Analysis of correlated multivariate degradation data in accelerated reliability growth

Modern engineering systems have become increasingly complex and at the same time are expected to be developed faster. To shorten the product development time, organizations commonly conduct accelerated testing on a small number of units to help identify failure modes and assess reliability. Many times design changes are made to mitigate or reduce the likelihood of such failure modes. Since failure-time data are often scarce in reliability growth programs, existing statistical approaches used for predicting the reliability of a system about to enter the field are faced with significant challenges. In this work, a statistical model is proposed to utilize degradation data for system reliability prediction in an accelerated reliability growth program. The model allows the components in the system to have multiple failure modes, each associated with a monotone stochastic degradation process. To take into account unit-to-unit variation, the random effects of degradation parameters are explicitly modeled. Moreover, a mean-degradation-stress relationship is introduced to quantify the effects of different accelerating variables on the degradation processes, and a copula function is utilized to model the dependency among different degradation processes. Both a maximum likelihood (ML) procedure and a Bayesian alternative are developed for parameter estimation in a two-stage process. A numerical study illustrates the use of the proposed model and identifies the cases where the Bayesian method is preferred and where it is better to use the ML alternative.     

Arrhenius and the temperature dependence of non-constant failure rate

This paper examines the temperature dependence of component hazard rate for the cases of log-normal and Weibull failure-time distributions and shows that the common belief that the temperature variation of component failure rate follows the Arrhenius rule can be substantially in error. Although most failures in present-day equipment are not due to defective components, the paper also examines the temperature dependence of equipment rate of occurrence of failure having a power-law or negative exponential variation with time for the temperature range where the majority of failures are due to rate processes obeying the Arrhenius equation. The consequences of a Gaussian distribution of failure-mechanism activation energy in a device population are also considered. Although the temperature dependence of failure rate can be very high, in most situations it is much less than that of the Arrhenius acceleration factor. It is very improbable that the temperature dependence of component failure rate can be meaningfully modelled for reliability prediction purposes or for the purpose of optimizing thermal design component layout. Attention is drawn to the invalidity of determining the failure activation energy from the average failure rates in accelerated high-temperature time-terminated life tests.     

Using degradation data to assess reliability: a case study on train wheel degradation

Degradation experiments are usually used to assess the lifetime distribution of highly reliable products, which are not likely to fail under the traditional life tests or accelerated life tests. In such cases, if there exist product characteristics whose degradation over time can be related to reliability, then collecting ‘degradation data’ can provide information about product reliability. In general, the degradation data are modeled by a nonlinear regression model with random coefficients. If we can obtain the estimates of parameters under the model, then the failure‐time distribution can be estimated. In order to estimate those parameters, three basic methods are available, namely, the analytical, numerical and the approximate. They are chosen according to the complexity of the degradation path model used in the analysis. In this paper, the numerical and the approximate methods are compared in a simulation study, assuming a simple linear degradation path model. A comparison with traditional failure‐time analysis is also performed. The mean‐squared error of the estimated 100pth percentile of the lifetime distribution is evaluated for each one of the approaches. The approaches are applied to a real degradation data set. Copyright © 2008 John Wiley & Sons, Ltd.     

Degradation models and implied lifetime distributions

In experiments where failure times are sparse, degradation analysis is useful for the analysis of failure time distributions in reliability studies. This research investigates the link between a practitioner's selected degradation model and the resulting lifetime model. Simple additive and multiplicative models with single random effects are featured. Results show that seemingly innocuous assumptions of the degradation path create surprising restrictions on the lifetime distribution. These constraints are described in terms of failure rate and distribution classes.     

Comparison of Methods to Estimate the Time‐to‐failure Distribution in Degradation Tests

Degradation tests are alternative approaches to lifetime tests and accelerated lifetime tests in reliability studies. Based on a degradation process of a product quality characteristic over time, degradation tests provide enough information to estimate the time‐to‐failure distribution. Some estimation methods, such as analytical, the numerical or the approximated, can be used to obtain the time‐to‐failure distribution. They are chosen according to the complexity of the degradation model used in the data analysis. An example of the application and analysis of degradation tests is presented in this paper to characterize the durability of a product and compare the various estimation methods of the time‐to‐failure distribution. The example refers to a degradation process related to an automobile's tyre, and was carried out to estimate its average distance covered and some percentiles of interest. Copyright © 2004 John Wiley & Sons, Ltd.     

Predicting lifetime by degradation tests: A case study of ISO 10995

ISO 10995 is the international standard for the reliability testing and archival lifetime prediction of optical media. The standard specifies the testing conditions in terms of the combinations of stress variables—temperature and relative humidity. The periodically collected data from tests are the error rate of the device, and failure is defined as the error rate exceeding a predetermined level. The standard assumes that the projected failure time is the actual failure time, and these projected failure times are then analyzed by using an Eyring or Arrhenius model. Since true failure times are often not directly observed, the uncertainties in the failure time must be taken into account. In this paper, we present a hierarchical model for degradation that can directly infer failure time at the use condition and compare this model with the International Standard Organization (ISO) standard through a simulation study. Not accounting for the uncertainty in the projected failure times leads to unjustified confidence in the estimation for the median lifetime at both the stress conditions used in the experiments and at the use condition.     

Long‐term Reliability Prediction of 935 nm LEDs Using Failure Laws and Low Acceleration Factor Ageing Tests

Numerous papers have already reported various results on electrical and optical performances of GaAs‐based materials for optoelectronic applications. Other papers have proposed some methodologies for a classical estimation of reliability of GaAs compounds using life testing methods on a few thousand samples over 10 000 hours of testing. In contrast, fewer papers have studied the complete relation between degradation laws in relation to failure mechanisms and the estimation of lifetime distribution using accelerated ageing tests considering a short test duration, low acceleration factor and analytical extrapolation. In this paper, we report the results for commercial InGaAs/GaAs 935 nm packaged light emitting diodes (LEDs) using electrical and optical measurements versus ageing time. Cumulative failure distributions are calculated using degradation laws and process distribution data of optical power. A complete methodology is described proposing an accurate reliability model from experimental determination of the failure mechanisms (defect diffusion) for this technology. Electrical and optical characterizations are used with temperature dependence, short‐duration accelerated tests (less than 1500 h) with an increase in bias current (up to 50%), a small number of samples (less than 20) and weak acceleration factors (up to 240). Copyright © 2005 John Wiley & Sons, Ltd.     

Statistics: The Exploration and Analysis of Data

As an alternative to traditional life testing, degradation tests can be effective in assessing product reliability when measurements of degradation leading to failure can be observed. This article presents a degradation model for highly reliable light displays, such as plasma display panels and vacuum fluorescent displays (VFDs). Standard degradation models fail to capture the burn-in characteristics of VFDs, when emitted light actually increases up to a certain point in time before it decreases (or degrades) continuously. Random coefficients are used to model this phenomenon in a nonlinear way, which allows for a nonmonotonic degradation path. In many situations, the relative efficiency of the lifetime estimate is improved over the standard estimators based on transformed linear models.     

Likelihood-based inference for a frailty-copula model based on competing risks failure time data

A competing risks phenomenon arises in industrial life tests, where multiple types of failure determine the working duration of a unit. To model dependence among marginal failure times, copula models and frailty models have been developed for competing risks failure time data. In this paper, we propose a frailty-copula model, which is a hybrid model including both a frailty term (for heterogeneity among units) and a copula function (for dependence between failure times). We focus on models that are useful to investigate the reliability of marginal failure times that are Weibull distributed. Furthermore, we develop likelihood-based inference methods based on competing risks data, including accelerated failure time models. We also develop a model-diagnostic procedure to assess the adequacy of the proposed model to a given dataset. Simulations are conducted to demonstrate the operational performance of the proposed methods, and a real dataset is analyzed for illustration. We make an R package “gammaGumbel” such that users can apply the suggested statistical methods to their data.     

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.