Effect of Field Stress Variance on Test to Field Correlation in Accelerated Reliability Demonstration Testing

This paper discusses the effect of field stress variance on the value of demonstrated reliability. In many cases, the acceleration factor for a reliability demonstration test is calculated based on a high percentile field stress level, typically corresponding to severe user or environmental conditions. In those cases, the actual field reliability for the population will be higher than that demonstrated by the test. This paper presents a mathematical approach to estimating ‘true’ field reliability based on the acceleration model and stress variable distribution over the product field population. This method is illustrated by an example of automotive electronics reliability demonstration testing and has a wide range of practical applications. Copyright © 2014 John Wiley & Sons, Ltd.     

Bayes approach in RDT using accelerated and long-term life data

A common problem of reliability demonstration testing (RDT) is the magnitude of total time on test required to demonstrate reliability to the consumer’s satisfaction, particularly in the case of high reliability components. One solution is the use of accelerated life testing (ALT) techniques. Another is to incorporate prior beliefs, engineering experience, or previous data into the testing framework. This may have the effect of reducing the amount of testing required in the RDT in order to reach a decision regarding conformance to the reliability specification. It is in this spirit that the use of a Bayesian approach can, in many cases, significantly reduce the amount of testing required.We demonstrate the use of this approach to estimate the acceleration factor in the Arrhenius reliability model based on long-term data given by a manufacturer of electronic components (EC). Using the Bayes approach we consider failure rate and acceleration factor to vary randomly according to some prior distributions. Bayes approach enables for a given type of technology the optimal choice of test plan for RDT under accelerated conditions when exacting reliability requirements must be met. These requirements are given by a hypothetical consumer by two different ways. The calculation of posterior consumer’s risk is demonstrated in both cases.The test plans are optimum in that they take into account Var{λ|data}, posterior risk, E{λ|data}, Median λ or other percentiles of λ at data observed at the accelerated conditions. The test setup assumes testing of units with time censoring.     

A Bayes approach to reliability prediction utilizing data from accelerated life tests and field failure observations

A Bayes approach is proposed to improve product reliability prediction by integrating failure information from both the field performance data and the accelerated life testing data. It is found that a product's field failure characteristic may not be directly extrapolated from the accelerated life testing results because of the variation of field use condition that cannot be replicated in the lab‐test environment. A calibration factor is introduced to model the effect of uncertainty of field stress on product lifetime. It is useful when the field performance of a new product needs to be inferred from its accelerated life test results and this product will be used in the same environment where the field failure data of older products are available. The proposed Bayes approach provides a proper mechanism of fusing information from various sources. The statistical inference procedure is carried out through the Markov chain Monte Carlo method. An example of an electronic device is provided to illustrate the use of the proposed method. Copyright © 2008 John Wiley & Sons, Ltd.     

Bayesian Analysis of Step‐Stress Accelerated Life Test with Exponential Distribution

In this article, we propose a general Bayesian inference approach to the step‐stress accelerated life test with type II censoring. We assume that the failure times at each stress level are exponentially distributed and the test units are tested in an increasing order of stress levels. We formulate the prior distribution of the parameters of life‐stress function and integrate the engineering knowledge of product failure rate and acceleration factor into the prior. The posterior distribution and the point estimates for the parameters of interest are provided. Through the Markov chain Monte Carlo technique, we demonstrate a nonconjugate prior case using an industrial example. It is shown that with the Bayesian approach, the statistical precision of parameter estimation is improved and, consequently, the required number of failures could be reduced. Copyright © 2011 John Wiley & Sons, Ltd.     

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.     

Reliability demonstration test planning: A three dimensional consideration

Increasing customer demand for reliability, fierce market competition on time-to-market and cost, and highly reliable products are making reliability testing more challenging task. This paper presents a systematic approach for identifying critical elements (subsystems and components) of the system and deciding the types of test to be performed to demonstrate reliability. It decomposes the system into three dimensions, (i.e. physical, functional and time) and identifies critical elements in the design by allocating system level reliability to each candidate. The decomposition of system level reliability is achieved by using criticality index. The numerical value of criticality index for each candidate is derived based on the information available from failure mode and effects analysis (FMEA) document or warranty data from a prior system. It makes use of this information to develop reliability demonstration test plan for the identified (critical) failure mechanisms and physical elements. It also highlights the benefits of using prior information in order to locate critical spots in the design and in subsequent development of test plans. A case example is presented to demonstrate the proposed approach.     

A case study on the benefits of combining reliability stress tests

This paper discusses two distinct benefits associated with product reliability qualifications by combining individual reliability stress tests into a single test. First, a combined test will make better use of test equipment, personnel and product samples required for the qualification, implying a cost benefit. Secondly, a combined test allows interaction between the stress sources to occur on all failure causes. These benefits were realized as a result of a power supply application. Each individual test was designed to address specific causes which are assumed to be totally independent of other failures. A combined test can verify or deny independence and therefore provide a stronger practical test. Hence, this paper will demonstrate that a combined reliability test will provide more efficient testing with solid engineering product performance coverage. In addition, an approach is proposed for combining tests which fixes the acceleration rates between stress tests as the same ratio as under the nominal operating product environmental conditions.     

Total System Reliability: Integrated Model for Growth and Test Termination

Reliability demonstration testing is not the most efficient method of assuring product reliability prior to shipment. It is costly, time consuming and has inherent technical and social limitations. The dilemma facing the reliability and quality engineer is whether to continue demonstration testing and risk shipping a product late or ship the product and risk warranty and field service returns. Either option can cause the company to lose significant market share and profit. This paper sets out to solve this dilemma by meeting both the time to market constraints and the product reliability goals. The weaknesses of existing reliability demonstration techniques are explored and a comprehensive methodology is introduced involving controlled development processes, stress testing, root cause determination and process change feedback mechanisms. All prototype products are manufactured on the final volume process line resulting in the early identification and correction of process‐related problems. Testing commences on the first available prototypes with system stress/robust testing being employed to stimulate failures, determine their root cause and correct them. Reliability growth modelling assesses the ongoing improvements occurring in reliability during the development cycle, while a statistical stopping rule is used to determine the optimal product release time without risking product warranty. The approach is applicable to systems incorporating both hardware and software elements. The methodology has been validated on three development projects of telecommunication systems comprising hardware and software. In addition to enhancing team behaviour and performance, the development times have been reduced by 14% and the ramp‐up time to full worldwide product shipments has been reduced by 50%. Copyright © 2005 John Wiley & Sons, Ltd.     

Integrated Approach for Field Reliability Prediction Based on Accelerated Life Testing

ABSTRACT

To predict field reliability using analytical modeling, several important reliability activities should be conducted, including failure mode and effect analysis, stress and usage condition analysis, physics of failure analysis, accelerated life testing and modeling, and cumulative damage modeling if needed. With all of the mentioned activities and results, the field reliability confidence limit can be predicted at a certain confidence level, if a modeling framework can be established. This article builds such an integrated process and comprehensive modeling framework, especially with cumulative damage rules when the certain field stresses are random processes. An engineering product is provided as an application to illustrate the effectiveness of proposed method.     

Generation and validation of loading profiles for highly accelerated durability tests of ground vehicle components

Accelerated durability tests are designed to quantify the life characteristics of ground vehicle components under normal use conditions by testing at a higher stress level to accelerate the occurrence of failure. Presently, conducting durability tests with a high acceleration factor has become increasingly demanding for the reduction of the time and the cost involved in long period field/durability tests. In previous work, to accelerate the field test, the standard ‘test tailoring approach’ has been modified due to the limitations of testing implementation and required high acceleration factors. In this modified approach, a full period durability loading profile has to be shortened to an equivalent partial period test loading profile, which is repeated in the tests keeping the same amount of damage contents. To apply this new modified approach to industrial durability tests, it needs to be validated. In this work, a computer-aided testing method is developed for the validation of this modified ‘test tailoring approach’. Hence, a new test-piece has been designed by a conjugative approach involving the finite element technique and fatigue analysis for a specific durability life. Afterwards, the loading profiles with various acceleration factors synthesized via the modified approach have been applied on the designed test-piece and the fatigue lives have been simulated to verify the effectiveness of those loading profiles. Simulation results show that, loading profiles with high acceleration factors can be successfully generated with the accuracy above 95%. In addition, synthesized accelerated loading profiles result failure from the identical locations determined using the proposed conjugative approach.     

Bayesian Reliability Demonstration

A Bayesian approach to reliability demonstration testing is described and differences between the Bayesian viewpoint and the commonly employed classical approach are highlighted. A procedure for selecting a specific inverted gamma probability density to characterize the prior distribution of the MTBF of electronic hardware is developed and a table of Bayesian demonstration plans for a practical range of input parameters is provided. In addition, procedures for the implementation of the plans and two illustrative examples are given. Finally, two commonly employed classical plans are compared to a Bayesian plan illustrating the efficiency of the latter in terms of demonstration test time requirements.     

Acceleration Factor Constant Principle and the Application under ADT

Accelerated degradation test (ADT) has become an efficient approach to evaluate the reliability for highly reliable products. However, when modeling accelerated degradation data with degradation models, it is difficult to exactly figure out the changing rules of parameters with stress variables varying. At present, the changing rules are mainly assumed according to engineering experience or subjective judgements, which probably results in inaccurately extrapolating the reliability. To figure out the changing rules of parameters with stress variables varying, the acceleration factor constant principle and its application under ADT are studied in the paper. It is well known that the acceleration factor between any two different stress levels should be a constant under an effective ADT. For each degradation model, its parameters should obey special changing rules to satisfy that the acceleration factor maintains a constant throughout an ADT. Taking three extensively used stochastic process models as examples, including Wiener process model, gamma process model, and inverse Gaussian process model, the method of deducing the changing rules of the parameters according to the acceleration factor constant principle was demonstrated. A simulation test was conducted to validate the deduced changing rules of the parameters for the three stochastic process models. An illustrative example involving self‐regulating heating cables was used to illustrate the application of the acceleration factor constant principle under ADT. Results indicate that the acceleration factor constant principle offers an appealing and credible approach to help model accelerated degradation data. Copyright © 2016 John Wiley & Sons, Ltd.     

A Comparison of Accelerated Test Plans to Estimate the Survival Probability at a Design Stress

In a previous paper [3], the authors presented large sample optimum accelerated test plans to estimate the survival probability at a design stress assuming a linear logistic model, i.e. a linear relationship between stress and the log survival odds at that stress. The optimum plans required testing at two accelerated stresses with a larger allocation of units assigned to the lower of the two stresses. In practice, however, it is often desirable to conduct the accelerated tests at more than two stresses and/or use equal or otherwise prespecified allocation. In this paper we compare the large sample variance of each of ten such non-optimum test plans (and also that of testing exclusively at the design stress) with that of the optimum plan under a variety of conditions.     

An analytical procedure for estimating field lifetime and failure rate of electronic packages

To understand the reliability characteristics of electronic packages under field conditions, accelerated life tests (ALT) with higher stress levels are needed in practice. Instead of the time-consuming and costly ALT, an analytical procedure based on finite element simulation and a Weibull statistical method to estimate the lifetime and failure rate of electronic packages subjected to thermal cycling loadings is proposed in the present study. To consider uncertainties, geometric parameters and material properties are assumed as random variables and incorporated into numerical simulation. The result shows that the mean time to failure (MTTF) of a studied electronic package under a specific thermal cycling loading condition can be predicted accurately. From either the proposed analysis or based on a particular model found in literature, the acceleration factor (AF) can be predicted accurately as well. Furthermore, according to the outcome from the Weibull statistical method, the failure rate under either the field or a particular test condition can be determined. Accordingly, the MTTF and failure rate of the package under field conditions can be estimated from the result of a simulated accelerated test as well as the AF model. The present study indicates that the proposed analytical procedure can help engineers evaluate the reliability of electronic packages rapidly and effectively.     

Reliability analysis of exponentiated Poisson-exponential constant stress accelerated life test model

Accelerated life testing is an efficient tool frequently adopted for obtaining failure time data of test units in a lesser time period as compared to normal use conditions. We assume that the lifetime data of a product at constant level of stress follows an exponentiated Poisson-exponential distribution and the shape parameter of the model has a log-linear relationship with the stress level. Model parameters, the reliability function (RF), and the mean time to failure (MTTF) function under use conditions are estimated based on eight frequentist methods of estimation, namely, method of maximum likelihood, method of least square and weighted least square, method of maximum product of spacing, method of minimum spacing absolute-log distance, method of Cramér-von-Mises, method of Anderson–Darling, and Right-tail Anderson–Darling. The performance of the different estimation methods is evaluated in terms of their mean relative estimate and mean squared error using small and large sample sizes through a Monte Carlo simulation study. Finally, two accelerated life test data sets are considered and bootstrap confidence intervals for the unknown parameters, predicted shape parameter, predicted RF, and the MTTF at different stress levels, are obtained.     

Component reliability assessment and assurance using a new step-stress test

Several features of accelerated reliability testing are surveyed in this paper. A new technique for the practical evaluation of reliability under thermally induced acceleration is introduced. This procedure is termed the reverse-step-stress test, and involves a decrease in applied stress after some pre-specified failure criterion has been met within a fixed sample of components. An analysis is presented which confirms that the reverse-step-stress test can reveal failures having low activation energies that would not be detectable in conventional constant-stress, high temperature testing.     

A two-stage sampling plan for bogey tests

When accelerated life tests can be applied to simulate the normal product operating conditions, engineers usually terminate the test upon successfully running to a multiple of a prespecified bogey without any failure to demonstrate a required minimum reliability level. This testing philosophy is called ‘bogey test’ (or extended test) in the automotive industry and is a subset of type I censored tests in standard reliability literature. Sometimes engineers encounter the difficulty of using this reliability demonstration approach when incidents do occur during the test. The incident might be a legitimate failure or a withdrawal caused by external forces such as a broken fixture of a non-functional power supply. This paper derives a two-stage sampling plan for possible back-up solution on planning and running a bogey test with possible occurrence of incidents. A Weibull distribution with a given shape parameter is assumed for the underlying life characteristic.     

An Approach for Reliability Demonstration Test Based on Power‐Law Growth Model

Reliability demonstration test (RDT) is a critical and necessary step before the acceptance of an industrial system. Generally, a RDT focuses on designing a test plan through which one can judge whether the system reliability indices meet specific requirements. There are many established RDT plans, but few have incorporated the reliability growth aspects of the corresponding products. In this paper, we examine a comprehensive test plan that involves information concerning the reliability growth stage. An approach for RDT under the assumption of the power‐law model is proposed. It combines data related to the growth stage with those pertaining to the test stage of the product to reduce the cost of the test. Through simulation studies and numerical examples, we illustrate the characteristics of the test plan and significant reduction in test costs through our approach. Copyright © 2017 John Wiley & Sons, Ltd.     

Reliability assessment and mechanical characterization of Cu and Au ball bonds in BGA package

Extended reliability and mechanical characterisation of Au and Pd-coated Cu (Cu) ball bonds are useful technical information for Au and Cu wire deployment in semiconductor device packaging. This paper discusses the influence of wire type on the package reliability and mechanical performance after several component reliability stress tests. Failure analysis has been conducted to identify the associated failure mechanisms of Au and Cu ball bonds after reliability tests. Wire pull strength and ball bond shear (with its break modes) of both wire types are investigated after unbiased highly accelerated temperature and humidity stress test (UHAST), temperature cycling (TC) and high temperature storage life test (HTSL) at various aging temperatures. Reliability Weibull plots have been plotted for each reliability stresses. Obviously Au ball bond is found with longer time-to-failure in Unbiased HAST stress compare to Cu ball bonds. Cu wire exhibits equivalent package and or better reliability margin compare to Au ball bonds in TC and HTSL tests. Failure mechanisms of UHAST and HTSL have been proposed and its mean-time-to failure (t₅₀), characteristics life (t_63.2, η) and shape parameter (ß) have been discussed in this paper.     

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.