Reliability : probabilistic models and statistical methods/ Leemis

xv, 319 hal : ill. ; 25 cm

Nonparametric estimation and variate generation for a nonhomogeneous Poisson process from event count data

Given a finite time horizon that has been partitioned into subintervals over which event counts have been accumulated for multiple realizations of a population NonHomogeneous Poisson Process (NHPP), this paper develops point and confidence-interval estimators for the cumulative intensity (or mean value) function of the population process evaluated at each subinterval endpoint. As the number of realizations tends to infinity, each point estimator is strongly consistent and the corresponding confidence-interval estimator is asymptotically exact. If the NHPP has a piecewise constant intensity (rate) function, then the proposed point and confidence-interval estimators for the cumulative intensity function are valid over the entire time horizon and not just at the subinterval endpoints; and in this case algorithms are presented for generating event times from the estimated NHPP. Event count data from a call center illustrate the point and interval estimators. 1

Variate Generation for Accelerated Life and Proportional Hazards Models

The accelerated life and proportional hazards lifetime models are used to account for the effects of covariates on a random lifetime. Variate generation algorithms for Monte Carlo simulation in both the renewal and nonhomogeneous Poisson process cases are a simple extension of the inverse-cdf technique

Lower System Reliability Bounds from Binary Failure Data Using Bootstrapping

Binary failure data are collected for each of the independent components in a coherent system. Bootstrapping is used to determine a (1 − α)100 % lower confidence bound on the system reliability. When a component with perfect test results is encountered,a beta prior distribution is used to avoid an overly optimistic lower bound. Key Words: Beta distribution,Binomial confidence interval,Coherent system,Computer algebra system. WE CONSIDER the problem of determining a (1 − α)100 % lower confidence bound on the system reliability for a coherent system of k components using the failure data (yi,ni), where yi is the number of components of type i that pass the test and ni is the number of components of type i on test, i =1, 2,...,k.We assume throughout that the components fail independently, e.g., no commoncause failures.The outline of the article is as follows. We begin with the case of a single (k = 1) componen

Nonparametric estimation of the cumulative intensity function for a nonhomogeneous Poisson process

Anonparametric technique for estimating the cumulative intensity function of a nonhomogeneous Poisson process from one or more realizations is developed. This technique does not require any arbitrary parameters from the modeler, and the estimated cumulative intensity function can be used to generate a point process for Monte Carlo simulation by inversion. Three examples are given