Nonparametric Predictive Inference for Order Statistics of Future Observations

Proceedings of the Institution of Mechanical Engineers, Part O:

Coolen‐Maturi

Al-Nefaiee

2014

Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. AbstractThe 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.

Section: Nonparametric Predictive Inference For System Failure Timementioning

confidence: 98%

Nonparametric predictive inference for system reliability using the survival signature

Proceedings of the Institution of Mechanical Engineers, Part O:

Coolen‐Maturi

Al-Nefaiee

2014

“…The justification of (14) is similar to that of (8) for components of type B (all future observations 'at' the left end-point of each interval) [9]. The corresponding NPI upper probability for the event T a ≤ T b is derived and justified similarly, and is…”

Section: Two Systems With Different Types Of Componentsmentioning

confidence: 85%

Nonparametric predictive inference for failure times of systems with exchangeable components

Proceedings of the Institution of Mechanical Engineers, Part O:

Al-Nefaiee

2011

Additional information: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. The theory of system signatures [1] provides a powerful framework for reliability assessment for systems consisting of exchangeable components. For a system with m components, the signature is a vector containing the probabilities for the events that the system fails at the moment of the j-th ordered component failure time, for all j = 1, . . . , m. As such, the signature represents the structure of the system. This paper presents how signatures can be used within nonparametric predictive inference, a statistical framework which uses few modelling assumptions enabled by the use of lower and upper probabilities to quantify uncertainty. The main result is the use of signatures to derive lower and upper survival functions for the failure time of systems with exchangeable components, given failure times of tested components that are exchangeable with those in the system. In addition, it is shown how the failure times of two such systems can be compared. This paper is the first in which signatures are combined with theory of lower and upper probabilities, related research challenges are briefly discussed.

“…Let the random quantity S i j be defined as the number of m future observations in I j = (x j−1 , x j ) given a specific ordering, which is denoted by O i , of the m future observations among n data observations, for i = 1, … , n + m n , so that S i j = #{X n+l ∈ I j , l = 1, … , m|O i } . Then the A (n) assumptions lead to [10] where s i j are non-negative integers with ∑ n+1 j=1 s i j = m . Equation (1) implies that all n + m n orderings O i of the m future observations among the n data observations are equally likely.…”

Section: Nonparametric Predictive Inferencementioning

confidence: 99%

Robustness of Nonparametric Predictive Inference for Future Order Statistics

Alqifari

2018

J Stat Theory Pract

Self Cite

This paper considers robustness of Nonparametric Predictive Inference (NPI), in particular considering inference involving future order statistics. The concept of robust inference is usually aimed at development of inference methods which are not too sensitive to data contamination or to deviations from model assumptions. In this paper we use it in a slightly narrower sense. For our aims, robustness indicates insensitivity to small change in the data, as our predictive probabilities for order statistics and statistical inferences involving future observations depend upon the given observations. We introduce some concepts for assessing the robustness of statistical procedures to the NPI framework, namely sensitivity curve and breakdown point; these classical concepts require some adoption for application in NPI. Most of our nonparametric inferences have a reasonably good robustness with regard to small changes in the data.