scholarly journals Nonparametric predictive inference for failure times of systems with exchangeable components

2011 ◽  
Vol 226 (3) ◽  
pp. 262-273 ◽  
Author(s):  
F P A Coolen ◽  
A H Al-nefaiee
Keyword(s):  
Failure Time ◽  
Predictive Inference ◽  
Survival Functions ◽  
Component Failure ◽  
Nonparametric Predictive Inference ◽  
Failure Times ◽  
Statistical Framework ◽  
Lower And Upper Probabilities ◽  
Modelling Assumptions ◽  
The Moment

The theory of system signatures (Samaniego, 2007) 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 jth 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.

scholarly journals Failure Time of Loaded Wooden Beams During Fire

1983 ◽  
Vol 1 (4) ◽  
pp. 297-303 ◽  
Author(s):  
M.H. Do ◽  
G.S. Springer
Keyword(s):  
Cross Section ◽  
Elevated Temperatures ◽  
Failure Time ◽  
Rectangular Cross Section ◽  
Full Scale ◽  
National Bureau ◽  
Southern Pine ◽  
Simply Supported ◽  
Failure Times

A model is presented for predicting the failure time of loaded wooden beams of rectangular cross-section exposed to elevated temperatures or to fire. Failure times calculated by the model were compared to failure times measured in this study using 19.05 mm x 19.05 mm simply supported southern pine beams, and to failure times measured by the National Bureau of Standards during the fire of a full scale room. Reasonable agreements were found between the calculated failure times and the data.

BAYESIAN SOFTWARE RELIABILITY MODEL COMBINING TWO PRIORS AND PREDICTING TOTAL NUMBER OF FAILURES AND FAILURE TIME

2014 ◽  
Vol 21 (06) ◽  
pp. 1450031 ◽  
Author(s):  
D. DAMODARAN ◽  
B. RAVIKUMAR ◽  
VELIMUTHU RAMACHANDRAN
Keyword(s):  
Bayesian Approach ◽  
Software Reliability ◽  
Failure Time ◽  
Reliability Model ◽  
Software Failure ◽  
Failure Times ◽  
Failure Data ◽  
Time Between Failures ◽  
Software Reliability Model ◽  
Proposed Model

Reliability statistics is divided into two mutually exclusive camps and they are Bayesian and Classical. The classical statistician believes that all distribution parameters are fixed values whereas Bayesians believe that parameters are random variables and have a distribution of their own. Bayesian approach has been applied for the Software Failure data and as a result of that several Bayesian Software Reliability Models have been formulated for the last three decades. A Bayesian approach to software reliability measurement was taken by Littlewood and Verrall [A Bayesian reliability growth model for computer software, Appl. Stat. 22 (1973) 332–346] and they modeled hazard rate as a random variable. In this paper, a new Bayesian software reliability model is proposed by combining two prior distributions for predicting the total number of failures and the next failure time of the software. The popular and realistic Jelinski and Moranda (J&M) model is taken as a base for bringing out this model by applying Bayesian approach. It is assumed that one of the parameters of JM model N, number of faults in the software follows uniform prior distribution and another failure rate parameter Φi follows gama prior distribution. The joint prior p(N, Φi) is obtained by combining the above two prior distributions. In this Bayesian model, the time between failures follow exponential distribution with failure rate parameter with stochastically decreasing order on successive failure time intervals. The reasoning for the assumption on the parameter is that the intention of the software tester to improve the software quality by the correction of each failure. With Bayesian approach, the predictive distribution has been arrived at by combining exponential Time between Failures (TBFs) and joint prior p(N, Φi). For the parameter estimation, maximum likelihood estimation (MLE) method has been adopted. The proposed Bayesian software reliability model has been applied to two sets of act. The proposed model has been applied to two sets of actual software failure data and it has been observed that the predicted failure times as per the proposed model are closer to the actual failure times. The predicted failure times based on Littlewood–Verall (LV) model is also computed. Sum of square errors (SSE) criteria has been used for comparing the actual time between failures and predicted time between failures based on proposed model and LV model.

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