Reliability Theory Based on Uncertain Lifetimes

Preface
Contents
1 Uncertain Mathematical Foundation
	1.1 Probability Theory
		1.1.1 Probability Measure
		1.1.2 Random Variable
		1.1.3 Probability Distribution
		1.1.4 Independence
		1.1.5 Identical Distribution
		1.1.6 Expected Value
		1.1.7 Conditional Probability
		1.1.8 Ranking Criteria
	1.2 Credibility Theory
		1.2.1 Credibility Measure
		1.2.2 Fuzzy Variable
		1.2.3 Membership Function
		1.2.4 Credibility Distribution
		1.2.5 Independence
		1.2.6 Identical Distribution
		1.2.7 Expected Value
	1.3 Random Fuzzy Theory
		1.3.1 Random Fuzzy Variable
		1.3.2 Chance Measure
		1.3.3 Independence
		1.3.4 Expected Value
2 Nonrepairable Systems with Stochastic Lifetimes
	2.1 Series and Parallel Systems
		2.1.1 The Series System
		2.1.2 The Parallel System
		2.1.3 The Series–Parallel System
		2.1.4 The Parallel–Series System
	2.2 Cold Standby Systems
		2.2.1 The Perfect Conversion Switch Case
		2.2.2 The Imperfect Conversion Switch Case: The Lifetime of the Conversion Switch Has 0–1 Distribution
		2.2.3 The Imperfect Conversion Switch Case: The Lifetime of the Conversion Switch Has an Exponential Distribution
	2.3 Warm Standby Systems
		2.3.1 The Perfect Conversion Switch Case
		2.3.2 The Imperfect Conversion Switch Case: The Lifetime of the Conversion Switch Has 0–1 Distribution
		2.3.3 The Imperfect Conversion Switch Case: The Lifetime of the Conversion Switch Has an Exponential Distribution
	2.4 Shock Models and the Bivariate Exponential Distribution
		2.4.1 Shock Models
		2.4.2 The Bivariate Exponential Distribution
3 Nonrepairable Systems with Fuzzy Lifetimes
	3.1 Series and Parallel Systems
		3.1.1 The Series System
		3.1.2 The Parallel System
		3.1.3 The Series–Parallel System
		3.1.4 The Parallel–Series System
	3.2 Cold Standby Systems
		3.2.1 The Perfect Conversion Switch Case
4 Nonrepairable Systems with Random Fuzzy Lifetimes
	4.1 Series and Parallel Systems
		4.1.1 The Series System
		4.1.2 The Parallel System
		4.1.3 The Series–Parallel System
		4.1.4 The Parallel–Series System
	4.2 Cold Standby Systems
		4.2.1 The Perfect Conversion Switch Case
		4.2.2 The Imperfect Conversion Switch Case: The Lifetime of the Conversion Switch has 0–1 Distribution
		4.2.3 The Imperfect Conversion Switch Case: The Lifetime of the Conversion Switch is Continuous
	4.3 Warm Standby Systems
		4.3.1 The Perfect Conversion Switch and Identical Component Case
		4.3.2 The Perfect Conversion Switch and Nonidentical Component Case
		4.3.3 The Imperfect Conversion Switch Case: The Lifetime of the Conversion Switch is Continuous
	4.4 Random Fuzzy Shock Models and the Bivariate Random Fuzzy Exponential Distribution
		4.4.1 Random Fuzzy Shock Models
		4.4.2 The Bivariate Random Fuzzy Exponential Distribution
5 Repairable Systems with Stochastic Lifetimes and Repair Times
	5.1 Renewal Processes and Markov Renewal Processes
		5.1.1 Renewal Processes
		5.1.2 Markov Renewal Processes
	5.2 The Single Component System
	5.3 The Series System
	5.4 The Parallel System
	5.5 Cold Standby Systems
		5.5.1 The Cold Standby System with Two Identical Components
		5.5.2 The Cold Standby System with Two Nonidentical Components
	5.6 The Coherent System
6 Repairable Systems with Random Fuzzy Lifetimes and Repair Times
	6.1 The Series System
	6.2 The Parallel System
	6.3 Cold Standby Systems
		6.3.1 The Two Identical Components Case
		6.3.2 The Two Nonidentical Components Case
	6.4 The Repairable Coherent System
Bibliography