Reliability Estimation from Linear Degradation and Failure Time Data With Competing Risks Under a Step-Stress Accelerated Degradation Test

Abstract

The accelerated degradation test (ADT) has become critical for product reliability assessment. In performing the ADT for newly developed products, a constant-stress ADT may be impractical or sometimes impossible where the available size of testing units and the testing duration are heavily bounded to meet the short development period of the products. As an alternative, a step-stress accelerated degradation test (SSADT) can be a useful tool for satisfying the test limitation, and for making up for uncertainty in selecting appropriate levels of stress. Occasionally, the elevated stress under SSADT not only accelerates the performance degradation of products, but it may also expedite traumatic failures. This paper proposes a modeling approach to simultaneously analyze linear degradation data and traumatic failures with competing risks in an SSADT experiment. Under the modeling approach, a cumulative exposure model is considered. The failure rate corresponding to each failure mode is described as a function of the degradation level at the moment of failure. No parametric assumptions are made regarding the failure-time distribution to extend the proposed method to more general cases. We derive maximum likelihood estimates of the model parameters, then estimate failure rates and product reliability based on the degradation level to failure. Asymptotic properties of the maximum likelihood estimates are also discussed. The proposed model is applied to accelerated degradation data from plastic substrate active matrix light-emitting diodes (AMOLEDs), along with sensitivity analysis.