Constant-stress Accelerated Life Test Research Articles

Optimization Design Method for Non-Rectangular Constant Stress Accelerated Testing Considering Parameter Estimation Precision

In addressing the design challenges for constant-stress accelerated life testing in non-rectangular experimental domains, we aim to optimize the precision in estimating parameters for the product reliability statistical model. Following the principles of regression orthogonal design theory to determine the combinations of stress levels, we constrain the maximum stress levels of each experimental stress along the boundary curve of the non-rectangular experimental domain. The remaining stress levels and the allocation ratios of specimens for each test serve as design variables in the optimization process. We establish a mathematical model for the optimal design of constant-stress accelerated life testing in non-rectangular experimental domains. The results of the optimized design for comprehensive stress accelerated life testing in non-rectangular experimental regions of aerospace electrical connectors indicate that, with the same sample size, the optimized testing scheme not only enhances the precision of model parameter estimation but also reduces the number of required tests. At an equivalent number of tests and testing duration, the optimization scheme proposed in this study demonstrates an improvement of over 63% in the precision of model parameter estimation compared to the EM-optimized testing scheme in non-rectangular experimental regions. Using the mean, standard deviation, and coefficient of variation of the determinant values of the information matrix as criteria for evaluating the precision and robustness of experimental designs, a simulated evaluation was conducted for the optimized experimental design, a conventional experimental design, and an EM experimental design. The results indicate that the optimal experimental design outperforms both the conventional experimental design and the EM experimental design in terms of precision and robustness.

Statistical Inference of Weighted Exponential Distribution Under Partially Constant-Stress Accelerated Life Tests with Type-II Censoring Scheme

Statistical Inference of Weighted Exponential Distribution Under Partially Constant-Stress Accelerated Life Tests with Type-II Censoring Scheme

Reliability analysis at usual operating settings for Weibull Constant-stress model with improved adaptive Type-Ⅱ progressively censored samples

<abstract><p>An improved adaptive Type-Ⅱ progressive censoring scheme was recently introduced to ensure that the examination duration will not surpass a specified threshold span. Employing this plan, this paper aimed to investigate statistical inference using Weibull constant-stress accelerated life tests. Two classical setups, namely maximum likelihood and maximum product of spacings, were explored to estimate the scale, shape, and reliability index under normal use conditions as well as their asymptotic confidence intervals. Through the same suggested classical setups, the Bayesian estimation methodology via the Markov chain Monte Carlo technique based on the squared error loss was considered to acquire the point and credible estimates. To compare the efficiency of the various offered approaches, a simulation study was carried out with varied sample sizes and censoring designs. The simulation findings show that the Bayesian approach via the likelihood function provides better estimates when compared with other methods. Finally, the utility of the proposed techniques was illustrated by analyzing two real data sets indicating the failure times of a white organic light-emitting diode and a pump motor.</p></abstract>

Bayes analysis of one-shot device testing data with correlated failure modes using copula models

Copula models are capable of modeling the dependence structure among the random variables, a phenomenon that is often required in the statistical analysis. Such models are the flexible substitutes of multivariate distributions because they model both the marginal distributions and the joint dependence structure distinctly. Because of such important features, the models are recognized as popular tools in a variety of situations including reliability engineering and survival analysis. The present paper studies a Bayesian approach using three Archimedean copulas, namely, the Gumbel Hougaard copula, the Frank copula and the Joe copula for analyzing one-shot device testing data with two correlated failure modes collected from a constant stress accelerated life test. One-shot devices are units that can be used only once and destroyed immediately after the use. Obviously, one obtains either left or right censored data on the failure times instead of actual failure times of the devices. Finally, all the considered copula models are compared using the Bayesian model selection tools. A real dataset is analyzed as an illustration of the proposed Bayesian methodology.

Study on life distribution and prediction method of flexible graphite composite reinforced gasket

PurposeThis paper aims to prevent gasket sealing failure in engineering, accurately predict gasket life, extend system life and improve sealing reliability. The accelerated life test method of flexible graphite composite–reinforced gaskets is established, the life distribution law of flexible graphite composite–reinforced gaskets is revealed, and the life prediction method of flexible graphite composite–reinforced gaskets with different allowable leakage rates is proposed, which can provide a reference for the life prediction of other types of gaskets.Design/methodology/approachIn this study, flexible graphite composite–reinforced gaskets were tested for long-term high-temperature sealing performance on a multi-sample gasket accelerated life test rig. The data were also analyzed using the least squares method and the K-S hypothesis calibration method. A gasket time-dependent leakage model and an accelerated life model were also developed. Constant stress-accelerated life tests were conducted on flexible graphite composite–reinforced gaskets. On this basis, a gasket life prediction method at different allowable leakage rates was proposed.FindingsThe life distribution law of flexible graphite composite–reinforced gaskets is revealed. The results show that the life of the gasket obeys the Weibull distribution. The time-correlated leakage model and accelerated life model of the gasket were established. And the accelerated life test method of the flexible graphite composite–reinforced gasket was established. The life distribution parameters, accelerated life model parameters and life estimates of gaskets were obtained through tests. On this basis, a gasket life prediction method under different leakage rates was proposed, which can be used as a reference for other types of gaskets.Practical implicationsThe research in this paper can better provide guidance for the use and replacement of gaskets in the project, which is also very meaningful for predicting the leakage condition of gaskets in the bolted flange connection system and taking corresponding control measures to reduce energy waste and pollution and ensure the safe operation of industrial equipment.Originality/valueA multi-specimen gasket-accelerated life test device has been developed, and the design parameters of the device have reached the international advanced level. The life distribution law of the flexible graphite composite–reinforced gasket was revealed. The accelerated life test method for the flexible graphite composite–reinforced gasket was established. The life prediction method of the flexible graphite composite–reinforced gasket under different allowable leakage rates was proposed.Peer reviewThe peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-08-2023-0254/

Constant-Stress Modeling of Log-Normal Data under Progressive Type-I Interval Censoring: Maximum Likelihood and Bayesian Estimation Approaches

This paper discusses inferential approaches for the problem of constant-stress accelerated life testing when the failure data are progressive type-I interval censored. Both frequentist and Bayesian estimations are carried out under the assumption that the log-normal location parameter is nonconstant and follows a log-linear life-stress model. The confidence intervals of unknown parameters are also constructed based on asymptotic theory and Bayesian techniques. An analysis of a real data set is combined with a Monte Carlo simulation to provide a thorough assessment of the proposed methods.

Parameter Estimation of Gompertz Distribution Under Constant Stress Accelerated Life Testing Using Progressive Type-II Censoring

In this paper, the problem of estimation of parameters of Gompertz distribution under constant stress accelerated life testing model using a progressively type II censored sample is considered. The maximum likelihood and Bayesian methods are used for estimating the unknown parameters. Markov chain Monte Carlo techniques are employed to carry out Bayesian estimation. A simulation study is carried out to assess and compare the different estimators discussed in this paper. Finally, real data are analyzed to illustrate the results.

Reliability Estimation under Normal Operating Conditions for Progressively Type-II XLindley Censored Data

This paper assumes constant-stress accelerated life tests when the lifespan of the test units follows the XLindley distribution. In addition to the maximum likelihood estimation, the Bayesian estimation of the model parameters is acquired based on progressively Type-II censored samples. The point and interval estimations of the model parameters and some reliability indices under normal operating conditions at mission time are derived using both estimation methods. Using the Markov chain Monte Carlo algorithm, the Bayes estimates are calculated using the squared error loss function. Simulating the performances of the different estimation methods is performed to illustrate the proposed methodology. As an example of how the proposed methods can be applied, we look at two real-life accelerated life test cases. According to the numerical outcomes and based on some criteria, including the root of the mean square error and interval length, we can conclude that the Bayesian estimation method based on the Markov chain Monte Carlo procedure performs better than the classical methods in evaluating the XLindley parameters and some of its reliability measures when a constant-stress accelerated life test is applied with progressively Type-II censoring.

Optimal design of reliability acceptance sampling plan based on constant‐stress accelerated life testing considering the uncertainty of accelerated factor

AbstractWith the increasing marketplace demand for decreasing test time and cost, constant‐stress accelerated life testing (CSALT) is widely used for reliability demonstration in practice. The existing accelerated acceptance sampling plans (AASPs) do not consider the uncertainty of accelerated factor (AF), which makes it difficult to accurately describe the producer's and consumer's risks. Previous AASP studies on CSALT were mainly carried out under a fixed accelerated stress level, and the influence of accelerated stress level is not concerned. Therefore, considering the uncertainty of AF and taking the lognormal distribution as an example, the AASP design method with time‐censoring is proposed, where the life‐stress relationship between the location parameter and stress level is expressed by an inverse power law model. First, considering the uncertainty of AF expressed by a distribution, the acceptance probability can be obtained by the mathematic expectation of conditional acceptance probability, and the producer's and consumer's risks can be accurately expressed. Then, to reduce the total cost furtherly, the accelerated stress level is considered as a new decision variable, the optimum AASP including the sampling plan and the decision‐making criterion can be designed by minimizing the total cost and solving the risk constraint equations of both sides. A real case study of white organic light‐emitting diodes is carried out to verify the effectiveness of the proposed method.

Copula Approach for Dependent Competing Risks of Generalized Half-Logistic Distributions under Accelerated Censoring Data

In medicals sciences and reliability engineering, the failure of individuals or units (I/Us) occurs due to independent causes of failure. In general, the symmetry between dependent and independent causes of failure is essential to the nature of the problem at hand. In this study, we considered the accelerated dependent competing risks model when the lifetime of I/Us was modeled using a generalized half-logistic distribution. The data were obtained with respect to constant stress accelerated life tests (ALTs) with a type-II progressive censoring scheme. The dependence structure was formulated using the copula approach (symmetric Archimedean copula). The model parameters were estimated with the maximum likelihood method; only two dependent causes of failure and bivariate Pareto copula functions were proposed. The approximate confidence intervals were constructed using both the asymptotic normality distribution of MLEs and bootstrap techniques. Additionally, an estimator of the reliability of the system under a normal stress level was constructed. The results from the estimation methods were tested by performing a Monte Carlo simulation study. Finally, an analysis of data sets from two stress levels was performed for illustrative purposes.

Accelerated life test for Pareto distribution under progressive type-II censored competing risks data with binomial removals and its application in electrode insulation system

In this article, based on progressive type-II censored competing risks data with binomial removals, a constant-stress accelerated life testing is discussed when the lifetime of experiment units follows the Pareto distribution. Under the assumption that the failure time of each cause is statistically independent, the estimation of unknown parameters is obtained by maximum likelihood estimation and Bayesian estimators under symmetric and asymmetric loss functions. The corresponding confidence and credible intervals are constructed with approximation theory, bootstrap method, and MCMC technique respectively. Additionally, the log-linear model is established for the life test and two goodness-of-fit test statistics are constructed. Finally, a simulation study is carried out for the power analysis of different censoring ratio schemes and the numerical results verify the feasibility of the constructed test statistics for the censored data with competing risks.

Interval estimation of the two-parameter exponential constant stress accelerated life test model under Type-II censoring

ABSTRACT In this paper, interval estimation of the two-parameter exponential distribution based on constant-stress accelerated life test data under Type-II censoring is studied. The life-stress models of the scale and location parameters are assumed to be log-linear. The maximum likelihood estimators of the model parameters are obtained. The exact and approximate confidence intervals for the parameters in the life-stress model of the scale parameter are developed. The generalized confidence intervals for the parameters in the life-stress model of the location parameter, and mean and reliability function at the designed stress level are derived. The performance of the proposed generalized confidence intervals is assessed by the Monte Carlo simulation. Finally, a real example is used to illustrate our methods.

Inferences of generalized inverted exponential distribution based on partially constant-stress accelerated life testing under progressive Type-II censoring

The problem of testing the product units under stress higher than normal stress conditions is widely used in reliability analysis specially, in a high reliable products to saving time and cost which is known by accelerated life tests (ALTs) model. In this paper, we are adopted partially constant-stress ALTs model for product units have generalized inverted exponential (GIE) lifetime. And, the test is running under progressive Type-II censoring scheme. The model parameters are estimated with maximum likelihood and Bayes methods. The corresponding asymptotic confidence intervals as well as credible intervals are also constructed. The theoretical results are assessed and compared through Monte Carlo simulation study. The numerical data set is analyzed under the proposed model for illustrative purpose. Finally, we reported some comments about numerical computation.

Inference for constant stress accelerated life test under the proportional reverse hazards lifetime distribution

AbstractIn this paper, we consider small sample statistical inference methods for the constant stress accelerated life test (CSALT) under the proportional reverse hazards family (PRHF). The model parameters are assumed to be the exponential functions of the stress. The generalized confidence intervals (GCIs) are derived for the model parameters and some commonly used reliability metrics such as the quantile and the reliability function of the lifetime at the designed stress level. The generalized prediction interval (GPI) is also proposed for the future failure time (FFT) and the remaining useful life (RUL) at the designed stress level. The Monte Carlo simulation study for the generalized Lindley distribution (GLD) and the inverse Weibull distribution are used to illustrate the performance of the proposed GCIs and GPI. The simulation results indicate that the performance of the proposed GCIs and GPI is better than the Wald confidence intervals (CIs) and bootstrap‐p CIs in terms of the coverage probability (CP). Finally, a real example is used to illustrate the developed procedures.

Reliability Analysis of Hybrid System Using Geometric Process in Multiple Level of Constant Stress Accelerated Life Test through Simulation Study for Type-II Progressive Censored Masked Data

Numerous studies have already been attempted to explore the reliability of systems considering mask data, though the mass of them has largely focused on basic series or parallel systems, where component failures are assumed to follow an exponential or Weibull distribution. However, most electrotonic products and systems are made up of numerous components integrated in parallel-series, series-parallel, and other bridge hybrid structures, and the number of studies in the area of accelerated life testing (ALT) employing masked data for hybrid systems is limited. In this paper, the constant-stress ALT (CSALT) is explored based on type-II progressive censoring scheme (TIIPCS) for a four-component hybrid system using geometric process (GmP). The failure times of the components of the system are assumed to follow the generalized Pareto (GP) distribution. The maximum likelihood estimate (MLE) technique is used to establish statistical inference for the model's unknown parameters under the premise that the failure reasons are unknown for the hybrid system. In addition, the asymptotic confidence intervals (ACIs) are also obtained by inverting the fisher information matrix. Finally, a simulation study is given to explain the proposed techniques and to evaluate the performance of the estimates. The performance of MLEs is assessed in terms of root mean square errors (RMSEs) and relative absolute biases (RABs), whereas the performance of ACIs is assessed in terms of their interval length (IL) and coverage probabilities (CPs). The findings show that the technique can deliver good estimation performance with small and intermediate sample sizes, and the estimates are more accurate when more failures are observed, showing the estimation method's efficiency.

Statistical Inference and Optimal Design of Accelerated Life Testing for the Chen Distribution under Progressive Type-II Censoring

This paper discusses statistical inference and optimal design of constant-stress accelerated life testing for the Chen distribution under progressive Type-II censoring. The scale parameter of the life distribution is assumed to be a logarithmic linear function of the stress level. The maximum likelihood estimates of the parameters are obtained. Then, the observed Fisher information matrix is derived and utilized to construct asymptotic confidence intervals. Meanwhile, the parametric bootstrap methods are provided for the interval estimation. In addition, the Bayes estimates under the squared error loss function are obtained by applying the Tierney and Kadane technique and Lindley’s approximation. As for the optimal design, D- and A-optimality criteria are considered to determine the optimal transformed stress level. Finally, the simulation is carried out to demonstrate the proposed estimation techniques and the optimal criteria, and a real data set is discussed.

Constant Stress Accelerated Life Test: Different Methods of Estimation Under the Exponentiated Power Lindley Distribution

Constant Stress Accelerated Life Test: Different Methods of Estimation Under the Exponentiated Power Lindley Distribution

Optimal Constant-Stress Accelerated Life Test Plans for One-Shot Devices with Components Having Exponential Lifetimes under Gamma Frailty Models

Optimal designs of constant-stress accelerated life test plans is one of the important topics in reliability studies. Many devices produced have very high reliability under normal operating conditions. The question then arises of how to make the optimal decisions on life test plans to collect sufficient information about the corresponding lifetime distributions. Accelerated life testing has become a popular approach to tackling this problem in reliability studies, which attempts to extrapolate from the information obtained from accelerated testing conditions to normal operating conditions. In this paper, we develop a general framework to obtain optimal constant-stress accelerated life test plans for one-shot devices with dependent components, subject to time and budget constraints. The optimal accelerated test plan considers an economical approach to determine the inspection time and the sample size of each accelerating testing condition so that the asymptotic variance of the maximum likelihood estimator for the mean lifetime under normal operating conditions is minimized. This study also investigates the impact of the dependence between components on the optimal designs and provides practical recommendations on constant-stress accelerated life test plans for one-shot devices with dependent components.

A Bayes Analysis and Comparison of Arrhenius Weibull and Arrhenius Lognormal Models under Competing Risk

The paper considers constant stress accelerated life test situations under a competing risk scenario. The different groups of experimental units are operated at different accelerated levels of stress and, at each level, the units are exposed to fail from two competing causes of failures. For modeling the failure times resulting from such a test, the paper considers two competing risk models. The first model is based on the minimum of two Weibull failure times whereas the second one is based on the minimum of two lognormal failure times. In order to study the effect of covariates on failure times, the scale parameter of component models in each modeling framework has been regressed using the Arrhenius relationship. The paper performs a complete Bayes analysis of both the considered models for a real dataset arising from a temperature accelerated life test experiment and compares the two models using a few standard Bayesian tools. Bayes analysis is done using vague but proper priors for the parameters. Moreover, the considered models result in to intractable posterior distributions and, therefore, the paper uses the Metropolis algorithm to draw the desired posterior based inferences. For censored data situations, however, the intermediate Gibbs steps are used as updating mechanism by defining full conditionals corresponding to unknown censored data. The plausibility of both the models for entertained dataset has also been checked before performing their comparison. A numerical example based on a real dataset is provided for illustration.

Estimation of Lindley constant-stress model via product of spacing with Type-II censored accelerated life data

Accelerated Life Test has been introduced as a tool to aid in obtaining sufficient failure time data of test units quickly and extrapolating lifetime information under use conditions. When the lifetime of units is distributed by the Lindley model, the estimations for the unknown parameters and the reliability function are established based on two frequentist methods and Bayesian method of estimation using Type-II censored data under constant-stress accelerated life test. In the frequentist methods, besides, the conventional likelihood-based estimation, another competitive method, known as the maximum product of spacing method is proposed for estimating the parameters and the reliability function under normal conditions as an alternative approach to the common likelihood method. In Bayesian estimation, both maximum likelihood and maximum product of spacing-based Bayesian estimates are discussed for unknown parameters as well as the reliability function. Moreover, the approximate confidence intervals and highest posterior density credible intervals of the parameters and reliability function are also obtained. Extensive Monte-Carlo simulation studies are conducted to evaluate the performance of the proposed estimates. Finally, to demonstrate the proposed methodology, two real-life accelerated life test data are considered to show the applicabilities of the proposed methods.