Quickest Detection of a Failed Component with Unknown Distribution

Vaibhav Kumar

National Institute of Science and Technology, Berhampur, Odisha 761008

Professor Rajesh Sundaresan

Robert Bosch Center For Cyber-Physical Systems , Indian Institute of Science, Bengaluru 560012

Dr. Alexandre Reiffers

Post Doctoral Fellow, Robert Bosch Center For Cyber-Physical Systems , Indian Institute of Science, Bengaluru 560012

Abstract

Inspection is considered as a vital part of any maintenance process. It can be defined as an organized examination or an evaluation exercise of a component. Suppose an operator inspects a component to prevent a failure. The goal is to decide when to replace the component without knowing the distribution of the given component. The decision maker can choose the instant of inspections and when to replace the component. Taking more frequent inspection yields accurate estimates of the failure distribution but incurs a higher measurement cost. Making a replacement too soon incurs a given cost. Having a failure incurs a high penalty. There are mainly two replacement practices which are considered optimal for inspection models. One is block replacement policy in which preventive replacements occur at a given date, regardless of the age of the component. The second one is age replacement policy, where the preventive replacement occurs depending on the component age. We try to find the optimal intervals for inspecting a component in order to minimize the cost. For the optimal sequential strategy for the decision maker, we propose to study two approaches. In the first approach, we model this problem as an adaptive control problem where the time for next inspection will depend on the previous failure frequency of the component and hence it will be updated according to previous data. The algorithm used in this case is called the rolling horizon algorithm. A model is proposed for multiple components inspection too. Various types of distributions were studied and their simulations were observed in python and the graph for the corresponding sequential estimation of parameters were simulated.

Keywords: Conjugate Prior, Adaptive Control, Bellman's equation, Markov Decision Process, Rolling horizon algorithm