A General Simulation‐Based Optimisation Framework for Multipoint Constant‐Stress Accelerated Life Tests

One may think that the design of bivariate accelerated life tests (ALTs) with one main effect and one interaction effect can be extended directly from the design proposed by Escobar and Meeker (1995) for bivariate ALTs with no interaction between the two variables. However, it can be shown that the “split” method, which is used in pursuing bivariate ALTs designs with no interaction term, can not be used here directly since it is found that the standardized test region is now a trapezoid instead of a square. In this article, this problem is solved. Test plans are developed to determine test conditions and allocate test units for constant-stress ALTs with Type-I censoring. The test criterion is to minimize , which is the asymptotic variance of the maximum likelihood estimator of the 100pth quantile of the lifetime distribution. An example is presented to illustrate the proposed approach.

The optimal plan of a time-censored accelerated life test (ALT) depends on unknown parameters in the ALT model. The general strategy for coping with this problem is to replace the unknown parameters with their a priori estimated values, after which we can design test plans that are robust to deviations of the estimated values. In an ALT with log-location-scale lifetime distribution and linear acceleration relation function, the slope parameter of the acceleration relation function usually has the highest uncertainty. Instead of prespecifying the slope parameter in the ALT design, in this article, we propose a new design criterion that minimizes the risk of misclassifying whether the product's pth quantile meets the design specification. Through a case study of a circular electric connector, we illustrate the proposed method, and compare it with other test criteria. The comparison result shows that the proposed plan exhibits good performance in both estimating and s-testing the product's pth quantile.

Warranty is an important sales feature for many products, especially consumer products. Manufacturers usually want to predict the warranty cost as early as possible for various purposes. This can be done by using the accelerated life tests conducted in the early stages of the product life cycle. This paper describes a method for predicting the warranty cost, and its confidence interval for a product population that will experience varying stress levels in the field. The paper also presents 3-level best compromise accelerated life test plans. The plans choose the optimal values of the low stress level and the corresponding sample allocation to minimize the asymptotic variance of the maximum likelihood estimate of the warranty cost. An application example is presented to illustrate the test plans. The test plans are robust against the misspecification of the warranty length, and other parameters.

Accelerated Degradation Testing (ADT) is proposed as a means to obtain degradation data of products in a short time period and extrapolate the lifetime and reliability of products under use condition. There are two optimality criterion could be defined in designing an accelerated test plan. Criterion D : some testing planners are interest in the prediction of products' lifetime, so their objective is minimizing the variance (or asymptotic variance) of the MLE of parameter Θ which can include the quantiles and the mean of the lifetime distribution at a pre-specified stress level. Criterion II : if engineers are interest in the estimation of model parameters, their objective may be maximizing the determinant of the Fisher information matrix, which has a reciprocal relationship with variance-covariance matrix. This criterion is D-optimality, wherein the `information' is maximized and the `variance' is minimized at the same time. Criterion I for Step Stress Accelerated De gradation Testing (SSADT) planning is already proposed, however Criterion II (D-optimality) is seldom discussed. In this study, a method to optimal design for SSADT based on D-optimality is present. First, drift Brownian motion is applied to describe a typical SSADT problem. Next, under the constraint that the total experimental cost does not exceed a predetermined budget, the optimal plan gives sample size, total testing time, stress levels and testing time at each stress level. Finally, an example is used to illustrate this test planning method.

A newly designed hinge kit system (HKS) of a commercial refrigerator was subjected to a robust reliability methodology during the design phase of the system. This methodology included setting the overall parametric accelerated life test (ALT) plan of product and identifying failure mechanisms and modes in field. The ALT included a sample size equation to improve several of the HKS design parameters. Reliability of the new HKS was targeted to be 10 years over B1. Failure sites in the HKS were identified through returned products from the field. The first ALT confirmed a failure that occurred at the housing of HKS. The missing design parameters of HKS housing for the refrigerator were that it had no support ribs in the original design. The supporting structure of HKS in the refrigerator was modified based on the action plan. Cracks were identified in a second ALT that was generated in the torsional shaft. Due to it having squared off corners, the HKS torsional shaft did not have not enough strength to withstand repetitive stresses. The shaft was modified as a consequence of the ALTs. The reliability of redesigned HKS is now guaranteed as B1 10 years. The design methods - load analysis and three ALTs were very effective in identifying the missing design parameters during the design phase. The robust design method presented in this paper might be applicable to the other mechanical systems.

Accelerated life tests (ALTs) are widely used in industry and many optimal ALT test plans are developed in literature. To achieve an efficient optimal test plan, one needs to make sure that the planning values used in the test planning are not far away from the true parameters, which is challenging because lifetime data are not collected yet in the planning stage to estimate the true parameters. To overcome the weakness, sequential designs are developed and the parameter estimates are updated during the sequential testing process. Due to the sequential nature, one drawback of the sequential strategy is that it usually requires a long total testing time (TTT). Motivated by industrial needs, we propose batch sequential design (BSD) in ALT setting, in which multiple units are tested simultaneously while sequential parameter updates are also made. The proposed BSD for ALT can not only reduce the TTT but also preserves the advantage of sequential designs. After proposing two types of BSD strategies, we use a comprehensive simulation study to demonstrate the advantages of the proposed BSD in ALT setting. We also develop a method to find the optimal batch size which is essential for the deployment of the BSD in practice.

Estimating the long term performance of highly reliable products has been a difficult problem as accelerated life testing (ALT), which involves testing at highly elevated stresses, often results in too few failures for drawing useful inferences. To overcome this problem, accelerated degradation testing (ADT) has been proposed as a means to predict performance for highly reliable products. It requires one to identify a performance measure that would exhibit degradation and to monitor it over time. Product reliability can then be inferred from the degradation paths without the need of observing actual failures. Although physical failures are not needed in ADT, one usually defines failure as the first time when the degradation process exceeds a pre-specified threshold, so that the degradation path can be correlated to product reliability. As a result, reliability information of a product is embedded in degradation paths of units tested under ADT. In this paper, we look into planning of an ADT in which the test stress is increased in steps from lower stress to higher stress during the test, so that specimens are gradually conditioned to the stressed environment thus avoiding over-stressing. Our objective is to minimize the cost of testing, which is a function of sample size, test duration and number of inspections, as well as obtaining a reliability estimate of a requisite level of precision. Data from degradation paths are used to characterize the appropriate stochastic model underlying the product degradation process. We then derive the maximum likelihood estimators and the mean life at the use stress and its asymptotic variance. This variance is then used as a constraint, in a test plan which minimizes the testing cost. The optimal test plan gives the optimal sample size, number of inspections at each intermediate stress level and number of total inspections.

In the case of operating conditions in a much shorter time, the accelerated life test models are commonly used method since these models let the experimenters control the higher stress levels to be used for components or items in the life tests. Among different accelerated life test methods, constant stress accelerated life test models have a relationship between “failure time” and “stress” and these models are quite popular since they help the experimenters save time and cost. In this study, we evaluate the performances of the parameter estimations of the two-parameter bathtub-shaped lifetime distribution introduced by Chen (Stat Probab Lett 49(2):155–161, 2000) under the constant stress accelerated life test model using the well-known eight different inference methods. Then, we investigate the optimal stress levels using some popular criteria. Then, the performances of the estimations are compared with simulation schemes. Simulation results showed that the maximum likelihood method provides better estimation performances than others. The estimation performances of the other methods can be changed according to the stress level of the accelerated life test model. Further, it is observed that increasing stress levels provide optimal accelerated life test schemes under fixed first stress levels. Finally, we use a real data example to illustrate the theoretical outcomes.

This article describes Bayesian methods for accelerated life test planning with one accelerating variable, when the acceleration model is linear in the parameters, based on censored data from a log-location-scale distribution. We use a Bayesian criterion based on estimation precision of a distribution quantile at a specified use condition to find optimum test plans. We also show how to compute optimized compromise plans that satisfy practical constraints. A large-sample normal approximation provides an easy-to-interpret yet useful simplification to this planning problem. We present a numerical example using the Weibull distribution with type I censoring to illustrate the methods and to examine the effects of the prior distribution, censoring, and sample size. The general equivalence theorem is used to verify that the numerically optimized test plans are globally optimum. The resulting optimum plans are also evaluated using simulation.

Accelerated life testing (ALT) is widely used in industry to obtain the lifetime estimate of a product which is expected to last years or even decades. It is important to find an effective experimental design of ALT with the consideration of certain optimality criteria. In this paper, we discuss a new approach to designing ALT test plans when readout data (i.e., interval censoring) are collected. We utilize the proportional hazard (PH) model for a failure time distribution, and formulate a generalized linear model (GLM) for censored data. The optimal design is obtained such that the prediction variance of the expected product lifetime at the product's use condition is minimized.

In today's global environment, accelerated life testing is becoming a competitive advantage when time spent from conceptual stage to the final product development needs to be minimized (project costs and development time) in order to be successful. Using accelerated life testing techniques for mechanical and structural applications have strong challenges when defining the actual operational loading but also the fatigue lifemodel to represent actual field performance. Such common problems as well as some helpful strategies using accelerated life testing are presented for faster planning of structural testing. Examples from the transport refrigeration industry are used to demonstrate the utility of this strategy. Loading and test fixtures were designed as needed to simulate the normal operating levels and to accelerate specific failure modes while replicating field performance. In conclusion the test and analysis were effectively used to increase the degree of reliability improvements and to reduce the total number of test hours resulting in a shorter design cycle.

This study examines the estimation of parameters for the Shifted Weibull Distribution (SWD) using several robust metaheuristic algorithms, with a focus on enhancing precision and reliability in investment data analysis. Utilizing investment return data from the Malaysian property sector, we evaluate the performance of five metaheuristic models: Election Algorithm (EA), Artificial Dragonfly Algorithm (ADA), Genetic Algorithm (GA), Differential Evolution (DE), and Ant Colony Optimization (ACO). The evaluation criteria include Bayesian Information Criterion (BIC), Root Mean Squared Error (RMSE), and accuracy. Results reveal that EA consistently outperforms other models, achieving the lowest BIC value of 147.2 and an impressive accuracy rate of 94.90% at a sample size of 1,000. The Genetic Algorithm (GA) shows the lowest RMSE of 0.99, indicating strong predictive performance. Tukey's HSD test highlights significant accuracy variations among the models, with EA and GA notably outperforming ACO and DE. However, RMSE and BIC metrics do not demonstrate clear variations among the models. These findings underscore the superior performance of the EA model in the context of SWD parameter estimation, making it the preferred choice for modeling investment return data. Future research should explore additional factors influencing model performance and validate these models with diverse real-world datasets to further enhance their applicability in financial decision-making.

Windy conditions challenge precise payload delivery by unmanned aerial vehicle (UAV), but wind variability defined within lower and upper bounds at any instance can assist to optimize candidate release points. Therefore, at first, it is crucial to collect candidate release points caused by wind variability. In this paper, knowledge of candidate release points is drawn by applying ballistic equation. The knowledge about the points then initializes differential evolution (DE) optimization to search an optimum payload release point. Therefore, the proposed method is named as DE with knowledge‐based initialization (KI), that is, DE‐KI. Simulations demonstrate DE‐KI's effectiveness by measuring landing error as root mean square error (RMSE) and achieve an average reduction in RMSE compared to existing methods. For instance, DE‐KI outperforms two other alternative approaches by an average RMSE of and with varying payload weight, and and with varying wind speed.

In an accelerated life test, inferences on extreme quantiles of the lifetime distribution at the use condition are obtained via extrapolation in two directions: in time, and in stress levels. Extrapolation is known to highly depend on the working model, and ignoring model uncertainty can result in over-confidence. This paper explores the use of Bayesian model averaging for estimating quantiles in an accelerated life test. Two of the most commonly used lifetime regression models, lognormal, and Weibull log-location-scale regression models, are considered in this paper as candidate models. To illustrate, we analyse complementary metal-oxide semiconductor integrated circuit data. We also construct a simulation study to compare the performance of the Bayesian model averaging -credibility intervals with other exiting interval estimators. The simulation study shows that, for estimating extreme quantiles, both the standard Bayesian and the maximum likelihood approaches can lead to an over-confident result, and Bayesian model averaging provides a -credibility interval with a wider average length, but a more accurate coverage probability.

: In this paper we propose a model for accelerated life testing which differs from those considered in the past. Our model does not require thd usual assumptions about the failure distributions and the acceleration functions. Our approach is Bayesian, and depends on the estimation of ordered failure rate functions at different stress levels. Since our model is nonprametric, and our approach is quite pragmatic, our results should be of use to engineers working on accelerated life tests, and biometricians involved in carcinogenic experiments. (Author)