Optimal Inspection Models with Their Applications

Preface
Contents
1 Introduction
	1.1 Importance of Reliability Engineering
	1.2 Stochastic Models and Practical Applications
	1.3 Two Problems of Inspection
	1.4 Standard and Random Inspections
	1.5 General Inspection
	1.6 Inspection Model with Minimal Repair
	1.7 Hierarchical Structure Reliability
	1.8 Application Examples
	1.9 Problems
	References
2 Standard Inspection Models
	2.1 Standard Inspection Policy
		2.1.1 Asymptotic Inspection Times
	2.2 Inspection for Finite Interval
		2.2.1 Asymptotic Inspection Times
	2.3 Inspection for Random Interval
	2.4 Modified Inspection Models
		2.4.1 Imperfect Inspection
		2.4.2 Intermittent Fault
		2.4.3 Inspection for Scale
	2.5 Problems
	References
3 Random Inspection Models
	3.1 Periodic and Random Inspections
		3.1.1 Sequential Inspection
		3.1.2 Comparison of Periodic and Random Inspections
	3.2 Random Inspection
	3.3 Inspection First and Last
		3.3.1 Inspection First
		3.3.2 Inspection Last
		3.3.3 Comparison of Inspection First and Last
	3.4 Inspection Overtime
		3.4.1 Comparisons of Periodic Inspection and Inspection Overtime
		3.4.2 Comparisons of Inspection Overtime with First and Last
	3.5 Problems
	References
4 General Inspection Models
	4.1 Inspection First and Last
		4.1.1 Inspection First
		4.1.2 Inspection Last
	4.2 General Inspection Models
		4.2.1 Inspection First
		4.2.2 Inspection Last
	4.3 Inspection Models with Three Variables
		4.3.1 Inspection First, Last and Middle
		4.3.2 Comparisons of Inspection First, Last and Middle
	4.4 Modified Inspection Models
		4.4.1 Modified Inspection First
		4.4.2 Modified Inspection Last
		4.4.3 Comparisons of Modified Inspection First and Last
	4.5 Problems
	References
5 Inspection Models with Minimal Repair
	5.1 Inspection with Two Failures
		5.1.1 Periodic Inspection
		5.1.2 Sequential Inspection
	5.2 Modified Inspection Model
		5.2.1 Periodic Inspection
		5.2.2 Sequential Inspection
	5.3 Inspection for a Finite Interval
		5.3.1 Standard Inspection
		5.3.2 Modified Inspection Model
	5.4 Problems
	References
6 Hierarchical Structure Reliability
	6.1 Basic System
		6.1.1 n-Unit Parallel System
		6.1.2 n-Unit Series System
		6.1.3 k-Out-of-n System
	6.2 Random K-Out-of-n System
		6.2.1 Series-Parallel System
		6.2.2 Parallel-Series System
		6.2.3 Consecutive K-Out-of-5:F System
	6.3 Comparison of Series-Parallel and Parallel-Series Systems
		6.3.1 Reliability Properties
		6.3.2 Replacement Time
		6.3.3 Inspection Time
	6.4 Problems
	References
7 Application Examples of Storage System
	7.1 Basic Inspection Model
	7.2 Modified Inspection Model
	7.3 Finite Number of Inspections
	7.4 Degradation at Inspection
	7.5 Problems
	References
8 Application Examples of Phased Array Radar
	8.1 Cost Model
		8.1.1 Cyclic Maintenance
		8.1.2 Delayed Maintenance
	8.2 Availability Model
		8.2.1 Cyclic Maintenance
		8.2.2 Delayed Maintenance
		8.2.3 Combined Cyclic and Delayed Maintenances
	8.3 Problems
	References
9 Application Examples of Power Generator
	9.1 Self-Diagnosis Policy for Gas Turbine FADEC
		9.1.1 Standard FADEC System
	9.2 Maintenance of Power Generator
		9.2.1 Shock Model with Damage Level
		9.2.2 Two Modified Schock Models
		9.2.3 Shock Model with Multi-echelon Risks
	9.3 Problems
	References
10 Application Examples of Airframe
	10.1 Optimal Multi-echelon Maintenance of Aircraft
		10.1.1 Multi-echelon Maintenance with Hazard Rates
		10.1.2 Operation Policy for Commercial Aircraft
	10.2 Airframe Maintenance with Crack Growth
		10.2.1 Airframe Cracks (1)
		10.2.2 Airframe Cracks (2)
	10.3 Commercial Airframe with Damage and Crack
		10.3.1 Damage Level and Crack Number
		10.3.2 Multiple Damage Levels and Crack Number
	10.4 Problems
		A.1 H(t)/t Increases Strictly with t to h(infty)
		A.2 L3(n,x) Increases Strictly with x to infty
		A.3 QK(N) Increases Strictly with N from exp(-wK) to 1
		A.4 QKM(N) Increases Strictly with N to 1
		A.5 Qf(N) Increases Strictly with N to 1-exp(-λ)
	References
Appendix  Answers to Selected Problems