A Bayesian reliability evaluation method with integrated accelerated degradation testing and field information

https://doi.org/10.1016/j.ress.2012.09.015Get rights and content

Abstract

Accelerated degradation testing (ADT) is a common approach in reliability prediction, especially for products with high reliability. However, oftentimes the laboratory condition of ADT is different from the field condition; thus, to predict field failure, one need to calibrate the prediction made by using ADT data. In this paper a Bayesian evaluation method is proposed to integrate the ADT data from laboratory with the failure data from field. Calibration factors are introduced to calibrate the difference between the lab and the field conditions so as to predict a product's actual field reliability more accurately. The information fusion and statistical inference procedure are carried out through a Bayesian approach and Markov chain Monte Carlo methods. The proposed method is demonstrated by two examples and the sensitivity analysis to prior distribution assumption.

Introduction

A product's lifetime or degradation data is the major data source for inferring its failure time distribution model. However, it is very time-consuming to obtain enough failure data from products operated under the field-use condition. To address this problem, accelerated life tests are widely used to obtain product failure information in a short time frame. But for highly reliable products, even accelerated life testing (ALT) may be inadequate due to a large amount of censoring. Therefore, accelerated degradation testing (ADT), in which product degradation data are collected and analyzed for reliability extrapolation, becomes a common approach to the reliability prediction for those highly reliable products.

However, the extrapolated reliability measurement using ADT only represents the reliability under the laboratory testing condition, which could be quite different from the product's field condition. For example, in ADT the testing tool cannot reproduce all the stresses and stress variations that a product will experience in the field. Therefore, one should pay close attention to the model-based extrapolation that has to be carried out for inferring the field reliability. The field failure data are usually sparse, but the laboratory testing data could be abundant, thus it is meaningful to establish the correlation between the laboratory and field data and to predict the field reliability using the information from both sources.

This paper aims to develop a reliability prediction model with data from multiple data sources. A brief literature review on ADT and ADT data analysis is given in the next section. Section 3 describes the degradation model, lifetime distribution and acceleration model considered in this paper. Section 4 provides the Bayesian inference approach to model parameter estimation. A synthetic example is used to demonstrate the proposed method in Section 5, along with the sensitivity analysis of this method. Section 6 describes a real product test and data analysis. Finally, the paper is concluded in Section 7.

Section snippets

Literature review

Accelerated degradation testing is an effective approach to the product reliability prediction, especially for a product with high reliability and long lifetime, where even accelerated life testing is difficult to obtain sufficient failure data within the limited time and budget. Same as ALT, ADT analysis is a method based on the assumption of identical failure mechanism; that is, the life characteristic of the product under the use stress level can be extrapolated from the degradation data

Degradation model

We assume that the degradation follows a Wiener process, and then the first passage time of this process to a threshold follows the inverse Gaussian distribution. Chhikara and Folks [21] discussed the use of this distribution as a lifetime distribution model. Whitmore and Schenkelberg [22] and Lu [5] had considered it for degradation data analysis. The degradation model of Wiener process isY(t)=σB(t)+d(s)t+y0,where Y(t) is the performance degradation process of product, B(t) is the standard

Bayesian inference

To understand the relationship between different environmental conditions and to estimate the reliability accurately, it is important to evaluate the parameters, such as β0, β1 and σ2, and the calibration factors k1 and k2. It is also a difficult task when the model is complex, with a high dimensional parameter space. Bayesian approach is a feasible method to integrate all available information to infer unknown parameters. In Bayesian approach parameters are treated as random variables and

Prior distribution selection

As the nature of prior distribution defined in Bayesian inference is subjective, it is important to select and compare feasible prior distributions. For β0, β1and σ2 are parameters in a normal regression model, according to Ntzoufras [26], the simplest approach is to assume that these parameters have independent priors withf(β,σ2)=j=0pf(βj)f(σ2),βjN(μβj,εj2),andσ2IGa(a,b),that is, βj follows the normal distribution and σ2 follows the inverse gamma distribution.

For the calibration factor k1

A real example

Super luminescent diode (SLD) is a semiconductor product that has a wide range of applications in optical fiber sensors, optical fiber communication systems, clinical systems, and so on. This product enjoys long lifetime and high reliability, as well as other design and manufacturing advantages. The structure of SLD is shown in Fig. 9. As failure time of SLD is difficult to obtain, degradation of SLD can be monitored to predict its reliability. The performance degradation measurement of SLD is

Conclusions

In this paper a Bayesian approach is proposed to integrate the product's reliability information from both the ADT and field-use conditions. The degradation model and calibration factors are introduced to bridge the reliability evaluation from the accelerated degradation testing in a testing laboratory to the product's actual performance in the field. These calibration factors model the uncertainty of stress fluctuations and the complexity of failure behaviors of the product in its field-use

References (28)

  • W.Q. Meeker et al.

    Statistical tools for the rapid development and evaluation of high-reliability products

    IEEE Transactions on Reliability

    (1995)
  • W.Q. Meeker et al.

    Statistical Methods for Reliability Data

    (1998)
  • Lu J, Degradation processes and related reliability models, Ph.D. thesis, McGill University;...
  • L.I. Pettit et al.

    Bayesian analysis for inverse Gaussian lifetime data with measures of degradation

    Journal of Statistical Computation and Simulation

    (1999)
  • Cited by (0)

    View full text