Design of statistically and energy-efficient accelerated life testing experiments

Lifetime data with covariates (e.g., temperature, humidity, and electric current) are frequently seen in science and engineering. An important example is accelerated life testing (ALT) data. In ALT, test units of a product are exposing to severer-than-normal conditions to expedite product failure. The resulting lifetime and/or censoring data with covariates are often modeled by a probability distribution along with a life-stress relationship. However, if the probability distribution and the life-stress relationship selected cannot adequately describe the underlying failure process, the resulting reliability prediction will be misleading. This paper develops a new method for modeling lifetime data with covariates using phase-type (PH) distributions and a general life-stress relationship formulation. A numerical study is presented to compare the performance of this method with a mixture of Weibull distributions model. This general method creates a new direction for modeling and analyzing lifetime data with covariates for situations where the data-generating mechanisms are unknown or difficult to analyze using existing parametric ALT models and statistical tools.

The optimal experimental design for an Accelerated Life Test (ALT) depends on the true life-stress relationship. It is however difficult to obtain exact coefficient values for an assumed regression model. Incorrect prior knowledge of the model coefficients may give rise to a very inefficient test outcome. Hence, it is beneficial to construct an ALT plan which is robust to the uncertainty of such planning values. In this paper, a new approach to construct a robust ALT plan is described by using a weighted clustering, which can be seen as a deterministic alternative to the original clustering approach. While the original clustering method requires a large number of locally optimal designs based on random samples of coefficient values, only a few of locally optimal designs are needed for the proposed method. A case study illustrates that the robust design constructed by the weighted clustering reveals more efficient measure in terms of the D-optimality criterion compared to the sampling based method while it substantially reduces the number of optimization procedures.

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.

The article is devoted to the formulation of the problem of improving methods for accelerated life tests of industrial equipment, as well as the problem of developing information and measurement systems for obtaining statistically significant measurement data during life tests. The service life of equipment can be determined through controlled operation. The difficulties of implementing such a method are shown. Using the method of accelerated life tests, the problem of reducing test time is solved, but the problem arises of determining a mathematical model for changing parameters to predict the life. The problems associated with the complexity of predicting equipment life using data from accelerated life tests are shown; problems with defining mathematical models for predicting the service life of various equipment elements, as well as equipment in general. Purpose, examples of mathematical models for resource assessment are given for such elements as bearings, blades of automotive turbochargers, seals and o-rings. It is shown that the wear of such equipment elements can be described by various mathematical models that take into account both the specific properties of the structure and the peculiarities of their operating conditions. It is indicated that as accelerated life tests are carried out, the mathematical forecast model can be refined and that in order to make a decision to change the model, the change in the controlled parameter must be statistically significant. The complexity of choosing a model that describes the equipment life is associated with the need to control a large number of parameters, carry out statistical processing of measurement results, control the impact on the test object and analyze the results of such impact. It is indicated that the listed set of actions is possible using information and measuring systems specially developed for these purposes.

An accelerated life test (ALT) is often well planned to yield the most statistical information given limited test resources. Nevertheless, ALT planning requires rough estimates of the model parameters as an input, called planning values. The discrepancy between the planning values and the true values may result in insufficient or even no failures at the low-stress level, making the subsequent data analysis difficult. Motivated by the need in the ALTs of data acquisition devices used in smart grids, an adaptive ALT scheme is proposed. The key idea is based on the observation that, when the product reliability is underestimated during the ALT design phase, it is unlikely to observe failures at the early stage of the test. Therefore, the low-stress level should be elevated to protect against insufficient failures. Under this adaptive ALT framework, order statistics techniques are used to derive the likelihood function by assuming a general log-location-scale distribution for the product lifetime. Confidence intervals for the parameters are constructed based on the large-sample approximation as well as the accelerated bootstrap method. A simulation study is conducted to demonstrate the advantages of the adaptive ALT compared with the simple constant-stress ALT. Its application is illustrated using the motivating example from smart grids.

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.

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.

Reliability design and case study of the domestic compressor subjected to repetitive internal stresses

Accelerated life testing (ALT) can be used to expedite failures of a product for predicting the product’s reliability under the normal operating conditions. The resulting ALT data are often modeled by a probability distribution along with a life-stress relationship. However, if the selected probability distribution cannot adequately describe the underlying failure process, the resulting reliability prediction would be misleading. It would be quite valuable if the distribution providing an adequate fit to the ALT data can be determined automatically. This chapter provides a new analytical method to assist reliability engineers in this regard. Essentially, this method uses Erlang-Coxian (EC) distributions, which belong to a particular subset of phase-type distributions, to characterize ALT data. Such distributions are quite efficient for approximating many non-negative distributions, such as Weibull, lognormal and gamma. The advantage of this method is that the best fit to the ALT data can be obtained by gradually changing the model structure, i.e., the number of phases of the associated continuous-time Markov chain (CTMC). To facilitate the implementation of this method, two statistical inference approaches are provided. First, a mathematical programming approach is formulated to simultaneously match the moments of the EC-based ALT model to the empirical moments at the corresponding test stress levels. This approach resolves the feasibility issue of the method of moments. In addition, the maximum likelihood estimation approach is presented, which can easily handle different types of censoring in ALT. Both approaches are accompanied with a stopping criterion for determining the number of phases of the resulting CTMC. Moreover, nonparametric bootstrap method is used to construct the pointwise confidence interval for the resulting reliability estimates. Numerical examples for constant-stress ALT with Type-I and multiple censoring schemes are provided to illustrate the capability of the method in modeling ALT data.

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 order to identify design weaknesses and improve reliability for a product as soon as possible, accelerated life-testing is extensively used. Accelerated life-testing (ALT) is either to accelerate the number of cycle per unit time (frequency acceleration) or to increase the stress-levels when operating (stress acceleration). In this paper, Constant-stress accelerated life-testing is used construct the accelerated function. Singly right censoring is considered to form the failure distributions at various stress levels. The characteristic parameters (location and scale) for each distribution are estimated by incorporating the methods of best linear unbiased estimators with the theory of order statistics. The scale parameter being minimum variance is derived out using the technique of Lagrange Multiplier. A log-linear life-stress relationship is suggested to formulate the accelerated equation. The unknown coefficients the accelerated equation are obtained using Gauss-Markov theorem. Once the scale parameter and the unknown coefficients determined, the life normal operating condition and the related reliability measures could then be evaluated. Typically, several cases involving various failure distributions are used as examples to depict the estimated procedures ALT.

Improving fatigue of mechanical systems such as freezer drawer subject to repetitive stresses

Degradation of TiAlN coatings by the accelerated life test using pulsed laser ablation

Thanks to continuously advancing technology and manufacturing processes, the products and devices are becoming highly reliable. However, performing the life tests of these products at normal operating conditions becomes extremely difficult, if not impossible, due to their long life spans. This can result in missed opportunities to introduce the products to the market in a timely manner and eventually loss of the market share. This problem is solved by accelerated life tests where the test units are subjected to higher stress levels than the normal usage level so that information on the lifetime parameters can be obtained more quickly. The lifetime at the design condition is then estimated through extrapolation using a regression model. In this work, the design optimization of a simple step‐stress accelerated life test under progressive type I censoring is studied with nonuniform step durations for assessing the reliability characteristics of a solar lighting device. Allowing the intermediate censoring to take place at the stress change time point, the nature of the optimal stress duration is demonstrated under various design criteria including D‐optimality, C‐optimality, A‐optimality, and E‐optimality. The existence of these optimal designs is investigated in detail for exponential lifetimes with a single stress variable, and the effect of the intermediate censoring proportion is assessed on the design efficiency.

Most of literature on accelerated life tests always assume that the domain of level of stress is known so that the life-stress relationship keeps unchanged as long as the level of stress applied is in this domain. However, in many practical situations the upper bound of such domain is usually unknown, especially for a new product. To consider such problem, we focus on the Weibull model and assume that, through some transformation, there is a linear relationship between the concerned parameter (involved in life distribution) and stress level. It is permitted that this relationship may change when the level of stress exceeds some bound, however its linearity is unchanged. To save time, we consider the data are either from type I or type II censored sampling. Some simulation results are also provided.