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On estimating survival for reliability models based on age‐related stochastic comparisons
Author(s) -
Reneau D. M.,
Rojo J.,
Samaniego F. J.
Publication year - 1993
Publication title -
naval research logistics (nrl)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.665
H-Index - 68
eISSN - 1520-6750
pISSN - 0894-069X
DOI - 10.1002/1520-6750(199308)40:5<603::aid-nav3220400505>3.0.co;2-e
Subject(s) - estimator , residual , mathematics , consistency (knowledge bases) , survival function , reliability (semiconductor) , stochastic ordering , nonparametric statistics , statistics , rate of convergence , convergence (economics) , failure rate , econometrics , kaplan–meier estimator , class (philosophy) , computer science , algorithm , economics , discrete mathematics , computer network , power (physics) , physics , channel (broadcasting) , quantum mechanics , artificial intelligence , economic growth
A new class of nonparametric reliability models is introduced and studied. A distribution is said to be better at age s than at age t ( s B t ) if the residual lifetime at age s is stochastically greater than or equal to the residual lifetime at age t . Applications to various forms of replacement policies, including the cannibalization of failed systems, are noted. For fixed s < t , the problem of estimating a survival curve assumed to belong to the s B t class is addressed using recursive methods. An s B t estimator is derived in closed form, and its uniform strong consistency at an optimal rate of convergence is demonstrated. A simulation study strongly supports the claim that the s B t estimator tends to outperform the empirical survivor function in small‐ and moderate‐size samples. © 1993 John Wiley & Sons, Inc.