using Type II progressive censored data in the presence of competing failure causes. Suppose that the occurrence time of the failure cause follows Pareto distribution under use stress levels. Based on the tampered failure rate model, the objective Bayesian estimates, Bayesian estimates, and E-Bayesian estimates of the unknown parameters and acceleration factor are obtained under the squared loss function. To evaluate the performance of the obtained estimates, the average relative errors (AREs) and mean squared errors (MSEs) are calculated. In addition, the comparisons of the three estimates of unknown parameters and acceleration factor for different sample sizes and different progressive censoring schemes are conducted through Monte Carlo simulations.

Statistical inference for competing risks model in step-stress partially accelerated life tests with progressively Type-I hybrid censored Weibull life data

In this paper, we discuss the maximum likelihood and Bayesian estimation under the progressively Type-I hybrid censored Weibull life data. The Weibull unknown parameters and acceleration factor in the step-stress partially accelerated life tests with competing risks are estimated based on the tampered failure rate model. The asymptotic confidence intervals and highest posterior density credible intervals are given by using the asymptotic normality theory and Gibbs sampling method. In particular, the acceptance–rejection algorithm is used to sample from the truncated density function, and the adaptive rejection algorithm is employed to sample from the log-concave density family. Finally, a simulation study is carried out to present simulated results and compare maximum likelihood estimates with Bayesian estimates. It is concluded that Bayesian estimation performs better.

The step-stress tampered failure rate model under interval monitoring

A step-stress accelerated life testing model is constructed that deals with type-I censored experiments for which a continuous monitoring of the tested items is infeasible and only their inspection at particular time points is possible, producing thus grouped data. A general scale family of distributions is considered for the underlying lifetimes, which allows for flexible modeling by permitting different lifetime distributions for different stress levels. The maximum likelihood estimators of its parameters and their density functions are derived explicitly only when the inspection points coincide with the points of stress-level change. In case of additional inspection points, the estimates are obtained numerically. Asymptotic, exact (whenever possible) and bootstrap confidence intervals (CIs) are considered. For the bootstrap CIs a smoothing-modification is introduced, accounting for the categorical nature of the data.

Reliability Analysis of Load-SharingK-out-of-NSystem Considering Component Degradation

TheK-out-of-Nconfiguration is a typical form of redundancy techniques to improve system reliability, where at leastK-out-of-Ncomponents must work for successful operation of system. When the components are degraded, more components are needed to meet the system requirement, which means that the value ofKhas to increase. The current reliability analysis methods overestimate the reliability, because using constantKignores the degradation effect. In a load-sharing system with degrading components, the workload shared on each surviving component will increase after a random component failure, resulting in higher failure rate and increased performance degradation rate. This paper proposes a method combining a tampered failure rate model with a performance degradation model to analyze the reliability of load-sharingK-out-of-Nsystem with degrading components. The proposed method considers the value ofKas a variable which is derived by the performance degradation model. Also, the load-sharing effect is evaluated by the tampered failure rate model. Monte-Carlo simulation procedure is used to estimate the discrete probability distribution ofK. The case of a solar panel is studied in this paper, and the result shows that the reliability considering component degradation is less than that ignoring component degradation.

Inference and Optimal Design Based on Step—Partially Accelerated Life Tests for the Generalized Pareto Distribution under Progressive Type-I Censoring

Various types of failure, censored and accelerated life tests, are commonly employed for life testing in some manufacturing industries and products that are highly reliable. In this article, we consider the tampered failure rate model as one of such types that relate the distribution under use condition to the distribution under accelerated condition. It is assumed that the lifetimes of products under use condition have generalized Pareto distribution as a lifetime model. Some estimation methods such as graphical, moments, probability weighted moments, and maximum likelihood estimation methods for the parameters are discussed based on progressively type-I censored data. The determination of optimal stress change time is discussed under two different criteria of optimality. Finally, a Monte Carlo simulation study is carried out to examine the performance of the estimation methods and the optimality criteria.

Models Comparison for Step-Stress Accelerated Life Testing

In this article, four basic models for step-stress accelerated life testing are introduced and compared: cumulative exposure model (CEM), linear cumulative exposure model (LCEM), tampered random variable model (TRVM), and tampered failure rate model (TFRM). Limitations of the four models are also introduced for better use of the models.

Statistical Analysis of MOBVE Distribution with TFR Model Under Step-Stress Accelerated Life Test

We obtain the maximum likelihood estimates of parameters of MOBVE distribution with tampered failure rate model under step-stress accelerated life test. Thereafter we show the feasibility of this method by using the Monte-Carlo simulation.

Optimal three step stress accelerated life tests under periodic inspection and type I censoring

The inferences of data obtained from periodic inspection and type I censoring for the three step stress accelerated life test are studied in this paper. The failure rate function that a log-quadratic relation of stress and the tampered failure rate model are considered under the exponential distribution. The optimal stress change times which minimize the asymptotic variance of maximum likelihood estimators of parameters is determined and the maximum likelihood estimators of the model parameters are estimated. A numerical example will be given to illustrate the proposed inferential procedures.

On Parameter Inference for Step-Stress Accelerated Life Test with Geometric Distribution

In this article, we present the parameter inference in step-stress accelerated life tests under the tampered failure rate model with geometric distribution. We deal with Type-II censoring scheme involved in experimental data, and provide the maximum likelihood estimate and confidence interval of the parameters of interest. With the help of the Monte-Carlo simulation technique, a comparison of precision of the confidence limits is demonstrated for our method, the Bootstrap method, and the large-sample based procedure. The application of two industrial real datasets shows the proposed method efficiency and feasibility.

Conditions for the coincidence of the TFR, TRV and CE models

Bhattacharyya and Soejoeti (1989) put forward the tampered failure rate model (TFR Model) for step-stress Accelerated Life Tests(ALT). This paper studies the conditions for the coincidence of the TRV, TFR and CE models, gives the definitions of the coincidence, offers a proof of the necessary and sufficient condition for the coincidence of the TRV and TFR models in [1], and points out a mistake that appeared in the counterexample provided in [3].

Uniqueness of the Maximum Likelihood Estimate of the Weibull Distribution Tampered Failure Rate Model

Bhattacharyya and Soejoeti (Bhattacharyya, G. K., Soejoeti, Z. A. (1989). Tampered failure rate model for step-stress accelerated life test. Commun. Statist.—Theory Meth. 18(5):1627–1643.) pro- posed the TFR model for step-stress accelerated life tests. Under the TFR model, this article proves that the maximum likelihood estimate of the shape parameters is unique for the Weibull distribution in a multiple step-stress accelerated life test, and investigates the accuracy of the maximum likelihood estimate using the Monte-Carlo simulation.