Systems with Multi-Components
The main purpose of this chapter is to construct a system structure function based on an observed set of the system output performance and the corresponding performances of its components. To do this, special techniques are proposed by looking at the structure function of a continuous-state system under the scope of a regression model. Multivariate smoothing and isotonic regression methods are adapted to the particular characteristics of the problem at hand.
KeywordsStructure Function Integrate Square Error Average Square Error Universal Generate Function Symmetric Density Function
This chapter is an extension into book-length form of the article Regression analysis of the structure function for reliability evaluation of continuous-state system, originally published in Reliability Engineering and System Safety 95(2), 134–142 (2010).
The authors express their full acknowledgment of the original publication of the paper in the journal cited above, edited by Elsevier.
- 3.Barlow RE, Proschan F (1975) Statistical theory of reliability and life testing. Holt, Rinehart and Winston, New YorkGoogle Scholar
- 8.Brunelle RD, Kapur KC (1999) Review and classification or reliability measures for multistate and continuum models. IIE Trans 31:1171–1180Google Scholar
- 9.Burdakow O, Grimwall A, Hussian M (2004) A generalised PAV algorithm for monotonic regression in several variables. COMPSTAT’2004 SymposiumGoogle Scholar
- 12.Fan J, Gijbels I (1996) Local polynomial modelling and its applications. Monographs on statistics and applied probability. Chapman & Hall, LondonGoogle Scholar
- 18.Levitin G (2005) The universal generating function in reliability analysis and optimization. Springer, LondonGoogle Scholar
- 24.Natvig B (1982) Two suggestions of how to define a multistate coherent system. Appl Prob 14:434–455Google Scholar
- 30.Turner R (2009) Iso: functions to perform isotonic regression http://CRAN.R-project.org/package=Iso