Life Test Model Research Articles

Inference and Optimal Design on Partially Accelerated Life Tests for the Power Half-Logistic Distribution Under Adaptive Type II Progressive Censoring

This study explores accelerated life tests to examine the durability of highly reliable products. These tests involve applying higher stress levels, such as increased temperature, voltage, or pressure, that cause early failures. The power half-logistic (PHL) distribution is utilized due to its flexibility in modeling the probability density and hazard rate functions, effectively representing various data patterns commonly encountered in practical applications. The step stress partially accelerated life testing model is analyzed under an adaptive type II progressive censoring scheme, with samples drawn from the PHL distribution. The maximum likelihood method estimates model parameters and calculates asymptotic confidence intervals. Bayesian estimates are also obtained using Lindley’s approximation and the Markov Chain Monte Carlo (MCMC) method under different loss functions. Additionally, D- and A-optimality criteria are applied to determine the optimal stress-changing time. Simulation studies are conducted to evaluate the performance of the estimation methods and the optimality criteria. Finally, real-world datasets are analyzed to demonstrate the practical usefulness of the proposed model.

Bayesian estimation strategy for multi-component geometric life testing model under doubly type-1 censoring scheme

This study develops a Bayesian approach for estimating the unknown parameters of the 3-component mixture of geometric (3-CMG) model under a doubly type-I censoring scheme (DT1CS). The derivations of the Bayes estimators (BEs) and Bayes risks (BRs) are presented under square error loss function (SELF), precautionary loss function (PLF) and DeGroot loss function (DLF) using Beta prior under DT1CS. The strategy is evaluated through extensive simulation and real-life data analysis, showing the strength and efficiency of the newly proposed model. The study recommends that the SELF is the optimal choice for accurately estimating the unknown parameters of the 3-CMG model.

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 inference for dual constant-stress accelerated life test with exponential distribution and progressively Type-II censoring

Accelerated life test provides a feasible and effective way to rapidly derive lifetime information by exposing products to higher-than-normal operating conditions. However, most of the previous research on accelerated life test has focused on the application of a single stress factor and a traditional censoring scheme. This article considers the reliability inference for a dual constant-stress accelerated life test model with exponential distribution and progressively Type-II censoring. Point estimates for model parameters are provided using maximum likelihood estimation and the weighted least squares method based on random variable transformation. In addition, we construct asymptotic confidence intervals, approximate confidence intervals, and bootstrap confidence intervals for the parameters of interest. Finally, extensive simulation studies and an illustrative example are presented to investigate the performance of the proposed methods.

Inference of multi‐sample stage life testing model under Weibull distribution

AbstractIn this article we consider the meta‐analysis of stage life testing experiments. We propose a method to combine the data obtained from number of independent stage life testing experiments. We have assumed that there are only two stress levels for each stage life testing experiment and lifetime of the experimental units follows Weibull distribution at each stress level. The distributions under two stress levels are connected through Khamis–Higgings model assumption. We assume that the shape parameters of Weibull distribution are same for all the samples; however, the scale parameters are different. We provide the maximum likelihood estimation and the asymptotic confidence intervals of the model parameters. We also provide the Bayesian inference of the model parameters. The Bayes estimates and the associated credible intervals are obtained using Gibbs sampling technique since the explicit forms of the Bayes estimates do not exist. We have performed an extensive simulation study to see the performances of the different estimators, and the analyses of two data sets for illustrative purpose. The results are quite satisfactory.

Lifetime reliability modeling on EMC performance of digital ICs influenced by the environmental and aging constraints: A case study

This paper aims to develop the lifetime reliability model on electromagnetic compatibility (EMC) performance of the Atmel Attiny85 microcontroller integrated circuit (IC) chip samples, depending on the observed variation of the conducted immunity to the electromagnetic interference imposed by the combined influence of various environmental and aging (i.e., thermal and electrical voltage stress) constraints. A constant-stress accelerated degradation tests plan was designed and implemented by applying different constant thermal (i.e., 70 and 110 °C) and electrical voltage (i.e., 4 and 5 V) stress magnitude levels simultaneously in various multiple stress combinations. Direct power injection (DPI) conducted immunity tests were performed in nominal condition on all the programmed device under test (DUT) samples in both the fresh and aged states at various stress time duration. The best-fit EMC degradation paths were generated using regression analysis, followed by evaluating the pseudo time-to-failure (TTF) data and estimating the unknown parameters of the developed degradation path model. The performance metrics for lifetime reliability were evaluated by combining the Weibull distribution function with the generalized Eyring accelerated life test model. The maximum likelihood estimation method was utilized to estimate the relevant reliability model parameters. The developed reliability model was found to have the capability to estimate the electromagnetic unreliability against the lifetime TTF data of all the selected DUT samples with good precision and acceptable accuracy in both nominal and aging stress conditions. It is demonstrated that the non-failure probability of the DUT samples would remain at 1 for the first 1200 h, and that, under nominal conditions, the prediction of corresponding TTF data for all of those IC samples would fluctuate between 1400 and 1600 h.

Statistical Inference Using Partially Accelerated Life Test Model for the Weibull Population Mean Unified Hybrid Censored Data

In this paper, estimates of the parameters and the acceleration factor of a new distribution known as the Weibull Population Mean Distribution (WPMD) are explored. We propose the use of the model suggested by Abd-Elrahman [A better alternative to the generalized Bilal distribution: A new model and applications, Int. J. Reliab. Qual. Saf. Eng. 30(6) (2023) 2350027, doi: 10.1142/S0218539323500274] for estimating these parameters. To accomplish this, we employ the maximum likelihood estimation method via a Constant-Stress Partially Accelerated Life Test (CSPALT) model. In this study, we have utilized Unified Hybrid (UH) censored data obtained from the WPMD. Confidence intervals for the model parameters and the acceleration factor are constructed based on the approximate Fisher information matrix. The average and Mean Squared Error (MSE) of estimates are computed to evaluate the performance of the proposed method under the CSPALT model. Additionally, a real data set is provided for illustrative purposes, and a numerical analysis of the UH Censoring Scheme (UHCS) is carried out. Finally, concluding remarks are presented.

Exponentiated gamma constant-stress partially accelerated life tests with unified hybrid censored data: Statistical inferences

This study considers one of the partially accelerated life testing models, mainly a constant-stress approach with unified hybrid censored data. The data represents the lifetime of units following the exponentiated gamma distribution (EGD). The estimation techniques for the parameter of EGD and the acceleration factor are discussed, along with the maximum likelihood estimation technique, the Bayesian and E-Bayesian estimation. Utilizing the squared error loss (SEL) and LINEX loss functions, the E-Bayesian and Bayesian estimates are generated. For deriving the estimates of Bayesian and E-Bayesian approaches, we use the MCMC method. Real-world data is also provided for illustration. Furthermore, unified hybrid censoring schemes (HCSs) are examined to determine their effectiveness in the light of the results. In the end, we compare among the proposed methods during their findings. The study's findings demonstrate how well the suggested techniques work when utilizing unified HCS. The study also makes clear how important it is to adopt the CSPALT model, as it yields more failed things in a shorter amount of time than items with typical use situations. In conclusion, it is suggested that this research be used to tasks like industrial product reliability testing.

Statistical Analysis and Theoretical Framework for a Partially Accelerated Life Test Model with Progressive First Failure Censoring Utilizing a Power Hazard Distribution

Monitoring life-testing trials for a product or substance often demands significant time and effort. To expedite this process, sometimes units are subjected to more severe conditions in what is known as accelerated life tests. This paper is dedicated to addressing the challenge of estimating the power hazard distribution, both in terms of point and interval estimations, during constant- stress partially accelerated life tests using progressive first failure censored samples. Three techniques are employed for this purpose: maximum likelihood, two parametric bootstraps, and Bayesian methods. These techniques yield point estimates for unknown parameters and the acceleration factor. Additionally, we construct approximate confidence intervals and highest posterior density credible intervals for both the parameters and acceleration factor. The former relies on the asymptotic distribution of maximum likelihood estimators, while the latter employs the Markov chain Monte Carlo technique and focuses on the squared error loss function. To assess the effectiveness of these estimation methods and compare the performance of their respective confidence intervals, a simulation study is conducted. Finally, we validate these inference techniques using real-life engineering data.

A Bayesian generalized Eyring‐Weibull accelerated life testing model

AbstractIn this paper, a novel approach to a Bayesian accelerated life testing model is presented. The Weibull distribution is used as the life distribution and the generalized Eyring model as the time transformation function. This is a model that allows for the use of more than one stressor, whereas other commonly used acceleration models, such as the Arrhenius and power law models, incorporate one stressor. The use of the generalized Eyring‐Weibull model developed in this paper is demonstrated in a case study, where Markov chain Monte Carlo methods are utilized to generate samples for posterior inference.

Bayesian acceptance sampling plan for simple step-stress model

This paper presents a Bayesian acceptance sampling plan for simple step-stress life testing model, when the stress changing time is random, and the experimental units are subject to Type-II censoring. It is assumed that the lifetime distribution of the experimental item is exponential at each stress level with different scale parameters. We first present the Bayes decision function under a specified loss function. Based on the Bayes decision function, the optimal Bayesian sampling plan is determined by minimizing the Bayes risk. We also present some optimal Bayesian sampling plan under specific cases. We further provide order restricted optimal Bayesian sampling plan also. The Bayesian sampling plans presented in this paper are quite beneficial when the experimental items are highly reliable, which is quite common in present days.

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.

Order restricted inference for a multiple step‐stress model with long‐term survivors for a general family of distributions

AbstractIn this article, we propose a failure rate based step‐stress accelerated life testing (SSALT) model assuming that the time‐to‐event distribution belongs to a fairly general family of distributions and the underlying population consists of long term survivors. With increase in stress levels, it is expected that the mean time to the event of interest gets shortened leading to an order restriction among the mean times‐to‐event. We propose here a method of obtaining order restricted maximum likelihood estimators (MLEs) based on expectation maximization (EM) algorithm coupled with the method of generalized isotonic regression technique. Additionally, we address the testing of hypothesis problem for the presence of long term survivors in the underlying population based on both asymptotic and non‐asymptotic approaches. To illustrate the effectiveness of the proposed method, extensive simulation experiments are carried out and a real data set is analyzed.

Reliability prediction and evaluation model of smart electricity meter based on edge computing

In order to solve the problems of poor measurement stability and failure time of smart electricity meter in the process of life reliability analysis, this paper based on the least square method of regression analysis to estimate the parameters of Weibull distribution and accelerated life test model. The reliability index of smart electricity meter predicted by the new Weibull parameter estimation method is similar to that predicted by the point estimation method, but the reliability error of smart electricity meter predicted by the component stress method is large, indicating that there is an error between the actual operation of smart electricity meter and the predicted results in the design stage. The method proposed in this paper predicts the reliability of smart electricity meters under actual operation conditions, and predicts the correction factors of smart electricity meters' failure rate. The correction factors of various models are summarized to improve the reliability of smart electricity meters. In addition, the failure time before the smart meter is deduced and the failure rate of smart meter is more accurate.

Estimation of step-stress life testing model using time-censoring: A Bayesian approach

Accelerated life tests (ALTs) of highly reliable products or materials are effective testing techniques to gather failure data rapidly in a limited time period. Also, partially accelerated life tests (PALTs) can enable us to achieve this goal without putting all test units under severe conditions. This article considers both frequent and Bayesian estimations of the step-stress PALTs model using time-censored data from generalized exponential distribution (GED). The maximum likelihood and Bayesian estimates of the model parameters are obtained. The posterior means and posterior variances are computed under the squared error (SE) loss function using Lindley’s procedure. The performance of the estimators is evaluated numerically for different parameter values and different sample sizes via their mean squared error (MSE). In addition, the average confidence intervals lengths (ACIL) of the model parameters are also obtained. For illustrative purposes, a simulation study is given.

Bayesian Estimation of a Geometric Life Testing Model under Different Loss Functions Using a Doubly Type‐1Censoring Scheme

In this article, we consider the doubly type‐1 censoring scheme that researchers frequently use in clinical trials and lifetime experiments. The Bayesian paradigm will be used to estimate the parameters of the Geometric Lifetime Model (GLTM) using a doubly type‐I censoring scheme. Bayes estimators and their associated Bayes risks are examined in terms of closed‐form algebraic expressions. This research also includes a strategy for eliciting hyperparameters based on prior prediction distributions. To evaluate the strength and effectiveness of the suggested estimating approach, thorough simulation studies as well as real‐life data analysis are presented. The results depict that Squared Error Loss Function (SELF) is more efficient, and the Beta prior is suitable while estimating the parameter of GLTM.

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.

Optimal Test Plan of Step Stress Partially Accelerated Life Testing for Alpha Power Inverse Weibull Distribution under Adaptive Progressive Hybrid Censored Data and Different Loss Functions

Accelerated life tests are used to explore the lifetime of extremely reliable items by subjecting them to elevated stress levels from stressors to cause early failures, such as temperature, voltage, pressure, and so on. The alpha power inverse Weibull (APIW) distribution is of great significance and practical applications due to its appealing characteristics, such as its flexibilities in the probability density function and the hazard rate function. We analyze the step stress partially accelerated life testing model with samples from the APIW distribution under adaptive type II progressively hybrid censoring. We first obtain the maximum likelihood estimates and two types of approximate confidence intervals of the distributional parameters and then derive Bayes estimates of the unknown parameters under different loss functions. Furthermore, we analyze three probable optimum test techniques for identifying the best censoring under different optimality criteria methods. We conduct simulation studies to assess the finite sample performance of the proposed methodology. Finally, we provide a real data example to further demonstrate the proposed technique.

Bayesian analysis for multiple step-stress accelerated life test model under gamma lifetime distribution and type-II censoring

PurposeThe step-stress accelerated test is the most appropriate statistical method to obtain information about the reliability of new products faster than would be possible if the product was left to fail in normal use. This paper presents the multiple step-stress accelerated life test using type-II censored data and assuming a cumulative exposure model. The authors propose a Bayesian inference with the lifetimes of test item under gamma distribution. The choice of the loss function is an essential part in the Bayesian estimation problems. Therefore, the Bayesian estimators for the parameters are obtained based on different loss functions and a comparison with the usual maximum likelihood (MLE) approach is carried out. Finally, an example is presented to illustrate the proposed procedure in this paper.Design/methodology/approachA Bayesian inference is performed and the parameter estimators are obtained under symmetric and asymmetric loss functions. A sensitivity analysis of these Bayes and MLE estimators are presented by Monte Carlo simulation to verify if the Bayesian analysis is performed better.FindingsThe authors demonstrated that Bayesian estimators give better results than MLE with respect to MSE and bias. The authors also consider three types of loss functions and they show that the most dominant estimator that had the smallest MSE and bias is the Bayesian under general entropy loss function followed closely by the Linex loss function. In this case, the use of a symmetric loss function as the SELF is inappropriate for the SSALT mainly with small data.Originality/valueMost of papers proposed in the literature present the estimation of SSALT through the MLE. In this paper, the authors developed a Bayesian analysis for the SSALT and discuss the procedures to obtain the Bayes estimators under symmetric and asymmetric loss functions. The choice of the loss function is an essential part in the Bayesian estimation problems.

Accelerated Life Test and Life Model Development of Ni-Cr-Based Quartz Tube Heater for Home Appliances

Purpose: This study identified the potential failure mechanisms of a quartz tube heater and established an accelerated life test (ALT) method through the two-stage quality function deployment (QFD) method.BRMethods: The equipment for the ALT was developed independently. The Weibull distribution was used as life distribution and the inverse power model was employed as the accelerated model. An optical microscope, field effect scanning electron microscope, and an energy dispersive spectrometer were used to analyze the failure of the failed quartz tube heater.BRResults: The acceleration model was confirmed as an inverse power model with a material constant of 15.7. From the failure analysis, the failure mechanism was identified to be the moisture penetrated by the breathing of the quartz tube heater corroded the Ni–Cr stranded wire.BRConclusion: Since the quartz tube heater continues to be widely used for industrial and home applications, it can be used as a helpful device in establishing reliability test methods for quartz tube heaters in the future. The established acceleration model can be applied not only to the quartz tube heater but also to the heater with a metal heating wire.