Nonparametric predictive inference for system failure time based on bounds for the signature

System signatures provide a powerful framework for reliability assessment for systems consisting of exchangeable components. The use of signatures in nonparametric predictive inference has been presented and leads to lower and upper survival functions for the system failure time, given failure times of tested components. However, deriving the system signature is computationally complex. This article presents how limited information about the signature can be used to derive bounds on such lower and upper survival functions and related inferences. If such bounds are sufficiently decisive they also indicate that more detailed computation of the system signature is not required.

[1]  A. Dempster.  On Direct Probabilities , 1963 .

[2]  B. M. Hill,et al.  Posterior Distribution of Percentiles: Bayes' Theorem for Sampling From a Population , 1968 .

[3]  Philip J. Boland,et al.  Signatures of indirect majority systems , 2001, Journal of Applied Probability.

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

[5]  J. Lawless,et al.  Frequentist prediction intervals and predictive distributions , 2005 .

[6]  Alexander Karlsson.  Imprecise Probability , 2006 .

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

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

[9]  Jon Williamson.  PHILOSOPHIES OF PROBABILITY , 2009 .

[10]  S Malkin,et al.  Effect of fluid application conditions on grinding behaviour , 2010 .

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

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

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

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

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

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

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

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

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

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