Contributions to Hardware and Software Reliability Modelling

by Kapur, P. K.; Garg, R. B.; Kumar, S.

• ISBN13: 9789810237516
• ISBN10: 9810237510
• Format: Hardcover
• Copyright: 1999-09-01
• Publisher: WORLD SCIENTIFIC PUB CO INC

Summary

Discusses those aspects that have relevance to computing systems and those where numerical computation was a problem.

Table of Contents

1 PRELIMINARY CONCEPTS AND BACKGROUND	1	(24)
1.1 INTRODUCTION	1	(1)
1.2 DEFINITIONS AND CONCEPTS IN RENEWAL THEORY	1	(9)
1.2.1 Definitions	1	(3)
1.2.2 Concepts in Renewal Theory	4	(6)
1.3 SOFTWARE RELIABILITY -- AN OVERVIEW	10	(6)
1.4 TERMS USED IN SOFTWARE RELIABILITY	16	(9)
2 REPLACEMENT POLICIES WITH MINIMAL REPAIRS	25	(34)
2.1 INTRODUCTION	25	(1)
2.2 DIFFERENT POLICIES	26	(2)
2.3 REPLACEMENT POLICIES WITH MINIMAL REPAIRS	28	(9)
2.3.1 Model I	28	(2)
2.3.2 Model II	30	(2)
2.3.3 Model III	32	(2)
2.3.4 Model IV	34	(2)
2.3.5 Model V	36	(1)
2.4 OPTIMISATION	37	(1)
2.5 APPLICATIONS	38	(1)
2.6 ORDERING POLICIES UNDER MINIMAL REPAIRS	39	(8)
2.6.1 Ordering policies based on repair cost limit criterion	39	(8)
2.7 GENERALISED ORDERING POLICIES	47	(5)
2.7.1 The Policies	47	(5)
2.8 APPENDIX A	52	(1)
2.9 APPENDIX B	52	(7)
3 PROBLEMS WITH APPLICATIONS TO COMPUTING SYSTEMS	59	(26)
3.1 INTRODUCTION	59	(1)
3.1.1 Interval Reliability Computation	59	(1)
3.1.2 Inspection Policies	60	(1)
3.1.3 A General Replacement Policy	60	(1)
3.2 RELIABILITY INDICATORS	60	(8)
3.2.1 Interval Reliability for Repairable Computing Systems	60	(2)
3.2.2 Interval Reliability Computation	62	(2)
3.2.3 Numerical Computation Procedure and Algorithm	64	(3)
3.2.4 Further Extension	67	(1)
3.3 OPTIMAL INSPECTION TIMES	68	(7)
3.4 MINIMAL REPAIRS BEFORE REPLACEMENT WITH REPAIR COST LIMIT	75	(10)
3.4.1 Optimisation	78	(1)
3.4.2 Further Applications	79	(6)
4 SOFTWARE RELIABILITY GROWTH MODELS BASED ON NHPP	85	(48)
4.1 INTRODUCTION	85	(1)
4.2 CONTINUOUS SRGMs	85	(7)
4.3 DISCRETE SRGMs	92	(4)
4.4 ESTIMATION OF PARAMETERS	96	(1)
4.4.1 Estimation of Parameters for Continuous SRGMs	96	(1)
4.4.2 Estimation of Parameters for Discrete SRGMs	96	(1)
4.5 COMPARISON CRITERIA	97	(1)
4.5.1 The Goodness of Fit Criterion	97	(1)
4.5.2 The Predictive Validity Criterion	97	(1)
4.6 DATA ANALYSIS BASED ON GENERALISED ERLAND MODEL	98	(3)
4.6.1 Goodness of Fit Analysis	98	(2)
4.6.2 Predictive Validity Analysis	100	(1)
4.7 GENERALISED ERLAND MODEL	101	(6)
4.7.1 Validation of the Extended Model	102	(5)
4.8 MODEL SELECTION	107	(1)
4.9 RELIABILITY MEASUREMENT FOR GENERALISED ERLAND MODEL WITH n TYPES OF FAULTS	108	(1)
4.10 MODEL FOR OBJECT ORIENTED SOFTWARE SYSTEMS	109	(24)
5 RELEASE POLICIES	133	(24)
5.1 INTRODUCTION	133	(1)
5.2 RELEASE POLICIES BASED ON DIFFERENT CRITERIA	133	(15)
5.2.1 Cost Criterion	134	(1)
5.2.2 Reliability Criterion	134	(1)
5.2.3 Cost and Reliability Criterion	134	(1)
5.2.4 Cost and Reliability Criteria Under Penalty Cost	135	(2)
5.2.5 Release Policy with Testing Effort	137	(1)
5.2.6 Release Policy When the Life Cycle Is Random	138	(1)
5.2.7 Bicriterion Release Policy	139	(4)
5.2.8 Post Optimality Analysis	143	(2)
5.2.9 Optimum Release Policy for a Log-Power Model	145	(3)
5.3 OPTIMAL RELEASE POLICY FOR A DISCRETE SRGM	148	(1)
5.4 TESTING EFFORT CONTROL PROBLEM	149	(3)
5.5 RESOURCE ALLOCATION FOR A MODULAR STRUCTURE	152	(5)
6 NUMERICAL COMPUTATIONS IN RENEWAL AND RELIABILITY THEORY	157	(34)
6.1 INTRODUCTION	157	(1)
6.2 RENEWALS IN CONTINUOUS TIME	158	(13)
6.2.1 Expected Number of Renewals in Time t: E(N(t))	158	(2)
6.2.2 Variance of the Number of Renewals	160	(3)
6.2.3 Approximations for Weibull and Gamma Distributions	163	(2)
6.2.4 First Two Moments of The Number of Renewals In Discrete Time	165	(6)
6.3 TRANSIENT SOLUTIONS IN DISCRETE TIME IN RELIABILITY	171	(9)
6.3.1 Reliability Analysis	174	(3)
6.3.2 Continuous-time Case	177	(1)
6.3.3 Some Particular Cases	177	(3)
6.4 SRGM WITH IMPERFECT DEBUGGING AND FAULTS	180	(11)
INDEX	191