Nonparametric estimation with recurrent competing risks data

Abstract

Nonparametric estimators of component and system life distributions are developed and presented for situations where recurrent competing risks data from series systems are available. The use of recurrences of components’ failures leads to improved efficiencies in statistical inference, thereby leading to resource-efficient experimental or study designs or improved inferences about the distributions governing the event times. Finite and asymptotic properties of the estimators are obtained through simulation studies and analytically. The detrimental impact of parametric model misspecification is also vividly demonstrated, lending credence to the virtue of adopting nonparametric or semiparametric models, especially in biomedical settings. The estimators are illustrated by applying them to a data set pertaining to car repairs for vehicles that were under warranty.

Parametric inference for multiple repairable systems under dependent competing risks

“…Specifically, the Nelson-Aalen estimators for the cause-specific cumulative intensity Λ k (t) and the overall cumulative intensity Λ(t) = ∑ K k=1 Λ k (t) are given bŷ where n ik (t) is the observed number of k-mode failures for the i-th system in time [0, t]. Note that the estimators in (12) are valid up to the censoring time . As the number of systems grows large (m −→ ∞), the centered and scaled pro-…”

“…One approach is to base the inference on models of gap times between successive failures. Such modeling can be entertained also in presence of competing risks . The capability of the gap‐time models to directly incorporate any effect of design or configuration changes is clearly quite attractive.…”

Convergence of the Nelson-Aalen Estimator in Competing Risks

“…A first extension of the previous simple case consists in considering situations in which there is no longer a single event of interest but several types of events, each due to a given risk. For more details, the interested reader may consult Satten & Datta (Satten & Datta, 1999), Datta & Satten (Datta & Satten, 2000), Latouche (Latouche, 2004), Belot (Belot, 2009), Njamen & Ngacthou (Njamen & Ngacthou, 2014), Taylor & Peña (Taylor & Peña, 2014). In 2001, Pe na & al.…”

Nonparametric estimation in trend-renewal processes

“…For example, Gamiz and Roman [12]; Xiao and Dohi [30] and Taylor and Pena [29] use nonparametric methods in applications related to repairable systems, while Gandy and Jensen [15]; Luo et al [24]; Bobrowski et al [6]; Zhao et al [32] use kernel smoothing methods in specific reliability applications.…”