Tools for analysis of accelerated life and degradation test data

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.

Degradation tests are widely used to assess the reliability of highly reliable products which are not likely to fail under traditional life tests or accelerated life tests. However, for some highly reliable products, the degradation may be very slow and hence it is impossible to have a precise assessment within a reasonable amount of testing time. In such cases, an alternative is to use higher stresses to extrapolate the product's reliability at the design stress. This is called an accelerated degradation test (ADT). In conducting an ADT, several decision variables, such s the inspection frequency, sample size and termination time, at each stress level are influential on the experimental efficiency. An inappropriate choice of these decision variables not only wastes experimental resources but also reduces the precision of the estimation of the product's reliability at the use condition. The main purpose of this paper is to deal with the problem of designing an ADT. By using the criterion of minimizing the mean‐squared error of the estimated 100$p$th percentile of the product's lifetime distribution at the use condition subject to the constraint that the total experimental cost does not exceed a predetermined budget, a nonlinear integer programming problem is built to derive the optimal combination of the sample size, inspection frequency and the termination time at each stress level. A numerical example is provided to illustrate the proposed method. Copyright © 2003 John Wiley & Sons, Ltd.

Designing an accelerated degradation experiment with a reciprocal Weibull degradation rate

The reliability of circular electrical connectors was usually assessed according to standards like MIL-HDBK-217 (Reliability Prediction of Electronic Equipment). Given to their limitations and mislead results, a new assessment method needs to be presented. Some concerns on the physics of failure (PoF) modeling and reliability assessment of circular electrical connectors are addressed in this paper to overcome this defect. An original approach combining laboratory accelerated degradation testing (ADT) and PoF modeling is proposed for effectively assessing connector reliability. Random vibration and current stress are selected as acceleration factors that affect the contact life of electrical connectors. Then, an appropriate multiple-stresses ADT scheme is derived. The PoF model for electrical connectors under multiple stresses yielded the generalized Eyring relationship. According to the system reliability model for multiposition connectors, connectors' life follows Weibull distribution, which is derived from extreme-value distribution theory. Through ADT and data gained from tests, statistical analysis result yielded the estimated value of reliability character of MIL-C-38999 I series electrical connectors under the action of vibration and current stresses.

Collecting accelerated degradation test (ADT) data can provide useful lifetime information for highly reliable products if there exists a product quality characteristic whose degradation over time can be related to reliability. However, conducting a constant-stress ADT is very costly. This is obviously not applicable for assessing the lifetime of a newly developed product because typically only a few test samples (prototypes) are available. To overcome this difficulty, we propose a step-stress accelerated degradation test (SSADT) in this paper. A case study of light emitting diodes data is used to illustrate the proposed procedure. It is seen that SSADT has several advantages over a constant-stress ADT. SSADT not only reduces the experimental cost significantly, but also provides the reliability analysts an efficient tool to assess the lifetime distribution of highly reliable products.

In order to evaluate the reliability guidelines for electronic equipment with high reliability and long life quickly, this paper presents the method of step-up-stress accelerated degradation testing. First expatriate step-up-stress accelerated degradation testing and the basic assumptions is detailed, then gives the data conversion method from step up stress degradation data to constant stress degradation data. As the basis, propose step up stress accelerated degradation reliability assessment arithmetic based on random degradation path. A numerical example was given to illustrate the method in the end. The testing method overcomes the shortages of constant degradation testing, which has higher testing efficiency.

A hydraulic gear motor for pump oil may be run as a component in an endurance type of accelerated life test (ALT) with several different applied stresses. The main failure modes may be first established and the life test developed based upon the failure modes. The purpose of an accelerated test is to demonstrate a minimum life in a simulated customer environment. The operating temperature range for his type of pump is typically -40/spl deg/C to 60/spl deg/C with a steady operating pressure load. The results of a hypothetical 1000 hour life test are shown for clarity. This closes the loop on the larger improvement process. The ALT results in the real world depend upon the applied stresses and should be well-behaved when the test conditions are not excessive or unusual. Simple reliability models may be employed to extrapolate the ALT to other customer conditions. Limits and conditions of the ALT are noted for this type of gear pump operating at pressures of greater than 100 PSI.

Super luminescent diode (SLD) is a typical product with long lifetime and high reliability which has great advantages and wide application prospects in many areas. Accelerated degradation testing (ADT) is used to obtain performance parameter data in a short time and extrapolate the lifetime and reliability of the products under normal operation conditions. However, in the application of Super luminescent diode (SLD) in ADT, on one hand, sometimes the sample size may be small for the limited cost, the evaluation accuracy of the lifetime and reliability would be low for the lack of information. On the other hand, with the developing of the SLD, usually a fixed number of samples are put into various tests besides ADT and extra information can be obtained in that process. So if all the available information can be used together in a feasible way, the evaluation accuracy of the lifetime and reliability would be improved. In this paper, Bayesian theory is introduced to solve the problems above for its great capability of data fusion. In this method, feasible degradation data of the SLD from different sources are collected, then processed and tested to make them have the same data format and physical meaning, finally fused to estimate the lifetime and reliability with the established degradation statistical model and reliability evaluation model of SLD. This paper provides a new ADT data evaluation method and the method is also suitable for other similar products.

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.

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 testing consists of a variety of methods aimed at shortening the life of a product or hastening its performance degradation in a short period of time. The purpose of these tests is to quickly obtain data that, when properly modeled and analyzed, can provide the desired information about a product’s lifetime or performance under normal use. Accelerated life testing will subject a product to conditions that exceed normal service parameters in order to uncover defects and potential failure modes. Since the guidelines for statistical analysis of thermal life test data in accelerated life tests (ANSI/IEEE Std. 101-1987) were enacted, they have been used to analyze the results of many experiments. However, Shim (2004) only used a small amount of data obtained from a limited environment for analysis of ANSI/IEEE Std. 101-1987 results, so simulations were conducted using previous research results to supplement the accuracy of the analysis. In this paper, two different systems or materials generated using the Arrhenius equation are compared in an accelerated life test to estimate the correct lifetime.

Space electronic products usually should meet the mission requirements of long life and low cost. Because of insufficient failure data, it is hard to assess the reliability precisely by using traditional reliability testing and statistical method. In this paper, a method of reliability assessment based on integration of highly accelerated life testing (HALT) and accelerated degradation testing (ADT) is proposed. Firstly, based on performance analysis of electronic products, the degradation of performance is modeled. Moreover, the data of drift performance is extracted, fitted and fused into the observation data in ADT. Lastly, the reliability assessment for electronic products is studied based on degradation data. This research provides an effective way for accelerated reliability testing of space electronic products, and it has been applied into practice.

Advent of VLSI technology has paved the way for Programmable Logic Devices (PLD), which are widely used as the basic building blocks in high integrity electronic systems. PLDs are considered for their robust features such as high gate density, performance, speed etc. For PFBR Instrumentation and Control systems, PLDs are extensively used to implement digital designs such as VME bus interface logic, control logic and sequencing logic etc. Types of PLDs, such as Field Programmable Gate Arrays, Complex Programmable Logic Devices and Gate Array Logic devices are used in Core Temperature Monitoring System and Safety logics of shutdown systems. Since these devices are reliable as per the manufacturer's specification, they were used in R & D facilities like Fast Breeder Test Reactor and Augmented Boron Enrichment Plant as test beds. However, in order to use PLDs in commercial Nuclear Power Plant (in PFBR), it is vital to know about their performance in other critical applications. The availability of required data is limited, other than for space applications. So, it is proposed to conduct Quantitative Accelerated Life Tests (QALT) for the PLDs. QALT is designed to produce the data required for accelerated life data analysis. This analysis method uses life data obtained under accelerated conditions to extrapolate an estimated probability density function for the product under normal use conditions. Accelerated life tests are conducted on products to understand their failure modes and life characteristics. The products are subjected to enhanced stresses in order to force the products to fail early than they would normally, under use conditions. This process reduces test time. This paper discusses the methodology adapted to perform the Accelerated Life Test for the above mentioned PLDs.

In engineering practice, to ensure the safety of complex engineering systems, the life prediction has attracted an increasing attention. In previous studies, few effective methods can be used to establish the life prediction model of a type of systems that have the following features: (1) the storage lives are much longer than the working lives, (2) lots of quantitative testing data are not available, (3) some expert knowledge can be used, and (4) the system’s performance degradation cannot be observed directly. As such, a life prediction method is constructed on the basis of belief rule base (BRB) and the accelerated degradation test, where two BRBs are involved, expressed by BRB_1 and BRB_2 respectively. Moreover, BRB_1 is employed to describe the relevance between the external stress and the hidden working state. BRB_2 is applied to establish the forecasting model of hidden working states. Once the predicted hidden working state achieves the boundary line, the corresponding working time is the life of the equipment and some measures need to be taken to maintain or change the equipment. Some uncertain parameters exist in the prediction model which can be determined by experts and it can lead to the inaccuracy of the model. Thus, an algorithm is proposed for updating parameters based on the maximum likelihood (ML). An experiment of the life prediction for aerospace relay is used to prove the reasonability of the life prediction model.KeywordsBelief rule base (BRB)Life predictionAccelerated degradation test

In this paper, we propose a practical method to estimate the milling head reliability based on the accelerated degradation test and Bayesian lifetime analysis method. By carefully analyzing the failure mechanism of the milling head, we adopt the accelerated degradation test to identify and parameterize the failure law of this component. The equivalent lifetime for the Bayesian lifetime analysis is also derived from the accelerated degradation data. Finally, the estimation is carried out based on the parametric failure law and the equivalent lifetime using the Bayesian Weibull lifetime analysis method. The reliability estimation of the milling head can be improved by the combination of the failure mechanical based accelerated degradation test and the Bayesian field lifetime data analysis. The proposed method is a practical and cost-effective reliability estimation method for highly reliable and expensive mechanical component with a pre-defined failure mechanism.