Accelerated Life Test Plans for Predicting Warranty Cost

The basic idea of Accelerated Life Testing (ALT) is to expose a limited number of test units of a product to harsher-than-normal operating conditions to expedite failures. Based on the failure time data collected in a short time period, an ALT model incorporating the underlying failure time distribution and life–stress relationship can be developed for predicting the reliability of the product under the normal operating condition. However, ALT experiments often consume significant amounts of energy due to the harsher-than-normal operating conditions created and controlled by test equipment. In this article, a new ALT design methodology is developed that has the objective of improving the statistical and energy efficiency of ALT experiments. The resulting statistically and energy-efficient ALT plan depends not only on the reliability of the product to be evaluated, but also on the physical characteristics of the test equipment and its controller. Particularly, the statistical efficiency of each candidate ALT plan needs to be evaluated and the corresponding controller capable of providing the required stress loadings must be designed and simulated to evaluate the total energy consumption of the ALT plan. In this article, mathematical formulations, computational algorithms, and simulation tools are provided to handle such complex experimental design problems. Numerical examples are provided to demonstrate the effectiveness of the proposed methodology in energy reduction in ALT.

Accelerated life testing (ALT) is a method of reducing the lifetime of components through exposure to extreme stress. This method of obtaining lifetime information involves the design of a testing experiment, that is, an accelerated test plan. In this work, we adopt a simulation‐based approach to obtaining optimal test plans for constant‐stress accelerated life tests with multiple design points. Within this simulation framework, we can easily assess a variety of test plans by modifying the number of test stresses (and their levels) and evaluating the allocation of test units. We obtain optimal test plans by utilising the differential evolution (DE) optimisation algorithm, where the inputs to the objective function are the test plan parameters, and the output is the RMSE (root mean squared error) of out‐of‐sample (extrapolated) model predictions. When the life‐stress distribution is correctly specified, we show that the optimal number of stress levels is related to the number of model parameters. In terms of test unit allocation, we show that the proportion of test units is inversely related to the stress level. Our general simulation framework provides an alternative approach to theoretical optimisation, and is particularly favourable for large/complex multipoint test plans where analytical optimisation could prove intractable. Our procedure can be applied to a broad range of experimental scenarios and serves as a useful tool to aid practitioners seeking to maximise component lifetime information through accelerated life testing.

For the case where the lifetime at a stress level has a Weibull distribution, statistically optimal and practical accelerated life test plans are developed under the assumptions of intermittent inspection and Type-I censoring. For a statistically optimal plan the low stress level, the proportion of test units allocated, and the inspection times are determined such that the asymptotic variance of the maximum-likelihood estimator of a certain quantile at the use condition is minimized. Although the practical plan adopts the same design criterion, it involves three rather than two overstress levels and easily calculated inspection schemes. Despite some loss in efficiency the practical plan has several advantages over the statistically optimal one. For instance, the practical plan can provide means for checking the validity of the assumptions made, may reduce the danger of extrapolation, and is more convenient to determine and implement. Computational experiments are conducted to evaluate the relative efficiency of a practical plan to the corresponding statistically optimal plan. Guidelines for selecting an appropriate practical plan are also described with an example.

Optimal design of accelerated life tests for the Weibull distribution under periodic inspection and type I censoring

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.

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.

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.

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.

Accelerated Life Testing (ALT) is an efficient approach to obtain failure observations by subjecting the test units to stresses severer than design stresses and utilize the test data to predict reliability at normal operating conditions. ALT is usually conducted under constant-stresses which need a long time at low stress levels to yield sufficient failure data. Many stress loadings, such as ramp-stresses obtain failure times faster than constant-stresses but the accuracy of reliability predictions based on such loadings has not yet been investigated. We develop test plans under different stress applications such that the reliability prediction achieves equivalent statistical precision to that of the constant-stress. The research shows indeed there are such equivalent plans that reduce the test time, minimize the cost and result in the same accuracy of reliability predictions.

The article discusses the issues of risk management at all stages of the life cycle of nuclear power plants. The definition and classification by types of risks that arise during the stages of the life cycle and operation of difficult objects such as nuclear power plants. Risk is anything that has the potential to affect each stage of a facility’s life cycle, performance, longevity, safety, or project budget. Thus, risk management is the process of identifying, classifying, prioritizing and planning risks. This article not only discusses the identification and classification by types of risks that arise during the construction and operation of such complex facilities as nuclear power plants, but also describes the methods for assessing and managing risks, taking into account the specifics of the construction of nuclear power facilities. There are two methods of risk assessment: quantitative and qualitative. The article describes such Quantitative methods as “Scenario Technology”, “Method - Sensitivity Analysis”, “Diagramming Technique - Tree Analysis”, as well as such Qualitative risk assessment methods as “Assessment of the probability of risk and its impact”, “Evaluation Matrix probability/risk of impact”, “Probability and impact”, “Risk classification and assessment of risk urgency. As a result of the analysis of existing risk management methods at all stages of the life cycle, the following conclusions were drawn: Risk identification can occur at any stage of the life cycle of a nuclear power plant, even after completion of construction work and delivery of the project. The maximum number of risks for all stages of the NPP life cycle should be identified at the stage of Sitting and design. The article proposes the format of the risk register table, provides a risk classification scheme, and develops a risk management flow chart at the stages of the NPP life cycle.

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.

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.

Accelerated Life Test Plans and Age-Replacement Policy under Warranty on Burr Type-X distribution with Type-II Censoring

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.