Contributed Session: Reliability Analysis

Session Chair: Asit Basu, Univ. of Missouri

Complex Systems of Weibull Components

James D. Lynch
Dept. of Statistics, Univ. of South Carolina

Three issues regarding reliability models for complex systems of components or complex materials are that the model (i) should incorporate (marginal) component information, (ii) should model component dependencies and interactions and (iii) be attractive from a data analytic standpoint. A reliability model for a system or material consisting of marginally i.i.d. Weibull components where the dependencies are determined by physical (mechanical/electrical/thermal) considerations, has been derived taking into account (i) and (ii). The resulting model is a mixed distributions model.

For complex materials and systems, the scourge of dimensionality becomes a problem due to the large number of parameters involved. An attractive feature of this model is that the "distribution" of these parameters is the mixing distribtuion in the model. This makes the problem tractable from a data analytic standpoint (but with its own peculiarities).

[James Lynch, Dept. of Statistics, Univ. of South Carolina, Columbia, SC 29208 USA; lynch@milo.stat.sc.edu ]

Failure Models for Fibrous Composite Materials Based on Cumulative Damage Arguments

William J. Padgett
Dept. of Statistics, Univ. of South Carolina

The probability distribution of tensile strength of materials, such as carbon fibers or carbon composite materials, generally depends on the size of the material specimen, i.e. there is a "size effect" on tensile strength. The most commonly used model for material tensile strength is the Weibull distribution, justified by the "weakest link of a chain" argument. However, in many cases the Weibull does not fit experimental strength data very well. Here, a general cumulative damage process, which allows either additive or multiplicative damage, is used to obtain new models for the strength of a general system, incorporating the size effect. The new models are represented as three-parameter generalizations of the Birbaum-Saunders distribution. Illustrations of the models are presented for experimental strength data on carbon fibers and micro-composite specimens.

[William J. Padgett, Dept. of Statistics, Univ. of South Carolina, Columbia, SC 29208 USA; padgett@stat.sc.edu ]

A Family of Alternative Discrete Reliability Growth Models Based on Duane Learning Curve Property

Ananda Sen
Dept. of Mathematical Sciences, Oakland Univ.

Arthur Fries
Institute for Defense Analyses

This talk will focus on the statistical inference of a family of discrete reliability-growth models potentially applicable to one-shot, success or failure, systems undergoing a test-analyze-and-fix development process. The common feature shared by the models is their connection to Duane's renowned learning-curve property. The major difference, however, lies in their applicability in the context of two intrinsically different sampling schemes. For each model, a summary of the properties of various estimators of the parameters as well as the reliability of the system, will be presented. For purposes of assessing model misspecification, a particular test execution scenario conforming to a inverse sampling scheme is adopted. In reliability applications, it is not an uncommon practice to borrow inference results from models which are inappropriate in this setting. A detailed study of the potential impact of such misspecification on the estimation of system reliability will be presented.

[Ananda Sen, Dept. of Mathematical Sciences, Oakland Univ., Rochester, MI 48309 USA; sen@vela.acs.oakland.edu ]

Some New Inference Procedures for the Censored Two-Sample Accelerated Life Model

Song Yang
Dept. of Mathematics, Texas Tech Univ.

We first introduce some new scale estimators for the censored two sample accelerated life model. They are zeros of some integrated weighted difference between the two hazard estimators. Some choices of the weight lead to density-free asymptotic distributions, so that the asymptotic variances can be consistently estimated using only the estimated hazard and survival functions. Then from these estimators some lack-of-fit tests for the accelerated life model are derived. These tests are related to some Gill and Schumacher (Biometrika 74 (1987):289--300) type tests and require little extra computing time once the estimator is obtained. Numerical experiments recommend some of the density-free weights that result in high asymptotic efficiency. The estimators and tests are illustrated in some examples.