Reliability and Maintenance Modeling with Optimization

13Phase-Type Expansion of Markov Regenerative Processes and Its Application to Reliability Problems

Hiroyuki Okamura

Hiroshima University

Junjun Zheng

Ritsumeikan University

Tadashi Dohi

Hiroshima University

CONTENTS

• 13.1 Introduction

• 13.2 Markov Regenerative Process

  • 13.2.1 Structured MRGP

  • 13.2.2 Stationary Analysis for Structured MRGP

• 13.3 PH Expansion of MRGP

  • 13.3.1 PH Approximation

  • 13.3.2 PH Expansion

• 13.4 Illustrative Examples

  • 13.4.1 MRSPN to MRGP

  • 13.4.2 PH Expansion

• 13.5 Conclusions

13.1 INTRODUCTION

Markov modeling is one of the most important techniques to evaluate reliability and performance of systems. In a family of stochastic processes possessing some degree of Markov property, a Markov regenerative process (MRGP) is ...