Using Accelerated Life Tests Results to Predict Product Field Reliability

Accelerated life tests (ALTs) provide timely assessments of the reliability of materials, components, and subsystems. ALTs can be run at any of these levels or at the full-system level. Sometimes ALTs generate multiple failure modes. A frequently asked question near the end of an ALT program is “what do these test results say about field performance?” ALTs are carefully controlled, whereas the field environment is highly variable. For example, products in the field have different average use rates across the product population. With good characterization of field use conditions, it may be possible to use ALT results to predict the failure time distribution in the field. When such information is not available but both life test data and field data (from, e.g., warranty returns) are available, it may be possible to find a model to relate the two data sets. Under a reasonable set of practical assumptions, this model then can be used to predict the failure time distribution for a future component or product operating in the same use environment. This paper describes a model and methods for such situations. The methods are illustrated by an example to predict the failure time distribution of a newly designed product with two failure modes. Supplemental material for this article is available online at the Technometrics website.     

COMPARISONS OF OPTIMAL ACCELERATED TEST PLANS FOR ESTIMATING QUANTILES OF LIFETIME DISTRIBUTION AT THE USE CONDITION

Accelerated life tests (ALTs) and accelerated degradation tests (ADTs) are widely used for the reliability assessment of components or materials. In an ALT, failure times of test units are observed while in an ADT the failure-causing performance characteristic is measured. This article develops optimal ALT and ADT plans for estimating the qth Quantile of the lifetime distribution at the use condition, the latter being an extension of Park and Yum. Then, the two test plans are compared in terms of the asymptotic efficiency in estimating the qth quantile and of the robustness to the mis-specifications of failure probabilities. Computational results show that the ADT provides a more precise estimator than the corresponding ALT, especially when the failure probabilities are small. Concerning the robustness of a test plan to the departures of the guessed failure probabilities from their true values, neither plan completely dominates the other.     

Design of PH-based accelerated life testing plans under multiple-stress-type

Accelerated life testing (ALT) is used to obtain failure time data quickly under high stress levels in order to predict product life performance under design stress conditions. Most of the previous work on designing ALT plans is focused on the application of a single stress. However, as components or products become more reliable due to technological advances, it becomes more difficult to obtain significant amount of failure data within reasonable amount of time using single stress only. Multiple-stress-type ALTs have been employed as a means of overcoming such difficulties. In this paper, we design optimum multiple-stress-type ALT plans based on the proportional hazards model. The optimum combinations of stresses and their levels are determined such that the variance of the reliability estimate of the product over a specified period of time is minimized. The use of the model is illustrated using numerical example, and sensitivity analysis shows that the resultant optimum ALT plan is robust to the deviation in model parameters.     

Discrimination between accelerated life models via Approximate Bayesian Computation

Accelerated life testing (ALT) is widely used in high-reliability product estimation to get relevant information about an item's performance and its failure mechanisms. To analyse the observed ALT data, reliability practitioners need to select a suitable accelerated life model based on the nature of the stress and the physics involved. A statistical model consists of (i) a lifetime distribution that represents the scatter in product life and (ii) a relationship between life and stress. In practice, several accelerated life models could be used for the same failure mode and the choice of the best model is far from trivial. For this reason, an efficient selection procedure to discriminate between a set of competing accelerated life models is of great importance for practitioners. In this paper, accelerated life model selection is approached by using the Approximate Bayesian Computation (ABC) method and a likelihood-based approach for comparison purposes. To demonstrate the efficiency of the ABC method in calibrating and selecting accelerated life model, an extensive Monte Carlo simulation study is carried out using different distances to measure the discrepancy between the empirical and simulated times of failure data. Then, the ABC algorithm is applied to real accelerated fatigue life data in order to select the most likely model among five plausible models. It has been demonstrated that the ABC method outperforms the likelihood-based approach in terms of reliability predictions mainly at lower percentiles particularly useful in reliability engineering and risk assessment applications. Moreover, it has shown that ABC could mitigate the effects of model misspecification through an appropriate choice of the distance function.     

A Bayesian framework for accelerated reliability growth testing with multiple sources of uncertainty

Reliability growth tests are often used for achieving a target reliability for complex systems via multiple test‐fix stages with limited testing resources. Such tests can be sped up via accelerated life testing (ALT) where test units are exposed to harsher‐than‐normal conditions. In this paper, a Bayesian framework is proposed to analyze ALT data in reliability growth. In particular, a complex system with components that have multiple competing failure modes is considered, and the time to failure of each failure mode is assumed to follow a Weibull distribution. We also assume that the accelerated condition has a fixed time scaling effect on each of the failure modes. In addition, a corrective action with fixed ineffectiveness can be performed at the end of each stage to reduce the occurrence of each failure mode. Under the Bayesian framework, a general model is developed to handle uncertainty on all model parameters, and several special cases with some parameters being known are also studied. A simulation study is conducted to assess the performance of the proposed models in estimating the final reliability of the system and to study the effects of unbiased and biased prior knowledge on the system‐level reliability estimates.     

Comparison of optimal accelerated life tests with competing risks model under exponential distribution

Accelerated life testing (ALT) is the process of testing products by subjecting them to strict conditions in order to observe more failure data in a short time period. In this study, we compare the methods of two-level constant-stress ALT (CSALT) and simple step-stress ALT (SSALT) based on competing risks of two or more failure modes with independent exponential lifetime distributions. Optimal sample size allocation during CSALT and the optimal stress change-time in SSALT are considered based on V- and D-optimality , respectively. Under Type-I censoring, numerical results show that the optimal SSALT outperforms the optimal CSALT in a wide variety of settings. We theoretically also show that the optimal SSALT is better than the optimal CSALT under a set of conditions. A real data example is analyzed to demonstrate the performance of the optimal plans for both ALTs.     

Accelerated Life Testing (ALT) Design Based on Computational Reliability Analysis

Accelerated life testing (ALT) design is usually performed based on assumptions of life distributions, stress–life relationship, and empirical reliability models. Time‐dependent reliability analysis on the other hand seeks to predict product and system life distribution based on physics‐informed simulation models. This paper proposes an ALT design framework that takes advantages of both types of analyses. For a given testing plan, the corresponding life distributions under different stress levels are estimated based on time‐dependent reliability analysis. Because both aleatory and epistemic uncertainty sources are involved in the reliability analysis, ALT data is used in this paper to update the epistemic uncertainty using Bayesian statistics. The variance of reliability estimation at the nominal stress level is then estimated based on the updated time‐dependent reliability analysis model. A design optimization model is formulated to minimize the overall expected testing cost with constraint on confidence of variance of the reliability estimate. Computational effort for solving the optimization model is minimized in three directions: (i) efficient time‐dependent reliability analysis method; (ii) a surrogate model is constructed for time‐dependent reliability under different stress levels; and (iii) the ALT design optimization model is decoupled into a deterministic design optimization model and a probabilistic analysis model. A cantilever beam and a helicopter rotor hub are used to demonstrate the proposed method. The results show the effectiveness of the proposed ALT design optimization model. Copyright © 2015 John Wiley & Sons, Ltd.     

Multi-state reliability demonstration tests

ABSTRACT

Reliability demonstration tests have important applications in reliability assurance activities to demonstrate product quality over time and safeguard companies’ market positions and competitiveness. With greatly increasing global market competition, conventional binomial reliability demonstration tests based on binary test outcomes (success or failure) at a single time point become insufficient for meeting consumers’ diverse requirements. This article proposes multi-state reliability demonstration tests (MSRDTs) for demonstrating reliability at multiple time periods or involving multiple failure modes. The design strategy for MSRDTs employs a Bayesian approach to allow incorporation of prior knowledge, which has the potential to reduce the test sample size. Simultaneous demonstration of multiple objectives can be achieved and critical requirements specified to avoid early/critical failures can be explicitly demonstrated to ensure high customer satisfaction. Two case studies are explored to demonstrate the proposed test plans for different objectives.     

Planning constant-stress accelerated life tests with multiple stresses based on D-optimal design

With the rapid technological advances, products are becoming more reliable. Then, multistress accelerated life testing (MALT) has been adopted in engineering to obtain failure information in a limited time. In order to make the testing procedure more efficient, it is necessary to better design the test plan. However, to date, relevant research on planning of MALT is limited. Multiple stresses will lead to plenty of stress-level combinations that require too much cost and time to implement. Besides, there may be interactions among multiple stresses, which need more experiments for parameter estimation. To solve these problems, we propose a novel planning method for constant-stress MALT under lognormal distribution using D-optimal design, which can reduce required test points efficiently and deal with second-order effects in models. In ALT, the log-linear model is often used to describe the life-stress relationship. Hence, D-optimal design is adopted in this paper to select test points from the whole test region. Then, optimal unit allocation plans are formulated under V/D-optimality criterion, respectively, where type I and type II censoring are both discussed. A real case of light-emitting device (LED) is presented to compare the proposed approach with other two existing methods. The results show that the proposed method performs better than other two existing methods both in prediction accuracy and estimation precision. Moreover, a sensitivity analysis reveals the robustness of the optimal plans determined by the proposed method.     

Reliability design and case study of refrigerator parts subjected to repetitive loads under consumer usage conditions

When newly designed refrigerator parts failed due to repetitive loads under consumer usage conditions in the field, a general method for reliability design was proposed. A newly designed refrigerator compressor system that brings greater energy efficiency to side-by-side (SBS) refrigerators was studied. The laboratory failure mode and mechanism of the compressor was a stopping nose due to design flaws. The data on the failed products in the field, accelerated life tests (ALT) and corrective action plans were used to identify the key control parameters for the mechanical compressor system. The missing controllable design parameters of the compressor system in the design phase were the gap between the frame and the upper due to the stator frame shape. After a tailored series of accelerated life tests with corrective action plans, the B₁ life of the new compressor system is now guaranteed to be over 10 years with a yearly failure rate of 0.1%.     

Improving the reliability of a water dispenser lever in a refrigerator subjected to repetitive stresses

Based on field data and a tailored set of accelerated life testing, the dispenser lever of the water dispensing system in a bottom-mounted freezer (BMF) was redesigned. Using force and moment balances, the simple mechanical loads of the dispensing process were analyzed. The failure modes and mechanisms found experimentally were similar to those of the failed samples returned from the field. Failure analysis, accelerated life testing (ALT) and corrective action plans were used to identify the key control parameters and level of the mechanical dispenser lever. The missing controllable design parameters of the dispenser lever in the design phase included corner rounding, rib thickness, and front lever thickness. The B₁ life of the new design is now guaranteed to be over 10 years with a yearly failure rate of 0.1%.     

Multiple dependent state repetitive group sampling plan for Burr XII distribution

In material engineering application, the failure time of material due to weakness in material (fatigue) is usually caused by repeated variations of stress. The failure time is modeled by statistical distributions. In this article, an attribute multiple state repetitive group sampling plan is developed assuming that the life time follows the Burr Type XII distribution. The plan parameters are determined by considering two points on operating characteristic (OC) curve. Tables are given for the practical use. The advantages of the proposed plan are discussed over the single sampling plans. Examples are given to illustrate the proposed plan.     

Accelerated Reliability Demonstration Testing Design Based on Reliability Allocation of Environmental Stresses

The traditional reliability demonstration testing based on statistical method requires a large number of samples and long testing time, failing to satisfy the demand for short cycle and low cost. This paper proposes a new accelerated approach for determining reliability target of each environment stress, accelerated test profile, and comprehensive acceleration factor for multi‐failure mode product to conduct assembly level accelerated demonstration testing under multiple stresses and levels. By decomposing the product from four levels, namely function, structure, mechanism, and stress, the products' weaknesses can be identified. The main failure modes and sensitive environmental stresses are determined based on environmental profile and FMMEA. In this design, the reliability is apportioned to each actual environmental stress by AHP. And the SSI model is used to establish accelerated stress profile. The overall acceleration factor can be derived from the model of assembly level accelerated testing. Combined with a statistical plan, the accelerated reliability demonstration testing plan and test profile is built. A case example is presented to illustrate the effectiveness of the proposed approach. Copyright © 2017 John Wiley & Sons, Ltd.     

Theory for Optimal Test Plans for the Random Fatigue-Limit Model

This article presents methodology for planning life tests based on the random fatigue-limit model (RFLM). The RFLM describes the relationship between fatigue life and the applied load in the presence of fatigue limits. A standardization of the RFLM is presented, and corresponding expressions for the elements of the Fisher information matrix are given. Different test plan criteria that express various objectives that the practitioner may have in conducting experiments under the RFLM are discussed. These criteria include estimation of life quantiles, estimation of stress/strain levels that yield a specific life quantile, estimation of fatigue-limit quantiles, and D and D_s optimality. Equivalence theorems used to verify optimality of test plans are also presented. The methods are sufficiently general so they can be applied to criteria based on any function of the model parameters. They are demonstrated using a nickel-base superalloy experiment.     

A literature review on planning and analysis of accelerated testing for reliability assessment

Accelerated testing has been widely used for several decades. Started with accelerated life tests with constant‐stress loadings, more interest has been focused prominently on accelerated degradation tests and time‐varying stress loadings. Because accelerated testing is crucial to the assessment of product reliability and the design of warranty policy, it is important to develop an efficacious test plan that encompasses and addresses important issues, such as design of stress profiles, sample allocation, test duration, measurement frequency, and budget constraint. In recent years, extensive research has been conducted on the optimal design of accelerated testing plans, and the consideration of multiple stresses with interactions has become a big challenge in such experimental designs. The purpose of this study is to provide a comprehensive review of important methods for statistical inference and optimal design of accelerated testing plans by compiling the existing body of knowledge in the area of accelerated testing. In this work, different types of test planning strategies are categorized, and their drawbacks and the research trends are provided to assist researchers and practitioners in conducting new research in this area.     

Field-Failure and Warranty Prediction Based on Auxiliary Use-Rate Information

Assessment of risk due to product failure is important both for purposes of finance (e.g., warranty costs) and safety (e.g., potential loss of human life). In many applications a prediction of the number of future failures is an important input to such an assessment.

Usually the field-data response used to make predictions of future failures is the number of weeks (or another unit of real time) in service. Use-rate information usually is not available (automobile warranty data are an exception, where both weeks in service and number of miles driven are available for units returned for warranty repair). With new technology, however, sensors and smart chips are being installed in many modern products ranging from computers and printers to automobiles and aircraft engines. Thus the coming generations of field data for many products will provide information on how the product was used and the environment in which it was used. This article was motivated by the need to predict warranty returns for a product with multiple failure modes. For this product, cycles-to-failure/use-rate information was available for those units that were connected to the network. We show how to use a cycles-to-failure model to compute predictions and prediction intervals for the number of warranty returns. We also present prediction methods for units not connected to the network. To provide insight into the reasons that use-rate models provide better predictions, we also present a comparison of asymptotic variances comparing the cycles-to-failure and time-to-failure models. This article has supplementary material online.     

Design evaluation of a French refrigerator drawer system subjected to repeated food storage loads

Based on field data and a tailored set of accelerated life tests, the drawer system of food storage in a French refrigerator was redesigned. Using a force balance analysis, the simple mechanical loads of the drawer system were evaluated. The failure modes and mechanisms found experimentally were similar to those of the failed samples in the field. Failure analysis, accelerated life tests and corrective action plans were used to identify the key control parameters and level for the mechanical drawer system. The missing controllable design parameters of the drawer system in the design phase included no corner rounding and rib thickness in the intersection areas between the box and its cover, the right, center support and left rail system. After a tailored series of accelerated life tests with corrective action plans, the B₁ life of the new draw system is now guaranteed to be over 10 years with a yearly failure rate of 0.1%.     

Warranty Data Analysis: A Review

Warranty claims and supplementary data contain useful information about product quality and reliability. Analysing such data can therefore be of benefit to manufacturers in identifying early warnings of abnormalities in their products, providing useful information about failure modes to aid design modification, estimating product reliability for deciding on warranty policy and forecasting future warranty claims needed for preparing fiscal plans. In the last two decades, considerable research has been conducted in warranty data analysis (WDA) from several different perspectives. This article attempts to summarise and review the research and developments in WDA with emphasis on models, methods and applications. It concludes with a brief discussion on current practices and possible future trends in WDA. Copyright © 2012 John Wiley & Sons, Ltd.     

A Bayesian Approach to Multiple Comparisons

This paper presents maximum likelihood theory for large-sample optimum accelerated life test plans. The plans are used to estimate a simple linear relationship between (transformed) stress and product life, which has a Weibull or smallest extreme value distribution. Censored data are to be analyzed before all test units fail. The plans show that all test units need not run to failure and that more units should be tested at low test stresses than at high ones. The plans are illustrated with a voltage-accelerated life test of an electrical insulating fluid.     

A Dependent Competing Risks Model for Technological Units Subject to Degradation Phenomena and Catastrophic Failures

This paper proposes a dependent competing risks model for the reliability analysis of technological units that are subject both to degradation phenomena and to catastrophic failures. The paper is mainly addressed to the reanalysis of real data presented in a previous work, which refer to some electronic devices subject to two failure modes, namely the light intensity degradation and the solder/Cu pad interface fracture, which in previous papers, were considered independent. The main reliability characteristics of the devices, such as the probability density functions, the cause‐specific cumulative distribution function and hazard rate of each failure mode in the presence of both modes, are estimated. Likewise, the fraction of failures caused by each failure mode during the whole life of the devices or their residual life is derived. Finally, the results obtained under the proposed dependent competing risks model are compared to those obtained in previous papers. Copyright © 2015 John Wiley & Sons, Ltd.