Modern Dynamic Reliability Analysis for Multi-state Systems: Stochastic Processes and the Lz-Transform

Preface
Contents
1 Generic Model of Multi-state System. Reliability, Availability and Performability in Dynamic Modes
	1.1 Generic Multi-state System Model
	1.2 Reliability, Availability and Performability of Multi-state System
		1.2.1 Reliability Measures of Multi-state Systems
		1.2.2 Availability Measures of Multi-state Systems
		1.2.3 Performability Measures of Multi-state Systems
	1.3 Summary
	References
2 Stochastic Processes Methods for MSS Reliability, Availability and Performability Assessment
	2.1 General Concepts of Stochastic Processes Theory
	2.2 Markov Models: Discrete-Time Markov Chains
		2.2.1 Basic Definitions and Properties
		2.2.2 Computation of n-Step Transition Probabilities and State Probabilities
	2.3 Markov Models: Continuous-Time Markov Chains
		2.3.1 Basic Definitions and Properties
		2.3.2 Markov Models for Evaluating Reliability of Multi-state Elements
	References
3 LZ-Transform and Inverse LZ-Transform of a Discrete-State Continuous-Time Markov Process
	3.1 LZ-Transform
		3.1.1 LZ-Transform Definition
		3.1.2 Existence and Uniqueness
		3.1.3 LZ-Transform’s Properties
		3.1.4 LZ-Transform Application to MSS Reliability Analysis
	3.2 Inverse LZ-Transform
		3.2.1 Computational Procedure for Determining Inverse LZ-Transform
		3.2.2 Determining Set of States and Set of Initial Conditions for Entire MSS
		3.2.3 Determining Matrix A
		3.2.4 The Method Application
		3.2.5 Calculation of Reliability Function and Mean Time to Failure
		3.2.6 Numerical Example
	3.3 Summary
	References
4 Short-Term Availability, Performability and Reliability Analysis for Power Systems
	4.1 Short-Term Availability and Performability Evaluation for Coal Fired Power Station by Using LZ-Transform
		4.1.1 Multi-state Model for a Single Coal Fired Power Generating Unit
		4.1.2 Short-Term Reliability Analysis for Power Station with Several Coal Fired Units
		4.1.3 Short-Term Analysis for Power Plant with Three Coal Fired Generating Units
	4.2 Short-Term Availability and Performability Analysis of Power Plants with Combined Cycle Units
		4.2.1 Multi-state Markov Model for a Single Combined Cycle Generating Unit and LZ-Transform for Its Output Generating Capacity Process
		4.2.2 Multi-state Reliability Analysis for Power System, Consisting of Number Combine Cycle Generating Units
		4.2.3 Short-Term Availability and Performability Analysis for Power Station with Three Combine-Cycle Units. Case Study
	4.3 Short-Term Reliability and Risk Evaluation for Power System Using Inverse LZ-Transform
		4.3.1 Inverse LZ-Transform Application to Risk Function Evaluation for Power Station
		4.3.2 Risk Evaluation for Power Station with Several Coal-Fired Generating Units. Case Study
	4.4 Summary
	References
5 The LZ-Transform Application for Availability Assessment of Air Conditioning System for Chemical Laboratories
	5.1 Description of Chemical Laboratory Air Conditioning System and Its Elements
		5.1.1 Description of the System
		5.1.2 Description of the System’s Elements
	5.2 Multi-state Models for an Air Conditioning System for a Chemical Laboratory
	5.3 Calculation of the Availability Indices of an Air Conditioning System for a Chemical Laboratory
	5.4 Summary
	References
6 Availability and Performability of the Reserved Cold Water Supply System for a Raw Material Manufacturing for Plastics Industry
	6.1 Multi-state Model of the Reserved Cold Water Supply System
		6.1.1 System’s Description
		6.1.2 Description of System’s Elements
	6.2 The LZ-Transform Application for Calculation of the Availability and Performability Indices of the Cold Water Supply System
	6.3 Calculation of the Reliability and Performability Indices of the Cold Water Supply System
	6.4 Summary
	References
7 Sensitivity Evaluation for an Aging Multi-state System
	7.1 Sensitivity Analysis for Aging MSS by Using LZ-Transform Method
	7.2 Multi-state Models of the Water Cooling System for Magnetic Resonance Inspection (MRI) Plant
		7.2.1 System’s Description
		7.2.2 Description of Sub-systems and System’s Elements
		7.2.3 The LZ-Transform Application for Calculation of the Reliability Indices of the Water Cooling System
	7.3 Sensitivity Analysis of the Water Cooling System
	7.4 Summary
	References
8 Birnbaum Importance Assessment for Aging Multi-state Water Cooling System
	8.1 Dynamic B-Availability Importance Assessment by Using the LZ-Transform Method
	8.2 B-Availability Importance Assessment for the Water Cooling System of Magnetic Resonance Inspection Equipment
		8.2.1 System Description and Corresponding Reliability Data
		8.2.2 Computation LZ-Transforms for System’s Elements and Sub-systems
		8.2.3 LZ-Transform for the Entire MRI Water Cooling System Availability
		8.2.4 B-Availability Importance Calculation
	8.3 Summary
	References
Appendix MATLAB Codes for Case Studies Calculations
A.1 Using MATLAB ODE Solvers
A.2 MATLAB Code for the Chap. 5—The LZ-Transform Application for Availability Assessment of Air Conditioning System for Chemical Laboratory