Abstract
This study proposes models to find the optimal non-periodic inspection interval over a finite planning horizon for two types of multi-component repairable systems. The first system consists of hard-type and soft-type components, and the second system is a k-out-of-m system with m identical components. The failures of components in both systems follow a non-homogeneous Poisson process. The failure of soft-type components and the failure of components in a k-out-of-m system when the number of failed components is still less than m-k+1, are soft failures. Soft failures are revealed only at scheduled inspections or when an event of opportunistic inspection or a system failure occurs. The failures of hard-type components or the failure of (m-k+1)th failed component in a k-out-of-m system are hard failures, and cause the system to stop functioning. Hard failures are revealed immediately and the failed components are fixed. In this study, a failed component is either replaced or minimally repaired according to its age at failure time. To find the optimal inspection schedules for the systems, we minimize the total expected cost of the systems over a finite planning horizon. The total cost for the first type of system includes the costs of components’ minimal repairs, replacements, downtimes, and the scheduled inspections. The total cost of a k-out-of-m system has an additional penalty cost for system failures. We consider a binary variable for a possible scheduled inspection’s time, in which 1 indicates performing a planned inspection at that time, and 0 shows no inspection to be performed. Thus, our goal is to find the optimal vector of binary decision variables which results in the minimum total cost of the system. A recursive formula is developed to calculate the expected number of minimal repairs, replacements and downtime of soft-type components. However since obtaining the expected values from the mathematical formula is cumbersome, we develop a simulation model to obtain the total expected cost for a given non-periodic inspection scheme. We then integrate the simulation model with a genetic algorithm to obtain the optimal inspection scheme.
Highlights
A thesis presented to Ryerson University in partial fulfillment of the requirements for the degree of Master of Applied Science in the program of Mechanical and Industrial Engineering
I authorize Ryerson University to lend this thesis to other institutions or individuals for the purpose of scholarly research
This study proposes models to find the optimal non-periodic inspection interval over a finite planning horizon for two types of multi-component repairable systems
Summary
Costs of maintenance and downtime for different components. Parameters of the power law intensity function, and the probability function of minimal repair for all components. Taghipour and Banjevic [36] consider optimal periodic inspection interval for complex multi-component systems with hard and soft failures. Their model considers two types of inspection – periodic and opportunistic. Another difference of our work is that we develop an optimization model for a system which is subject to non-periodic inspections, while Wang [47] considers periodic inspection We both assume that the failure times of soft-type components are unknown. Wang et al [50] propose a model for two-level inspection policy of a single component system based on a three-stage failure process They [50] jointly optimize the minor and major inspection intervals, as well as a threshold level for the planned maintenance by minimizing the expected cost per unit time. Since calculating the expected values from the recursive formula is computationally intensive, we develop a simulation model to obtain the expected costs in equation (2.5) and equation (2.6) for a given non-periodic inspection scheme
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