Practical Applications of a Family of Shock-Degradation Failure Models

Abstract

Many systems experience gradual degradation while simultaneously being exposed to a stream of random shocks of varying magnitude that eventually cause failure when a shock exceeds the residual strength of the system. This failure mechanism is found in diverse fields of application. Lee and Whitmore Shock-degradation failure processes and their survival distributions. Manuscript submitted for journal publication, 2016) presented a family of system failure models in which shock streams that follow a Fréchet process are superimposed on a degrading system described by a stochastic process with stationary independent increments. They referred to them as shock-degradation failure models. In this article, we discuss applications of these models and investigate practical issues and extensions that help to make these models more accessible and useful for studies of system failure. This family has the attractive feature of defining the failure event as a first passage event and the time to failure as a first hitting time (FHT) of a critical threshold by the underlying stochastic process. FHT models have found use in many real-world settings because they describe the failure mechanism in a realistic manner and also naturally accommodate regression structures. This article discusses a variety of data structures for which this model is suitable, as well as the estimation methods associated with them. The data structures include conventional censored survival data, data sets that combine readings on system degradation and failure event times, and data sets that include observations on the timing and magnitudes of shocks. This assortment of data structures is readily handled by threshold regression estimation procedures. Predictive inferences and risk assessment methods are also available. This article presents three case applications related to osteoporotic hip fractures in elderly women, divorces for cohorts of Norwegian couples, and deaths of cystic fibrosis patients. This article closes with discussion and concluding remarks.