Reliability and Maintenance Modeling with Optimization

15Alternating α-Series Process

Richard Arnold

Victoria University of Wellington, New Zealand

Stefanka Chukova

Victoria University of Wellington, New Zealand

Yu Hayakawa

Waseda University, Japan

Sarah Marshall

Auckland University of Technology, New Zealand

CONTENTS

• 15.1 Introduction

• 15.2 α-Series Process

• 15.3 Alternating α-Series Process

  • 15.3.1 Introduction

  • 15.3.2 Counting Process 1: N(t) Number of Cycles Completed by Time t

  • 15.3.3 Counting Process 2: M(t) Number of Failures up to Time t

• 15.4 Mean and Variance of the Counting Processes N(t) and M( t)

  • 15.4.1 Computing E(N( t)) and Var(N(t))

  • 15.4.2 Computing E(M( t)) and Var(M(t))

• 15.5 Numerical Results

• 15.6 Application of an AAS Process to Modelling Warranty Data

  • 15.6.1 Procedure for Fitting ...