Accelerated life models when the stress is not constant
Alternative parametric estimation in the exponential case under random censorship
An application of nonprarametric Cox regression model in reliability analysis: a case study
The contribution deals with an application of the nonparametric version of Cox regression model to the analysis and modeling of the failure rate of technical devices. The objective is to recall the method of statistical analysis of such a model, to adapt it to the real–case study, and in such a way to demonstrate the flexibility of the Cox model. The goodness-of-fit of the model is tested, too, with the aid of the graphical test procedure based on generalized residuals.
An Invariance Principle for Progressively Truncated Likelihood Ratio Statistics.
Análisis bayesiano de supervivencia basado en el modelo de Rayleigh: addendum.
In the printed version of the paper Bayesian survival analysis based on the Rayleigh model (Trabajos de Estadística Vol. 5, no. 1, 1990), figures num. 1, 2 and 3 mentioned on page 91 were not printed with the paper. That may create confusion and problems for the readers in understanding the conclusions, as in the absence of figures the paper is incomplete. For this reason we publish the figures in this issue.
Analysis of a two-unit standby redundant system with three states of units
A cold-standby redundant system with two identical units and one repair facility is considered. Units can be in three states> good (I), degraded (II), and failed (III). We suppose that only the following state-transitions of a unit are possible: . The repair of a unit of the type can be interpreted as a preventive maintenance. Its realization depends on the states of both units. Several characteristics of the system (probabilities, distribution functions or their Laplace-Stieltjes transforms...
Apollo 13 Risk Assessment Revisited
Fault tree methodology is the most widespread risk assessment tool by which one is able to predict - in principle - the outcome of an event whenever it is reduced to simpler ones by the logic operations conjunction and disjunction according to the basics of Boolean algebra. The object of this work is to present an algorithm by which, using the corresponding computer code, one is able to predict - in practice - the outcome of an event whenever its fault tree is given in the usual form.
Application des lois non paramétriques dans les systèmes d’attente et la théorie de renouvellement
Les distributions non paramétriques de survie trouvent, de plus en plus, des applications dans des domaines très variés, à savoir : théorie de fiabilité et analyse de survie, files d’attente, maintenance, gestion de stock, théorie de l’économie, L’objet de ce travail est d’utiliser les bornes inférieures et supérieures (en terme de la moyenne) des fonctions de fiabilité appartenant aux classes de distribution de type et , présentées par Sengupta (1994), pour l’évaluation de certaines caractéristiques....
Application des lois non paramétriques dans les systèmes d'attente et la théorie de renouvellement
Les distributions non paramétriques de survie trouvent, de plus en plus, des applications dans des domaines très variés, à savoir: théorie de fiabilité et analyse de survie, files d'attente, maintenance, gestion de stock, théorie de l'économie, ... L'objet de ce travail est d'utiliser les bornes inférieures et supérieures (en terme de la moyenne) des fonctions de fiabilité appartenant aux classes de distribution de type IFR, DFR, NBU et NWU, présentées par Sengupta (1994), pour l'évaluation de...
Approche non paramétrique en théorie de la fiabilité : revue bibliographique
Approximation of reliability for a large system with non-markovian repair-times
Approximation of Reliability for a large system with non-markovian repair-times
Consider a system of many components with constant failure rate and general repair rate. When all components are reliable and easily reparable, the reliability of the system can be evaluated from the probability q of failure before restoration. In [14], authors give an asymptotic approximation by monotone sequences. In the same framework, we propose, here, a bounding for q and apply it in the ageing property case.
Asymptotic expansions of functions of statistics
Bayes estimation of the reliability function and hazard rate of a Weibull failure time distribution.
Given the recorded life times from a Weibull distribution, Bayes estimates of the reliability function and hazard rate are obtained using the posterior distributions and some recent results on Bayesian approximations due to Lindley (1980). Based on a Monte Carlo study, these estimates are compared with their maximum likelihood counterparts.
Bayesian estimation of the 3-parameter inverse Gaussian distribution.
The three-parameter inverse Gaussian distribution is used as an alternative model for the three parameter lognormal, gamma and Weibull distributions for reliability problems. In this paper Bayes estimates of the parameters and reliability function of a three parameter inverse Gaussian distribution are obtained. Posterior variance estimates are compared with the variance of their maximum likelihood counterparts. Numerical examples are given.
Bayesian inference and optimal release times. For two software failure models
We carry out Bayesian inference for the Jelinski-Moranda and Littlewood software failure models given a sample of failure times. Furthermore, we illustrate how to assess the optimal length of an additional pre-release testing period under each of these models. Modern Bayesian computational methods are used to estimate the posterior expected utility of testing for and additional time.
Bayesian nonparametric estimation of hazard rate in monotone Aalen model
This text describes a method of estimating the hazard rate of survival data following monotone Aalen regression model. The proposed approach is based on techniques which were introduced by Arjas and Gasbarra [4]. The unknown functional parameters are assumed to be a priori piecewise constant on intervals of varying count and size. The estimates are obtained with the aid of the Gibbs sampler and its variants. The performance of the method is explored by simulations. The results indicate that the...
Bayesian Prediction of Weibull Distribution Based on Fixed and Random Sample Size
2000 Mathematics Subject Classification: 62E16, 65C05, 65C20.We consider the problem of predictive interval for future observations from Weibull distribution. We consider two cases they are: (i) fixed sample size (FSS), (ii) random sample size (RSS). Further, we derive the predictive function for both FSS and RSS in closed forms. Next, the upper and lower 1%, 2.5%, 5% and 10% critical points for the predictive functions are calculated. To show the usefulness of our results, we present some simulation...
Bayesian reference analysis for proportional hazards model of random censorship with Weibull distribution
This article deals with the objective Bayesian analysis of random censorship model with informative censoring using Weibull distribution. The objective Bayesian analysis has a long history from Bayes and Laplace through Jeffreys and is reaching the level of sophistication gradually. The reference prior method of Bernardo is a nice attempt in this direction. The reference prior method is based on the Kullback-Leibler divergence between the prior and the corresponding posterior distribution and easy...
Bayesian reliability analysis when multiple early failures may be present.
This paper discusses the Bayesian reliability analysis for an exponential failure mode on the basis of some ordered observations when the first p observations may represent early failures or outliers. The Bayes estimators of the mean life and reliability are obtained for the underlying parametric model referred to as the SB(p) model under the assumption of the squared error loss function, the inverted gamma prior for scale parameter and a generalized uniform prior for the nuisance parameter.