Reliability Engineering and System Safety, No. 95, pp. 912–920, (2010)

A Multi-component and Multi-failure Mode Inspection Model Based on the Delay Time Concept

Wenbin Wang
Salford Business School
University of Salford
Salford, UK
Prognostics and Health Management Center
City University of Hong Kong
Hong Kong, China

Department of Mechanical and Industrial Engineering
University of Toronto

Michael Pecht
Center for Advanced Life Cycle Engineering (CALCE),
University of Maryland
College Park, MD 20742 USA
Prognostics and Health Management Center
City University of Hong Kong
Hong Kong, China



The delay time concept and the techniques developed for modeling and optimizing plant inspection practices have been reported in many papers and case studies. For a system comprised of many components and subject to many different failure modes, one of the most convenient ways to model the inspection and failure processes is to use a stochastic point process for defect arrivals and a common delay time distribution for the duration between defect the arrival and failure of all defects. This is an approximation, but has been proven to be valid when the number of components is large. However, for a system with just a few key components and subject to few major failure modes, the approximation may be poor. In this paper, a model is developed to address this situation, where each component and failure mode is modeled individually and then pooled together to form the system inspection model. Since inspections are usually scheduled for the whole system rather than individual components, we then formulate the inspection model when the time to the next inspection from the point of a component failure renewal is random. This imposes some complication to the model, and an asymptotic solution was found. Simulation algorithms have also been proposed as a comparison to the analytical results. A numerical example is presented to demonstrate the model.

Index Terms—Delay time, Inspection, Optimal inspection interval, Maintenance

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