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Dive into the research topics where Thomas H. Savits is active.

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Featured researches published by Thomas H. Savits.


Probability in the Engineering and Informational Sciences | 1998

The Reversed Hazard Rate Function

Henry W. Block; Thomas H. Savits; Harshinder Singh

In this paper we discuss some properties of the reversed hazard rate function. This function has been shown to be useful in the analysis of data in the presence of left censored observations. It is also natural in discussing lifetimes with reversed time scale. In fact, ordinary hazard rate functions are most useful for lifetimes, and reverse hazard rates are natural if the time scale is reversed. Mixing up these concepts can often, although not always, lead to anomalies. For example, one result gives that if the reversed hazard rate function is increasing, its interval of support must be (—∞, b ) where b is finite. Consequently nonnegative random variables cannot have increasing reversed hazard rates. Because of this result some existing results in the literature on the reversed hazard rate ordering require modification. Reversed hazard rates are also important in the study of systems. Hazard rates have an affinity to series systems; reversed hazard rates seem more appropriate for studying parallel systems. Several results are given that demonstrate this. In studying systems, one problem is to relate derivatives of hazard rate functions and reversed hazard rate functions of systems to similar quantities for components. We give some results that address this. Finally, we carry out comparisons for k -out-of- n systems with respect to the reversed hazard rate ordering.


Journal of Applied Probability | 1982

A Decomposition for Multistate Monotone Systems.

Henry W. Block; Thomas H. Savits

A decomposition theorem for multistate structure functions is proven. This result is applied to obtain bounds for the system performance function. Another application is made to interpret the multistate structures of Barlow and Wu. Various concepts of multistate importance and coherence are also discussed.


Operations Research | 1984

Multivariate Phase-Type Distributions

David Assaf; Naftali A. Langberg; Thomas H. Savits; Moshe Shaked

A univariate random variable is said to be of phase type if it can be represented as the time until absorption in a finite state absorbing Markov chain. Univariate phase type random variables are useful because they arise from processes that are often encountered in applications, they have densities that can be written in a closed form, they possess some useful closure properties, and they can approximate any nonnegative random variable. This paper introduces and discusses several extensions to the multivariate case. It shows that the multivariate random variables possess many of the properties of univariate phase type distributions and derives explicit formulas for various probabilistic quantities of interest. Some examples are included.


Journal of Applied Probability | 1988

Some multivariate distributions derived from a non-fatal shock model

Thomas H. Savits

A non-homogeneous Poisson shock model has a continuous mean function Λ( t ). The k th shock S k causes simultaneous failure of the components j ∊ J ∊ {1, ···, n } with probability p J ( S k ). If T j is the lifetime of component j , it is shown that ( T 1 , · ··, T n ) belongs to various multivariate non-parametric life classes depending on the life class of .


Journal of Applied Probability | 1978

SHOCK MODELS WITH NBUE SURVIVAL

Henry W. Block; Thomas H. Savits

Conditions are given on a process so that a shock model governed by the process will have NBUE survival time. A related condition is given so that survival will be NBU and it is shown that a pure birth process satisfies this condition. A result of A-Hameed and Proschan is obtained as a corollary.


Journal of Applied Probability | 1993

REPAIR REPLACEMENT POLICIES

Henry W. Block; Naftali A. Langberg; Thomas H. Savits

In this paper we introduce the concept of repair replacement. Repair replacement is a maintenance policy in which items are preventively maintained when a certain time has elapsed since their last repair. This differs from age replacement where a certain amount of time has elapsed since the last replacement. If the last repair was a complete repair, repair replacement is essentially the same as age replacement. It is in the case of minimal repair that these two policies differ. We make comparison between various types of policies in order to determine when and under which condition one type of policy is better than another.


Statistics & Probability Letters | 1985

A Concept of Negative Dependence Using Stochastic Ordering.

Henry W. Block; Thomas H. Savits; Moshe Shaked

A concept of negative dependence called negative dependence by stochastic ordering is introduced. This concept satisfies various closure properties. It is shown that three models for negetive dependence satisfy it and that it implies the basic negative orthant inequalities. This concept is also satisfied by the multinomial, multivariate hypergeometric. Dirichlet and Dirichlet compound multinomial distributions. Furthermore, the joint distribution of ranks of a sample and the multivariate normal with nonpositive pairwise correlations also satisfy this condition. The positive dependence analog of this condition is also studied.


Operations Research | 2002

A Criterion for Burn-in That Balances Mean Residual Life and Residual Variance

Henry W. Block; Thomas H. Savits; Harshinder Singh

Optimum burn-in times have been determined for a variety of criteria such as mean residual life and conditional survival. In this paper we consider a residual coefficient of variation that balances mean residual life with residual variance. To study this quantity, we develop a general result concerning the preservation ofbathtub distributions. Using this result, we give a condition so that the residual coefficient of variation is bathtub-shaped. Furthermore, we show that it attains its optimum value at a time that occurs after the mean residual life function attains its optimum value, but not necessarily before the change point of the failure rate function.


Advances in Applied Probability | 1989

L-SUPERADDITIVE STRUCTURE FUNCTIONS

Henry W. Block; William S. Griffith; Thomas H. Savits

Structure functions relate the level of operations of a system as a function of the level of the operation of its components. In this paper structure functions are studied which have an intuitive property, called L-superadditive (L-subadditive). Such functions describe whether a system is more series-like or more parallel-like. L-superadditive functions are also known under the names supermodular, quasimonotone and superadditive and have been studied by many authors. Basic properties of both discrete and continuous (i.e., taking a continuum of values) L-superadditive structure functions are studied. For binary structure functions of binary values, El-Neweihi (1980) showed that L-superadditive structure functions must be series. This continues to hold for binary-valued structure functions even if the component values are continuous (see Proposition 3.1). In the case of non-binary-valued structure functions this is no longer the case. We consider structure functions taking discrete values and obtain results in various cases. A conjecture concerning the general case is made.


Mathematics of Operations Research | 1981

Multivariate Classes of Life Distributions in Reliability Theory

Henry W. Block; Thomas H. Savits

Four classes of life distributions which have been useful in describing aging where systems are assumed to have independent univariate component lifetimes are: 1 the increasing failure rate IFR class; 2 the increasing failure rate average IFRA class; 3 the new better than used NBU class; and 4 the new better than used in expectation NBUE class. These classes together with multivariate analogs of the IFR and IFRA classes are reviewed and discussed. An up to date survey of the literature on this topic is included. New multivariate definitions of the NBU and NBUE classes are introduced.

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Henry W. Block

University of Pittsburgh

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Yulin Li

University of Pittsburgh

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Jie Wang

University of Pittsburgh

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Jie Mi

Florida International University

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C. S. Chen

University of Pittsburgh

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Wagner Borges

University of São Paulo

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