Laurence A. Baxter

On the Tabulation of the Renewal Function

A generalized cubic splining algorithm enables us to evaluate recursively-defined convolution integrals for a wide variety of distribution functions. This algorithm has been used to evaluate the renewal function, the variance function, and the integral of the renewal function for five distributions (gamma, inverse Gaussian, lognormal, truncated normal, and Weibull) for a wide range of values of the shape parameter of each. The results of the computations are described and a comparison is made with previous tabulations.

A point process model for the reliability of a maintained system subject to general repair

A model for the general repair of a system subject to stochastic failure is introduced and studied. Properties of the stochastic point process generated by a sequence of general repairs are investigated. An application of the model to logistics is described

Renewal Tables: Tables of Functions Arising in Renewal Theory.

Abstract : The generalized cubic splining algorithm enables us to evaluate recursively-defined convolutions for a wide variety of distribution functions. The algorithm has been applied to evaluate the renewal function, variance function and the integral of the renewal function for five distributions (gamma, inverse Gaussian, lognormal, truncated normal and Weibull) for a wide range of values of the shape parameter. The results of the computations are discussed and a comparison is made with previous tabulations. (Author)

BOUNDING THE STOCHASTIC PERFORMANCE OF CONTINUUM STRUCTURE FUNCTIONS. I

Abstract : A continuum structure function gamma is a nondecreasing mapping from the unit hypercube to the unit interval. Minimal path (cut) sets of upper (lower) simple continuum structure functions are introduced and are used to determine bounds on the distribution of gamma (X) when X is a vector of associated random variables and when is right (left)-continuous. It is shown that, if gamma admits of a modular decomposition, improved bounds may be obtained. (Author)

On the optimal assembly of series-parallel systems

A heuristic for the optimal assembly of series-parallel systems is proposed. An asymptotic optimality property of this heuristic is derived by means of a probabilistic analysis. Bounds on the absolute and relative errors of an arbitrary heuristic for the optimal assembly of series-parallel systems are calculated.

Reliability Importance for Continuum Structure Functions.

Abstract : A continuum structure function is a nondecreasing mapping from the unit hypercube to the unit interval. A definition of the reliability importance, R (alpha) sub i say, of component i at level alpha (0 alpha or = 1) is proposed. Some properties of this function are deducted, in particualr conditions under which the limit as alpha approaches 0 of R (alpha) sub i = the limit as alpha approaches 1 of R (alpha) sub i = 0 and conditions under which R (alpha) sub i is positive (0 alpha 1). Keywords: Continuum structure function; Reliability importance; Key vector.

Axiomatic characterizations of continuum structure functions

A continuum structure function is a non-decreasing mapping from the unit hypercube to the unit interval. Axiomatic characterizations of the continuum structure functions based on the Barlow-Wu and Natvig multistate structure functions are derived.

Nonparametric Estimation of the Limiting Availability

The point availability of a repairable system is the probability that the system is operating at a specified time. As time increases, the point availability converges to a positive constant called the limiting availability. Baxter and Li (1994a) developed a technique for constructing nonparametric confidence intervals for the point availability. However, nonparametric estimators of the limiting availability have not previously been studied in the literature. In this paper, we consider two separate cases: (1) the data are complete and (2) the data are subject to right censorship. For each case, a nonparametric confidence interval for the limiting availability is derived. Applications and simulation studies are presented.

Towards a theory of confidence intervals for system reliability

Consider a binary coherent system of nonrepairable components, the lifelength distributions of which lie in the single parameter exponential family of distributions. Given observations of the lifelengths of the constituent components, it is shown how inversion of the likelihood ratio test can be used to calculate strongly consistent approximate confidence intervals for the survivor function of the system lifelength and for the mean time to system failure.

Some criteria for reliability growth

Abstract The sequence of failures of a system is assumed to be modelled by a stochastic point process. Criteria for the reliability growth of such a system are introduced. The relationships between the criteria are deduced and preservation of the criteria under the formation of series systems is discussed.