## The Annals of Applied Statistics

- Ann. Appl. Stat.
- Volume 8, Number 3 (2014), 1671-1689.

### Degradation-based residual life prediction under different environments

Rensheng Zhou, Nicoleta Serban, and Nagi Gebraeel

#### Abstract

Degradation modeling has traditionally relied on historical signals to estimate the behavior of the underlying degradation process. Many models assume that these historical signals are acquired under the same environmental conditions and can be observed along the entire lifespan of a component. In this paper, we relax these assumptions and present a more general statistical framework for modeling degradation signals that may have been collected under different types of environmental conditions. In addition, we consider applications where the historical signals are not necessarily observed continuously, that is, historical signals are sparse or fragmented. We consider the case where historical degradation signals are collected under known environmental states and another case where the environmental conditions are unknown during the acquisition of these historical data. For the first case, we use a classification algorithm to identify the environmental state of the units operating in the field. In the second case, a clustering step is required for clustering the historical degradation signals. The proposed model can provide accurate predictions of the lifetime or residual life distributions of engineering components that are still operated in the field. This is demonstrated by using simulated degradation signals as well as vibration-based degradation signals acquired from a rotating machinery setup.

#### Article information

**Source**

Ann. Appl. Stat., Volume 8, Number 3 (2014), 1671-1689.

**Dates**

First available in Project Euclid: 23 October 2014

**Permanent link to this document**

https://projecteuclid.org/euclid.aoas/1414091229

**Digital Object Identifier**

doi:10.1214/14-AOAS749

**Mathematical Reviews number (MathSciNet)**

MR3271348

**Zentralblatt MATH identifier**

1304.62125

**Keywords**

Degradation modeling residual life prediction time-varying environments

#### Citation

Zhou, Rensheng; Serban, Nicoleta; Gebraeel, Nagi. Degradation-based residual life prediction under different environments. Ann. Appl. Stat. 8 (2014), no. 3, 1671--1689. doi:10.1214/14-AOAS749. https://projecteuclid.org/euclid.aoas/1414091229

#### Supplemental materials

- Supplementary material: Proofs and Derivations. The supplemental material consists of two parts. In Appendix A, we present an available lemma that will be frequently used in our estimation and prediction algorithms. In Appendix B, we provide details about our proposed EM algorithm for estimating the model parameters.Digital Object Identifier: doi:10.1214/14-AOAS749SUPP