Multistate Systems Reliability Theory With Applications

Bent Natvig is Professor in Mathematics Statistics, University of Oslo. Member of Research Education Committee, Faculty of Mathematics and Natural Sciences, 2000-. Member of User Committee, G.H. Sverdrup's Building, 2000-. Guest/Invited speaker at numerous lectures around Europe and America for the past 30 years. Speaking on reliability theory and mathematics and statistics. Research interests include: Reliability theory and risk analysis, Bayesian statistics, Bayesian forecasting and dynamic models and queuing theory. Currently Associate Editor of Methodology and Computing in Applied Probability.

Preface. Acknowledgements. List of abbreviations. 1 Introduction. 1.1 Basic notation and two simple examples. 1.2 An offshore electrical power generation system. 1.3 Basic definitions from binary theory. 1.4 Early attempts to define multistate coherent systems. 1.5 Exercises. 2 Basics. 2.1 Multistate monotone and coherent systems. 2.2 Binary type multistate systems. 2.3 Multistate minimal path and cut vectors. 2.4 Stochastic performance of multistate monotone and coherent systems. 2.5 Stochastic performance of binary type multistate strongly coherent systems. 2.6 Exercises. 3 Bounds for system availabilities and unavailabilities. 3.1 Performance processes of the components and the system. 3.2 Basic bounds in a time interval. 3.3 Improved bounds in a time interval using modular decompositions. 3.4 Improved bounds at a fixed point of time using modular decompositions. 3.5 Strict and exactly correct bounds. 3.6 Availabilities and unavailabilities of the components. 3.7 The simple network system revisited. 3.8 The offshore electrical power generation system revisited. 4 An offshore gas pipeline network. 4.1 Description of the system. 4.2 Bounds for system availabilities and unavailabilities. 5 Bayesian assessment of system availabilities. 5.1 Basic ideas. 5.2 Moments for posterior component availabilities and unavailabilities. 5.3 Bounds for moments for system availabilities and unavailabilities. 5.4 A simulation approach and an application to the simple network system. 6 Measures of importance of system components. 6.1 Introduction. 6.2 Measures of component importance in nonrepairable systems. 6.3 The Birnbaum and Barlow-Proschan measures of component importance in repairable systems and the latter's dual extension. 6.4 The Natvig measure of component importance in repairable systems and its dual extension. 6.5 Concluding remarks. 7 Measures of component importance - a numerical study. 7.1 Introduction. 7.2 Component importance in two three-component systems. 7.3 Component importance in the bridge system. 7.4 Application to an offshore oil and gas production system. 7.5 Concluding remarks. 8 Probabilistic modeling of monitoring and maintenance. 8.1 Introduction and basic marked point process. 8.2 Partial monitoring of components and the corresponding likelihood formula. 8.3 Incorporation of information from the observed system history process. 8.4 Cause control and transition rate control. 8.5 Maintenance, repair and aggregation of operational periods. 8.6 The offshore electrical power generation system. 8.7 The data augmentation approach. Appendix A Remaining proofs of bounds given in Chapter 3. A.1 Proof of the inequalities 14, 7 and 8 of Theorem 3.12. A.2 Proof of inequality 14 of Theorem 3.13. A.3 Proof of inequality 10 of Theorem 3.17. Appendix B Remaining intensity matrices in Chapter 4. References. Index.