Optimization of Availability-Redundancy in Multiple Multi-State Parallel-Series Systems Considering Multi-Stage Failures and Supplier Selection

Abstract

Introduction: Given the competitive and globalized nature of markets, availability has become a crucial aspect of product design in recent decades. Modern availability includes functional requirements, adherence to standards, design considerations, predictability of availability, modeling, and evaluation. One objective of availability is to design systems with maximum accessibility. System availability is often improved by enhancing the availability of individual components or by allocating redundant components. These improvements are achieved through better materials, improved manufacturing processes, and the application of design principles. Method: This paper introduces an innovative approach to optimizing multiple parallel-series multi-state systems. Unlike traditional methods that focus on optimizing a single system, this approach simultaneously optimizes multiple systems to enhance their overall efficiency and performance. These systems contain parallel subsystems with multi-state components that can operate in various states, providing different performance outcomes. A significant aspect of this model is the impact of multi-stage failure rates on the systems, analyzed through state diagrams. The model also considers various assumptions, including the capability to select suppliers with different conditions and constraints. Additionally, the effects of technical and organizational activities on continuous optimization intervals are analyzed. The model is refined using a genetic algorithm, showing considerable improvements in system performance.Results and discussion: An optimization mathematical model is presented to address the problem under specified assumptions. A numerical example is provided where the state transition distribution function is exponential, and technical and organizational activities have varying performance intensities. In this example, the performance rate of each subsystem equals the sum of the performance rates of its components, and the system's performance is at least as good as the minimum performance rate of its subsystems. Based on these assumptions, the system's availability probability and cost can be calculated using the model's objective function. The example problems are then solved using a genetic algorithm, and the results are reported. Conclusions: Recent research indicates that scholars in the field of redundancy allocation models for both binary and multi-state systems have continuously aimed to make these problems more realistic by incorporating new assumptions or eliminating simplifying ones. These efforts underscore the importance of developing mathematical optimization models that consider all system conditions and constraints, addressing the broader issues faced by decision-makers. Our research demonstrates that expanding the dimensions of optimization problems related to redundancy allocation can produce models that better reflect real-world conditions.

Keywords

• availability
• redundancy allocation problem
• supplier selection
• genetic algorithm
• multi-state parallel-series system