Citation for Published Item: Use Policy Nonparametric Predictive Inference for System Reliability Using the Survival Signature

The survival signature has recently been presented as an attractive concept to aid quantification of system reliability. It has similar characteristics as the system signature, which is well established, but contrary to the latter it is easily applicable to systems with multiple types of components. We present an introductory overview of the survival signature together with new results to aid computation. We develop nonparametric predictive inference for system reliability using the survival signature. The focus is on the failure time of a system, given failure times of tested components of the same types as used in the system.

[1]  Lev V. Utkin.  Interval reliability of typical systems with partially known probabilities , 2004, Eur. J. Oper. Res..

[2]  Frank P. A. Coolen,et al.  Nonparametric predictive utility inference , 2012, Eur. J. Oper. Res..

[3]  Frank P. A. Coolen,et al.  Nonparametric predictive reliability of series of voting systems , 2013, Eur. J. Oper. Res..

[4]  Frank P. A. Coolen,et al.  Imprecise Probability , 2011, International Encyclopedia of Statistical Science.

[5]  Jorge Navarro,et al.  Comparisons and bounds for expected lifetimes of reliability systems , 2010, Eur. J. Oper. Res..

[6]  AbdullahHomodO Al-Nefaiee,et al.  Nonparametric Predictive Inference forSystem Failure Time , 2014 .

[7]  Pauline Coolen-Schrijner,et al.  Nonparametric predictive inference for system reliability with redundancy allocation , 2008 .

[8]  Stefan Pischinger,et al.  A contribution to the understanding of thermomechanical fatigue sensitivities in combustion engine cylinder heads , 2011 .

[9]  Frank P. A. Coolen,et al.  Nonparametric predictive inference for system failure time based on bounds for the signature , 2013 .

[10]  T Coolen-Maturi,et al.  Unobserved, re-defined, unknown or removed failure modes in competing risks , 2011 .

[11]  Frank P. A. Coolen,et al.  Nonparametric predictive system reliability with redundancy allocation following component testing , 2009 .

[12]  Jun Li,et al.  Automated multi-objective and multidisciplinary design optimization of a transonic turbine stage , 2012 .

[13]  F. Coolen,et al.  Nonparametric predictive inference with right-censored data , 2004 .

[14]  Vanderlei da Costa Bueno,et al.  Active redundancy allocation for a k , 2007, Eur. J. Oper. Res..

[15]  Quan-Lin Li,et al.  Algorithm for a general discrete k-out-of-n: G system subject to several types of failure with an indefinite number of repairpersons , 2011, Eur. J. Oper. Res..

[16]  F. Coolen,et al.  Generalizing the signature to systems with multiple types of components , 2013, SOCO 2013.

[17]  Frank P. A. Coolen,et al.  Imprecise Reliability , 2011, International Encyclopedia of Statistical Science.

[18]  L. M. M.-T..  Theory of Probability , 1929, Nature.

[19]  Pauline Coolen-Schrijner,et al.  A nonparametric predictive method for queues , 2003, Eur. J. Oper. Res..

[20]  Frank P. A. Coolen,et al.  Classification with decision trees from a nonparametric predictive inference perspective , 2014, Comput. Stat. Data Anal..

[21]  T. Maturi,et al.  Nonparametric predictive inference for competing risks , 2010 .

[22]  Frank P. A. Coolen,et al.  Nonparametric Predictive Inference for Order Statistics of Future Observations , 2010, SMPS.

[23]  Francisco J. Samaniego,et al.  System Signatures and Their Applications in Engineering Reliability , 2007 .

[24]  Frank P. A. Coolen,et al.  Imprecise reliability: An introductory overview , 2007, Intelligence in Reliability Engineering.

[25]  Kurt Weichselberger.  Elementare Grundbegriffe einer allgemeineren Wahrscheinlichkeitsrechnung I , 2001 .

[26]  N. Balakrishnan,et al.  Signature-based representations for the reliability of systems with heterogeneous components , 2011 .

[27]  Louis J. M. Aslett,et al.  MCMC for inference on phase-type and masked system lifetime models , 2012 .

[28]  Thomas Augustin,et al.  Nonparametric predictive inference and interval probability , 2004 .

[29]  P. Walley.  Statistical Reasoning with Imprecise Probabilities , 1990 .

[30]  Serkan Eryilmaz.  Review of recent advances in reliability of consecutive k-out-of-n and related systems , 2010 .

[31]  Gregory Levitin.  Intelligence in Reliability Engineering: New Metaheuristics, Neural and Fuzzy Techniques in Reliability , 2007, Studies in Computational Intelligence.

[32]  Serkan Eryilmaz,et al.  Circular consecutive k-out-of-n systems with exchangeable dependent components , 2011 .

[33]  Frank P. A. Coolen,et al.  Nonparametric predictive inference for failure times of systems with exchangeable components , 2012 .

[34]  Alexander Karlsson.  Imprecise Probability , 2006 .

[35]  F. Coolen.  Low structure imprecise predictive inference for Bayes' problem , 1998 .

[36]  Frank P. A. Coolen,et al.  Diversity in System Reliability following Component Testing , 2010 .

[37]  Taizhong Hu,et al.  On computing signatures of coherent systems , 2012, J. Multivar. Anal..

[38]  Frank P. A. Coolen,et al.  On Nonparametric Predictive Inference and Objective Bayesianism , 2006, J. Log. Lang. Inf..

[39]  Frank P. A. Coolen,et al.  Nonparametric Predictive Inference , 2011, International Encyclopedia of Statistical Science.

[40]  Frank P. A. Coolen,et al.  Maximising entropy on the nonparametric predictive inference model for multinomial data , 2011, Eur. J. Oper. Res..

[41]  Matthias C. M. Troffaes,et al.  Introduction to imprecise probabilities , 2014 .

[42]  Pauline Coolen-Schrijner,et al.  Opportunity-based age replacement with a one-cycle criterion , 2009, J. Oper. Res. Soc..

[43]  Serkan Eryilmaz,et al.  On the mean residual life of a k-out-of-n: G system with a single cold standby component , 2012, Eur. J. Oper. Res..

[44]  B. M. Hill,et al.  Theory of Probability , 1990 .