Maintenance Optimization of a 2-Component Swappable Series System Using the Delay-Time Concept

Liying Wang,Wenhua Zhang,Alessandro Rasulo

doi:10.1155/2021/9688043

Abstract

In the 2-component swappable series system, the two components undertake tasks with different loads and degrade at different speeds. To prolong the lifetime of the series system, these two components are swapped in the operating process of the system in practice. This is common in the maintenance of duplexing steelmaking systems, tires of vehicles, and steel rails in curves. The failure process of each component in the system is modeled based on a two-stage delay-time concept and divided into two stages: normal and defective. Inspections are carried out periodically on the system. Two components may be swapped once at an inspection time that the two components are both in the normal stage. Due to the increase or decrease of loads, normal and defective time distributions after the swap are assumed to be different from those prior to the swap. The system is subjected to failure, inspection, and age-based renewals. The number of inspections over the maximum usage time of the system and the swap time are optimized jointly by minimizing the expected cost per unit time in a long run. A numerical example is presented to demonstrate the model.

Highlights

Introduction e motivation of the paper comes from the operating process of the duplexing steelmaking system and maintenance of vehicles and steel rails in curves. e duplexing steelmaking system usually consists of two converters
To prolong the system’s lifetime, the decarburization converter will be used for dephosphorization at a later stage of the furnace life; that is, the two converters are swapped. e swap time is usually determined by engineers according to their experiences. e swap can be found in the process of vehicle maintenance
Delay-time-based maintenance models can capture the relationship between the number of failures and inspection intervals, so they are widely used in describing the degradation of plants and optimizing of inspection intervals (Baker and Wang [10]; Baker and Christer [11]; Jia and Christer [12]; Wang [13]; Aven and Castro [14]; Jones et al [15]; and Scarf et al [16])

Summary

Modeling Assumptions and Notations

We consider a series system with two components, namely, components 1 and 2. While on a failure renewal, a component fails and the other component may be in normal or defective states; it can be restored at a lower cost. In order to derive the long run expected cost per unit time, the renewal probabilities prior to and after the swap need to be formulated. Let fm(z) be the probability density function of the time that Z exceeds (m − 1)T in the scenario that the system fails at Tf, Tf ∈ ((m − 1)T, mT)(1 ≤ m ≤ M + 1), before which no defective stage has been identified by inspections. From assumption (4) and notations, after the swap, the pdf and cdf of the duration time in defective stage for component i(i 1, 2) are g􏽥i(u) and G􏽥 i(u), respectively.

Cost Models

Optimisation of the Number of Inspections and the Time of

Conclusions and Further Research