Using Degradation Measures to Estimate a Time-to-Failure Distribution

TLDR

Life tests that record few or no failures struggle to assess reliability, but degradation measurements over time can provide useful information about product reliability, especially when failure is defined by a specified degradation level. The study develops statistical methods for estimating a time‑to‑failure distribution from degradation data across a broad class of degradation models. A nonlinear mixed‑effects model combined with Monte Carlo simulation is used to obtain point estimates and confidence intervals for reliability assessment. Keywords: first crossing time, nonlinear estimation, random effect, reliability.

Abstract

Abstract Some life tests result in few or no failures. In such cases, it is difficult to assess reliability with traditional life tests that record only time to failure. For some devices, it is possible to obtain degradation measurements over time, and these measurements may contain useful information about product reliability. Even with little or no censoring, there may be important practical advantages to analyzing degradation data. If failure is defined in terms of a specified level of degradation, a degradation model defines a particular time-to-failure distribution. Generally it is not possible to obtain a closed-form expression for this distribution. The purpose of this work is to develop statistical methods for using degradation measures to estimate a time-to-failure distribution for a broad class of degradation models. We use a nonlinear mixed-effects model and develop methods based on Monte Carlo simulation to obtain point estimates and confidence intervals for reliability assessment. KEY WORDS: First crossing timeNonlinear estimationRandom effectReliability