By Anatoly Lisnianski, Ilia Frenkel
1. Signature illustration and maintenance effects for Engineered platforms and purposes to Statistical Inference.- 2. utilizing D-Spectra in community Monte Carlo: Estimation of approach Reliability and part Importance.- three. Signatures and Symmetry houses of Coherent Systems.- four. Multidimensional Spectra of Multistate platforms with Binary Components.- five. purposes of Samaniego Signatures to Bounds on Variances of Coherent and combined process Lifetimes.- 6. Lz-Transform for a Discrete-state Continuous-Time Markov strategy and Its functions to Multi-state method Reliability.- 7. Reliability judgements for grocery store Refrigeration method through the use of mixed Stochastic technique and common producing functionality approach: Case Study.- eight. value research of a Multi-State procedure in line with Multiple-Valued common sense Methods.- nine. optimum alternative and security method for Parallel Systems.- 10. Heuristic Optimization options for choosing optimum Reserve constitution of energy producing Systems.- eleven. choice of important actions in Reliability software for Multi-state process through the use of condominium of Reliability.- 12. Multi-State Availability Modeling in Practice.- thirteen. Reliability research of Redundant platforms with Unimodal chance cost Functions.- 14. Multiobjective Reliability Allocation in Multi-state platforms: determination Making by way of Visualization and research of Pareto Fronts and Sets.- 15. optimum Incomplete upkeep in Multi-state Systems.- sixteen. Nonparametric Estimation of Marginal Temporal Functionals in a Multi-state Model.- 17. Frailty or Transformation types in Survival research and Reliability.- 18. Goodness of healthy assessments for Reliability Modeling.- 19. at the Markov Three-state revolutionary Model.- 20. Multi-State Semi-Markov version of the Operation Reliability.- 21. Reliability of Continuous-State structures in View of Heavy-Tailed allotted functionality Features.- 22. On optimum keep watch over of structures on Their lifestyles Time
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Additional info for Recent advances in system reliability : signatures, multi-state systems and statistical inference
Commun Stat Theory Methods 36:175–191 Navarro J, Balakrishnan N, Samaniego FJ (2008a) Mixture representations of residual lifetimes of used systems. J Appl Probab 45:1097–1112 Navarro J, Samaniego FJ, Balakrishnan N, Bhattacharya D (2008b) On the application and extension of system signatures in engineering reliability. Naval Res Logist 55:313–327 Navarro J, Samaniego FJ, Balakrishnan N (2010) Joint signature of coherent systems with shared components. J Appl Probab 47:235–253 Ng HKT, Navarro J, Balakrishnan N (2011) Parametric inference for system lifetime data with signatures available under a proportional hazard rate model.
16); similarly we ðmÞ shall use the notation qðmÞ ; sðmÞ ; Rk:3 ; . . The event E1 is obviously equivalent to fTð1Þ ¼ T1 g and thus ðmÞ s1 À Á ¼ PðmÞ Tð1Þ ¼ T1 : 1 ; Now it is easy to check that PðmÞ ðTð1Þ ¼ T1 Þ ¼ PðmÞ ðT1 [ minðT2 ; T3 ÞÞ ¼ 1þ2m ðmÞ ðmÞ and thus the vectors q and s are necessarily different. 46 F. Spizzichino and J. Navarro On the other hand we can claim that the order-statistics exchangeability ðmÞ ðmÞ ðmÞ ðmÞ conditions R1:3 ðtjE1 Þ ¼ R1:3 ðtÞ and R2:3 ðtjE2 Þ ¼ R2:3 ðtÞ approximately hold.
Springer, New York Chapter 2 Using D-Spectra in Network Monte Carlo: Estimation of System Reliability and Component Importance Ilya B. Gertsbakh and Yoseph Shpungin Abstract We present a combinatorial definition of network-type system destruction spectrum (signature) and component importance D-spectra, and demonstrate how Birnbaum importance measures (BIMs) can be expressed via these spectra. We demonstrate an efficient algorithm which calculates simultaneously system reliability spectrum and BIM spectra for all its components.