One-shot Devices Research Articles

Optimal Designs of Multiple Step-Stress Accelerated Life Tests for One-Shot Devices With Weibull Lifetime Distributions

Optimal Designs of Multiple Step-Stress Accelerated Life Tests for One-Shot Devices With Weibull Lifetime Distributions

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.

Analysis of one-shot device testing data under logistic-exponential lifetime distribution with an application to SEER gallbladder cancer data

In the literature, the reliability analysis of one-shot devices is found under accelerated life testing in the presence of various stress factors. The application of one-shot devices can be extended to the bio-medical field, where we often evidence that inflicted with a certain disease, survival time would be under different stress factors like environmental stress, co-morbidity, the severity of disease etc. This work is concerned with a one-shot device data analysis and applies it to SEER gallbladder cancer data. The two-parameter logistic-exponential distribution is applied as a lifetime distribution. For robust parameter estimation, weighted minimum density power divergence estimators (WMDPDE) is obtained along with the conventional maximum likelihood estimators (MLE). The asymptotic behaviour of the WMDPDE and the robust test statistic based on the density power divergence measure are also studied. The performances of estimators are evaluated through extensive simulation experiments. Later those developments are applied to SEER gallbladder cancer data. Citing the importance of knowing exactly when to inspect the one-shot devices put to the test, a search for optimum inspection times is performed. This optimization is designed to minimize a defined cost function which strikes a trade-off between the precision of the estimation and experimental cost. The search is accomplished through the population-based heuristic optimization method genetic algorithm.

Non-destructive one-shot device test under step-stress experiment with lognormal lifetime distribution

Dealing with censored data is an important concern in reliability and survival analysis. Non-destructive one-shot devices are an extreme case of interval censoring, wherein we only know if a device has failed or not before an inspection time. Besides, non-destructive one-shot devices are frequently highly reliable with large lifetimes, and then long experimentation times would be needed for inference under normal operating conditions. Alternatively, accelerated life tests (ALTs) shorten the lifetime of the devices by increasing one or more stress factors causing failure. Then, after suitable inference, results can be extrapolated to normal conditions. In particular, step-stress ALT designs increase the stress level at which devices are tested throughout the experiment at some fixed times. Under the non-destructive one-shot device set-up, the number of failures is recorded at some inspection times, including the times of stress change, then resulting in censored data. Among the most popular lifetime distributions used to analyze survival data, the lognormal distribution has hazard function with an increasing–decreasing behavior, which is encountered often in practice as units usually experience early failure and then stabilize over time in terms of performance. However, the classical maximum likelihood estimator (MLE) of parameters of the lognormal lifetime distribution may get highly influenced by data contamination. In this paper we propose a family of divergence-based robust estimators for non-destructive one-shot device step-stress experiments under the lognormal lifetime distribution. Further, from the robust estimators, a generalization of the popular Wald-type test statistic based on the MLE for testing composite null hypothesis is defined, resulting in a robust divergence-based family of test statistics.

Robust inference for destructive one-shot device test data under Weibull lifetimes and competing risks

Data obtained from destructive one-shot devices are usually studied through a binary response variable indicating failure or success of the device. But, in many practical situations, it may be more realistic to consider that the failure of the device may be due to several competing risks. In this paper, we develop divergence-based inference for one-shot device testing under Weibull lifetimes. This inference is shown to be more robust than the classical MLE-based inference, without a significant loss in efficiency when the data arise from the true model. A detailed simulation study is done to show the behaviour of the proposed estimation method and the associated inference. Finally, the developed methods are applied to a motor insulation dataset for illustrative purposes.

Power divergence approach for one-shot device testing under competing risks

Most work on one-shot devices assume that there is only one possible cause of device failure. However, in practice, it is often the case that the products under study can experience any one of various possible causes of failure. Robust estimators and Wald-type tests are developed here for the case of one-shot devices under competing risks. An extensive simulation study illustrates the robustness of these divergence-based estimators and test procedures based on them. A data-driven procedure is proposed for choosing the optimal estimator for any given data set which is then applied to an example in the context of survival analysis.

Misspecification of copula for one-shot devices under constant stress accelerated life-tests

Copula models have attracted significant attention in the recent literature for modeling multivariate observations. An essential feature of copulas is that they enable us to specify the univariate marginal distributions and their joint behaviors separately. This paper provides asymptotic results for misspecification of copula models, and examines the consequences and detection of misspecification in copula models under constant-stress accelerated life-tests for one-shot devices. The one-shot device is considered as a two-component system. The reliability is an important factor in lifetime data applications, and we focus on the effect of misspecification on the estimation of the reliability of one-shot devices. Moreover, the Akaike information criterion is used as a specification test for copula model validation. A simulation study is carried out to evaluate the effect of misspecification under the Gumbel-Hougaard, the Frank and the Clayton copulas incorporated with Weibull and gamma distributions as marginal distributions, in terms of asymptotic bias, asymptotic relative bias, and root mean square error.

On reliability analysis of one-shot devices with manufacturing defects

One-shot device test data have attracted increased attention. The working condition of a one-shot device is unknown until testing the device. In this paper, we consider one-shot device test data with defects that are induced in a realistic manufacturing process. The maximum likelihood approach is proposed for estimating the mean-time-to-failure. In this study, masked data are also considered when we cannot distinguish whether a failed device is originally defective or not. A Monte Carlo simulation study is conducted to evaluate the impacts of the masking effect on the estimation under different settings. Some practical guidelines and recommendations are provided.

Robust statistical inference for one-shot devices based on divergences

Robust statistical inference for one-shot devices based on divergences

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.

One-shot device test data analysis using non-parametric and semi-parametric inferential methods and applications

A one-shot device, such as an automobile airbag, electro-explosive unit or munition, is a product that can be used only once. Its actual lifetime is unobservable, rendering the corresponding reliability analysis quite challenging. In this paper, two non-parametric methodologies—maximum likelihood estimation via EM-algorithm and Nelson–Aalen based estimation are developed for identical testing environment on one-shot devices. The EM-algorithm is usually used for unobserved failure times under some specific parametric models. But, here the EM-algorithm is adopted for the number of failures in each time interval in a non-parametric manner. Next, a semi-parametric approach, based on proportional hazards assumption, is developed for nonidentical testing environments, such as under an accelerated life-test. A Monte Carlo simulation study is then carried out for evaluating the performance of the inferential methods developed here. Finally, two data sets are analyzed for illustrative purpose.

Inference for One-Shot Devices with Dependent k-Out-of-M Structured Components under Gamma Frailty

A device that performs its intended function only once is referred to as a one-shot device. Actual lifetimes of such kind of devices under test cannot be observed, and they are either left-censored or right-censored. In addition, one-shot devices often consist of multiple components that could cause the failure of the device. The components are coupled together in the manufacturing process or assembly, resulting in the failure modes possessing latent heterogeneity and dependence. In this paper, we develop an efficient expectation–maximization algorithm for determining the maximum likelihood estimates of model parameters, on the basis of one-shot device test data with multiple failure modes under a constant-stress accelerated life-test, with the dependent components having exponential lifetime distributions under gamma frailty that facilitates an easily understandable interpretation. The maximum likelihood estimate and confidence intervals for the mean lifetime of k-out-of-M structured one-shot device under normal operating conditions are also discussed. The performance of the proposed inferential methods is finally evaluated through Monte Carlo simulations. Three examples including Class-H failure modes data, mice data from ED01 experiment, and simulated data with four failure modes are used to illustrate the proposed inferential methods.

Reliability of one-shot device with generalized gamma lifetime under cyclic accelerated life-test

One-shot devices are products or equipments that can be used only once. A nature characteristic of one-shot devices is that they get destroyed immediately after their use, and therefore their actual lifetimes are never observable. The only information observed is the condition whether they worked or not at the time they are used. These days the quality of products are significantly improved, so that the information obtained under a normal test during a short time is quite limited. A typical test to induce more failures is the accelerated life-test, which is developed by increasing the stress levels under test. In this paper, we will investigate the reliability of one-shot devices with generalized gamma fatigue life under accelerated life-tests with various cyclic temperature fluctuations by assuming a Norris-Landzberg model. Generalized gamma involves many common lifetime distributions, such as gamma, Weibull, lognormal, and positive stable distributions, as special cases. Norris-Landzberg model takes not only temperature change, highest testing temperature, but also the cycling frequency into account when modeling the number of cycles-to-failure, resulting a generalized model with the well-known Coffin-Manson model and Coffin-Manson-Arrhenius model as special cases. Associated inferences are developed. The performance of the proposed model and inferential methods will be evaluated with simulation study and model discrimination. Finally, the chip-scale package solder joints data is analyzed to illustrate the considered model and inferential methods developed in this paper.

A Hierarchical Bayes Analysis and Comparison of PH Weibull and PH Exponential Models for One-Shot Device Testing Experiment

The one-shot devices are highly reliable and, therefore, accelerated life tests are often employed to perform the experiments on such devices. Obviously, in the process, some covariates are introduced. This paper considers the proportional hazards model to observe the effect of covariates on the failure rates under the assumption of two commonly used models, namely the exponential and the Weibull for the lifetimes. The Bayes implementation is proposed using the hybridization of Gibbs and Metropolis algorithms that routinely extend to missing data situations as well. The entertained models are compared using the Bayesian and deviance information criteria and the expected posterior predictive loss criterion. Finally, the results based on two real data examples are given as an illustration.

Appropriate strategy selection for reliability-centered maintenance of one-shot systems using fuzzy model

PurposeThis paper addresses special reliability-centered maintenance (RCM) strategies for one-shot devices by providing fuzzy inferences system with the assumption that, to data, there is no data available on their maintenance. As far as one-shot devices are concerned, the relevant data is inadequate.Design/methodology/approachIn this paper, a fuzzy expert system is proposed to effectively select RCM strategies for one-shot devices. In this research: (1) a human expert team is provided, (2) spatial RCM strategies for one-shot devices and parameters bearing upon those strategies are determined, (3) the verbal variables of the expert team are transformed into fuzzy sets, (4) the relationship between parameters and strategies are designed whereupon a model is developed by MATLAB software, (5) Finally, the model is applied to a real-life one-shot system.FindingsThe finding of this study indicates that the proposed fuzzy expert system can determine the parameters affecting the choice of the appropriate one-shot RCM strategies, and a fuzzy inference system can help for effective decision making.Originality/valueThe developed model can be used as a fast and reliable method for determining an appropriate one-shot RCM strategy, whose results can be relied upon with a suitable approximation in respect of the behavior test. To the best authors’ knowledge, this problem is not addressed yet.

Determination of warranty length for one-shot devices with Rayleigh lifetime distribution

An important goal for the producers is to stimulate the purchase intention of consumers so that the profit can be increased. An attractive warranty policy can not only represent the quality of product but also enhance the purchase desire of consumers. A long warranty length usually stands for high quality. However, it is not suitable for the producers to provide an unlimited warranty length. The main purpose of this paper is to establish an approach to determine the optimal warranty length based on one-shot device sample. The one-shot device data are collected under a multiple-level constant-stress accelerated life test. The lifetime distribution at each stress level is assumed to be Rayleigh. A utility function is provided to measure the monetary profit based on a free-replacement warranty policy. The optimization problem is studied under the Bayesian framework. A numerical example is studied for illustrating purpose. Finally, the sensitivity analysis is performed to see the influence of some parameters on the optimal warranty length.

Reliability estimation for one-shot devices under cyclic accelerated life-testing

A one-shot device, like an automobile airbag, is a product or an equipment that can be used only once. Better quality and longer lifetime of one-shot devices nowadays increase the cost of life test experiment under normal operating condition. Cyclic stress test, adopted in life-testing experiments by increasing stress levels to induce more failures, has been used to investigate the reliability analysis of one-shot devices based on Coffin–Manson principle. However, the Coffin–Manson model only considers temperature change in each cycle. Moreover, it assumes that the reliability is independent of the cycling frequency, which may not be a realistic assumption in practice. Birnbaum–Saunders distribution, originally developed to model fatigue failure under cyclic loading, has been used widely to model lifetime data. As the Norris–Landzberg model is proposed for modeling fatigue life due to cyclic temperature fluctuation, it is used in this work together with Birnbaum–Saunders distribution for modeling lifetimes of one-shot devices under accelerated life-tests with different cyclic temperature fluctuations. It contains the Coffin–Manson model as a special case. Inferential methods for model parameters, reliability and mean lifetime are developed in this paper. Simulation study and model discrimination are carried out to evaluate the performance of the proposed model and inferential methods. Finally, an example is presented to illustrate the model and the inferential results developed here.

A new approach to select the reliable suppliers for one-shot devices

A one-shot device is referred to as a unit that performs its function only once, hence a one-shot device cannot be used for testing more than once. Missiles, airbags of automobiles, magnetorheological fluids, and thermal batteries are some examples of one-shot devices. Usually, one-shot devices are kept in storage or in the stand-by condition and taken into use when required. As a matter of fact, proper operation of such devices at designated times becomes an important issue. Thus, choosing appropriate and reliable suppliers of one-shot devices in preventive maintenance periods can be regarded as a critical measure. This paper presents a new approach to provide resilience in supplier selection for one-shot devices and its subsystems in response to risks. In this research: (1) an expert team is set up having experience and expertise in one-shot systems, (2) risks of suppliers are estimated using satisfying and simple additive weighting (SAW) methods, (3) risk related to each equipment are determined by a cause and effect matrix, (4) after presenting a novel integrated approach, the best combination for one-shot equipment suppliers is selected by using fault tree analysis, (5) finally, to evaluate the performance of the proposed approach, a real case study is also used. This approach can therefore be used for determining faults in the entire system evaluated along with allocating suppliers to each equipment by considering suppliers and equipment risks as well as making and selecting scenarios.

Optimal designs and reliability sampling plans for one-shot devices with cost considerations

In this paper, we investigate some statistical inference, optimal design, and reliability sampling plan problems related to multiple constant-stress accelerated life test with one-shot device testing. At each stress-level combination, a generalized exponential lifetime distribution is considered. The scale parameter of the proposed distribution is assumed to be a log-linear function of stresses. To conduct a one-shot device accelerated life test more efficiently, one has to address the problem of determining optimal setting that produces the best estimation results. In practice, the experimental budget is always limited. The size of budget usually influences the decision of experimental setting and hence, influences the precision of estimation. Therefore, this paper is to determine the optimal experimental setting under D-optimality criterion with cost constraint. In addition, reliability sampling plan is an important statistical tool in the area of quality control. This paper is also to explore the optimal reliability sampling plan which minimizes the total experimental cost of a one-shot device accelerated life test with specified producer’s risk and consumer’s risk.

Optimal design of simple step-stress accelerated life tests for one-shot devices under Weibull distributions

One-shot devices, such as rockets, airbags of automobiles, and electro-explosive devices, can be used only once and will be extensively destroyed. The actual lifetimes of the devices cannot be observed, no matter whether the outcomes are successful or not. Step-stress accelerated life tests, which are useful for shortening the lifetimes of devices and quickly collecting lifetime data in a limited time, are widely adopted in engineering reliability studies. However, optimal designs of step-stress accelerated life tests for one-shot devices have not been well studied. This paper provides a procedure of determining optimal designs of simple step-stress accelerated life tests for one-shot devices by minimizing the asymptotic variance of the maximum likelihood estimate of reliability at normal operating conditions under Weibull distributions, with respect to inspection times and sample allocations. Comprehensive simulation studies are carried out to study the optimal designs under Weibull distributions with various hazard rates, showing that the optimal designs can maintain the simulated standard deviations at the nominal level of standard error. Besides, sensitivity analysis is conducted to evaluate the robustness of determined designs when mis-specification on planning values of model parameters exists. Finally, an application in grease-based magnetorheological fluids is presented to illustrate the optimal designs.