Stress Accelerated Life Test Research Articles

Statistical analysis for progressive stress accelerated life test with transmutation Weibull distribution

The Transmutation Weibull distribution is derived from the quadratic rank transmutation map of the Weibull distribution. This distribution integrates the high adaptability of the Weibull distribution in engineering and materials fields, and has great potential utility for modeling lifetime data. Therefore, the article explores the progressive stress accelerated life test model for components under the Transmutation Weibull distribution, conducts statistical analysis using the maximum likelihood estimation (MLE), Lindley’s approximation, and Markov Chain Monte Carlo (MCMC) algorithm to provide approximate estimates for the model. Finally, by comparing the results of numerical simulations, it is confirmed that the Bayesian estimation is more accurate and effective.

Reliability estimation of s-out-of-k system with Kumaraswamy distribution based on partially constant stress accelerated life tests

In reliability theory, the reliability inference for s-out-of-k systems holds significant importance. In this paper, we explore the estimation of reliability for s-out-of-k systems based on partially constant stress accelerated life tests. Assume that the latent failure times of the components follow the Kumaraswamy distribution. Maximum likelihood estimates for the unknown parameters are established, and their uniqueness is demonstrated. In addition, confidence intervals for the unknown parameters are constructed using the covariance matrix. Confidence intervals for the reliability functions are determined by the Delta method, while Bootstrap intervals are provided for comparison purposes. Subsequently, Bayesian point and interval estimates based on MCMC techniques considering different loss functions are discussed. Lastly, we conduct an extensive simulation study and analyse one real data set, which reveals that the Bayesian approach yields the best results.

Statistical analysis of double stress accelerated life testing under adaptive type-Ⅱ progressive censoring

Aiming at the traditional accelerated life test only considering the single stress and single failure cause, the inference method of double stress accelerated competing risks data is studied under the adaptive type-Ⅱ progressively censored and the life of test units follow Weibull distribution. The maximum likelihood estimations and the asymptotic confidence intervals of unknown parameters are obtained by using the Newton-Raphson iteration and asymptotic likelihood theory. A Gibbs sampling combining with Metropolis-Hasting algorithm method is developed to obtain Bayes estimations, and the Monte Carlo method is employed to construct the HPD credible intervals. The simulated results show that the present method has good statistical inference performance, meanwhile the failure sample size and the expected experimentation time have significant effect on the estimations.

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.

Cyclic stress accelerated life test method for mechatronic products

AbstractThe reliability requirements for mechatronics continue to increase. Traditional life test methods make it difficult to obtain the data required to assess or predict the reliability of these mechatronic products within a reasonable time. Accelerated life tests can speed up the failure process of the product by using accelerated stress conditions. And then test data is obtained to predict the reliable life of the product under normal service conditions through modeling and analysis. The test efficiency of the accelerated life tests is higher than that of the life test. So, the method of accelerated life tests has become a solution for life and reliability prediction of highly reliable and long‐life mechatronic products. However, mechatronic products usually undergo cyclic stress during service. The use of cyclic stress as an accelerating stress in accelerated life tests can provide a realistic representation of service conditions and achieve higher test efficiency. Cyclic stress accelerated life test is an accurate and efficient solution for predicting the life and reliability of such mechatronic products. Current relative research is focused on constant stress, step stress and sequential stress accelerated life tests. A great challenge in engineering is modeling and analysis of cyclic stresses accelerated life tests. In this paper, we first describe the cyclic stress accelerated life test profile and its key parameters, then propose model assumptions and establish a modelling and analysis method for cyclic stress accelerated life test data, followed by an illustrative example to apply and validate the proposed method. The research results can provide technical support for the life and reliability assessment of mechatronic products under cyclic stress service conditions.

Optimal test plans for accelerated life tests based on progressive type-I censoring with engineering applications

In reliability engineering studies, the accelerated life tests with optimal test design that balances cost constraints is particularly important since the lifetimes of electro-mechanical, electronic, and mechanical goods are typically modelled with this characteristic. Comparative optimal test plans for accelerated life tests are developed in a variety of applications, including engineering, biological, medical, and other related fields. In this study, we compare, under cost restriction with a specified budget, optimum multiple constant stress and step stress accelerated life tests based on progressive-type-I censoring. The goal is to assess the advantage provided by step-stress testing over constant-stress testing. In order to conduct an accelerated life test effectively, stress durations need to be carefully specified during the design stage due to limited resources in engineering practice. The estimated accuracy of the parameters of interest and the expense of the experiment are directly impacted by the stress durations. Under a prespecified budget and cost constraints, this article examines the optimal stress durations based on D-, E-, T-, C-, R-, and P-optimal criteria. These criteria are also contrasted together. We illustrate the application of the optimal durations using numerical and simulation examples. A study is conducted to determine how sensitive the optimal duration is to model parameter misspecification.

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.

Statistical Analysis of Step Stress Acceleration Test Data

The step stress accelerated life test is the selection of a set of accelerated stress levels that are higher than normal stress levels. At the beginning of the test, a certain number of samples are placed under a certain stress level for life testing. After some time, the stress level is increased, and this continues until a certain number of samples fail. In this paper, the acceleration coefficient is used to convert the failure data under each acceleration stress level into life data. The life distribution is exponential distribution, Weibull distribution, and logarithmic normal distribution. Under a certain number of samples, the statistical analysis of step stress accelerated life test data is completed, and the estimation of each reliability index is calculated.

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/

Reliability and Failure Mode of Ti-Base Abutments Supported by Narrow/Wide Implant Systems.

To assess the reliability and failure modes of Ti-base abutments supported by narrow and wide-diameter implant systems. Narrow (Ø3.5 × 10 mm) and wide (Ø5 × 10 mm) implant systems of two different manufacturers with internal conical connections (16°) and their respective Ti-base abutments (3.5 and 4.5 mm) were evaluated. Ti-base abutments were torqued to the implants, standardized metallic maxillary incisor crowns were cemented, and step stress accelerated life testing of eighteen assemblies per group was performed in three loading profiles: mild, moderate, and aggressive until fracture or suspension. Reliability for missions of 100,000 cycles at 100 and 150 N was calculated, and fractographic analysis was performed. For missions at 100 N for 100,000 cycles, both narrow and wide implant systems exhibited a high probability of survival (≥99%, CI: 94-100%) without significant differences. At 150 N, wide-diameter implants presented higher reliability (≥99%, CI: 99-100%) compared to narrow implants (86%, CI: 61-95%), with no significant differences among manufacturers. Failure mode predominantly involved Ti-base abutment fractures at the abutment platform. Ti-base abutments supported by narrow and wide implant systems presented high reliability for physiologic masticatory forces, whereas for high load-bearing applications, wide-diameter implants presented increased reliability. Failures were confined to abutment fractures.

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.

Single geometry abutment for narrow and extra-narrow implant systems: Survival and failure modes

The use of identical prosthetic components for all implant diameters could reduce the production costs by companies and the complexity of component selection for the clinician and his team. However, it would imply in reduction of thickness of the cervical walls of tapered internal connection implants, which could compromise the reliability of narrow and extra-narrow implants. Therefore, this study aims to evaluate the probability of survival and failure modes of extra-narrow implant systems with the same internal diameter as standard-diameter implants using the same prosthetic components. It was used eigth different implant system configurations, including narrow (Ø 3.3 mm) (N) extra-narrow (Ø 2.9 mm) (EN) and extra-narrow-scalloped (Ø 2.9 mm) (ENS) implants, both with cementable abutments (Ce) or titanium bases (Tib) and one-piece implants (Ø 2.5 mm and Ø 3.0 mm) (OP) (Medens, Itu, SP, Brazil), comprising the following groups: OP 3.0; OP 2.5; N Ce; N Tib; EN Ce, EN Tib, ENS-Ce and ENS-Tib. The implants were embedded using polymethylmethacrylate acrylic resin in a 15 mm matrix. Standardized maxillary central incisor crowns were virtually designed and milled to fit on the different studied abutments and cemented using a dual self-adhesive resin cement. The specimens were submitted to SSALT (Step Stress Accelerated Life Testing) at 15 Hz in water until failure or suspension of the test, until a maximum load of 500 N. Fractographic analysis of the failed specimens were realized in scanning electron microscopy. All implant systems demonstrated high probability of survival (90–100%) for missions at 50 and 100 N and values of characteristic strength superior to 139 N. Failure modes were restricted to the abutment in all the implant configurations tested. Therefore, the use extra-narrow implants with standardized prosthetic components for different implant diameters is a viable option for the replacement of anterior teeth.

Bayesian Inference Under Ramp Stress Accelerated Life Testing Using Stan

Bayesian Inference Under Ramp Stress Accelerated Life Testing Using Stan

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.

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.

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.

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

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.

Estimations of accelerated Lomax lifetime distribution with a dependent competing risks model under type-I generalized hybrid censoring scheme

In a reliability theory, the statistical inference under accelerated competing risks model have a great significance. This model proposes the assumption of independence of variables for convenience. But, in general this assumption doesn't agree with the nature of the problem at hand. In this paper, we proposed a step stress accelerated life testing (ALT) model on the dependent competing risk modes of life Lomax distribution (LD). The structural problem of the dependence between variables discussed copula approach. Also, we are considering the units of the product fails under two dependent fatal risks and the failure times accelerated under step stress ALTs and censored with type-I generalized hybrid censoring scheme (GHCS). The parameters of this model are estimated by maximum likelihood method. Also, the confidence intervals are discussed with asymptotic and two bootstrap confidence intervals. The Monte Carlo simulation study conducted to measure the quality of the proposed methods. Finally, we report some points to describe the numerical results.