No abstract

We consider a multicomponent load-sharing system in which the failure rate of a given component depends on the set of working components at any given time. Such systems can arise in software reliability models and in multivariate failure-time models in biostatistics, for example. A load-share rule dictates how stress or load is redistributed to the surviving components after a component fails within the system. In this paper, we assume the load share rule is unknown and derive methods for statistical inference on load-share parameters based on maximum likelihood. Components with (individual) constant failure rates are observed in two environments: (1) the system load is distributed evenly among the working components, and (2) we assume only the load for each working component increases when other components in the system fail. Tests for these special load-share models are investigated.

An estimator for the load share parameters in an equal load-share model is derived based on observing k-component parallel systems of identical components that have a continuous distribution function F (·) and failure rate r(·). In an equal load share model, after the first of k components fails, failure rates for the remaining components change from r(t) to γ 1 r(t), then to γ 2 r(t) after the next failure, and so on. On the basis of observations on n independent and identical systems, a semiparametric estimator of the component baseline cumulative hazard function R = − log(1 − F) is presented, and its asymptotic limit process is established to be a Gaussian process. The effect of estimation of the load-share parameters is considered in the derivation of the limiting process. Potential applications can be found in diverse areas, including materials testing, software reliability and power plant safety assessment.

No abstract

No abstract

For any two random variables X and Y with distributions F and G de ned on 601ˆ5, X is said to stochastically precede Y if P4X µ Y 5 ¶ 1=2. For independent X and Y , stochastic precedence (denoted by X µ sp Y ) is equivalent to E6G4Xƒ57 µ 1=2. The applicability of stochastic precedence in various statistical contexts, including reliability modeling, tests for distributional equality versus various alternatives, and the relative performance of comparable tolerance bounds, is discussed. The problem of estimating the underlying distribution(s) of experimental data under the assumption that they obey a stochastic precedence (sp) constraint is treated in detail. Two estimation approaches, one based on data shrinkage and the other involving data translation, are used to construct estimators that conform to the sp constraint, and each is shown to lead to a root n-consistent estimator of the underlying distribution. The asymptotic behavior of each of the estimators is fully characterized. Conditions are given under which each estimator is asymptotically equivalent to the corresponding empirical distribution function or, in the case of right censoring, the Kaplan-Meier estimator. In the complementary cases, evidence is presented, both analytically and via simulation, demonstrating that the new estimators tend to outperform the empirical distribution function when sample sizes are suf ciently large.

No abstract

Each year, more than $3 billion is wagered on the NCAA Division I men's basketball tournament. Most of that money is wagered in pools where the object is to correctly predict winners of each game, with emphasis on the last four teams remaining (the Final Four). In this paper, we present a combined logistic regression/Markov chain (LRMC) model for predicting the outcome of NCAA tournament games given only basic input data. Over the past 6 years, our model has been significantly more successful than the other common methods such as tournament seedings, the AP and ESPN/USA Today polls, the RPI, and the Sagarin and Massey ratings.