BOYAN DIMITROVt, STEFANKA CHUKOVAt, AND DAVID GREEN, JR.t Abstract. Periodic random environments ... more BOYAN DIMITROVt, STEFANKA CHUKOVAt, AND DAVID GREEN, JR.t Abstract. Periodic random environments and mechanisms of their effect on imbedded random variables are discussed. The variables under consideration represent either waiting time until some event occurs ...
Two renewal processes, known in reliability maintenance as minimal repair and replacement policy,... more Two renewal processes, known in reliability maintenance as minimal repair and replacement policy, arc considered. Their properties are studied in the case where the generating random sequence has a distribution with periodic failure rate. A characterization theorem establishes necessary and sufficient conditions for a non-stationary Poisson process to have a periodic failure rate. Applications in risk theory are shown.
ABSTRACT A concept of the lack-of-memory property at a given time point c > 0 is introduce... more ABSTRACT A concept of the lack-of-memory property at a given time point c > 0 is introduced. It is equivalent to the concept of the almost-lack-of-memory (ALM) property of the random variables. A representation theorem is given for the cumulative distribution function of such random variables as well as for corresponding decompositions in terms of independent random variables. It is shown that a periodic failure rate for a random variable is equivalent to the ALM property. In addition some properties of the service time of an unreliable server are observed.On introduit la propriété d'ètre “sans mémoire” en un instant donné c > 0. Ceci est équivaleut au concept de variable aléatoire “presque sans mémoire”. On démontre un théorème de représentation pour la function de répartition de telles variables aléatoires ainsi que pour les décompositions correspondantes en variables aléatoires indépendantes. Il est démonré qu'un taux de panne périodeque est une condition néccessaire et suffisante pour qu'une variable aléatoire soit “presque sans mémoire” Finalement, on étudie quelques propriétés des temps de service d'un serveur non fiable.
A new characterization of the exponential distribution via an invariant property of probability d... more A new characterization of the exponential distribution via an invariant property of probability distributions of the execution time in queuing models with an unreliable server, and no more than two interruptions of service, is discussed. The original conditions of known similar characterizations have been weakened.
We consider a MAP/Mj2/K queueing model in which messages should leave the system in the order in ... more We consider a MAP/Mj2/K queueing model in which messages should leave the system in the order in which they entered into the system. In the case of infinite resequencing buffer, the steady-state probability vector is shown to be of matrix-geometric type. The total sojourn time of an admitted message into the system is shown to be of phase type. Efficient algorithmic procedure:; for computing various performance measures are given, and some interesting numerical examples are discussed. 0 1998 Elsl:vier Science B.V.
Journal of Applied Mathematics and Stochastic Analysis, 1993
... Flint, MI 850-898 USA J.-P. DION Universite du Quebec a Montreal Case postale 8888, succursal... more ... Flint, MI 850-898 USA J.-P. DION Universite du Quebec a Montreal Case postale 8888, succursale "A" Montreal (QC) H3C 3P3 CANADA ABSTCT ... [4], and Lau and Rao [7] are obtMned under weakened conditions and the proofs are s}mplfied. ...
An age-dependent repair model is proposed. The notion of the "age" of the product and the degree ... more An age-dependent repair model is proposed. The notion of the "age" of the product and the degree of repair are used to define the virtual age of the product. The virtual failure rate function and the virtual hazard function related to the lifetime of the product are discussed. Under a non-homogeneous Poisson process scenario the expected warranty costs for repairable products associated with linear pro-rata, non-renewing free replacement and renewing free replacement warranties are evaluated. Illustration of the results is given by numerical and graphical examples.
Communications in Statistics - Theory and Methods, 1996
Page 1. COMMUN. STATIST.-THEORY METH., 25(3), 609-630 (1996) SOME MOMENT PROPERTIES AND LIMIT THE... more Page 1. COMMUN. STATIST.-THEORY METH., 25(3), 609-630 (1996) SOME MOMENT PROPERTIES AND LIMIT THEOREMS OF THE REVERSED GENERALIZED LOGISTIC DISTRIBUTION WITH APPLICATIONS Ferris State ...
The paper introduces a technique for designing WWW-based distance education courses. It also comm... more The paper introduces a technique for designing WWW-based distance education courses. It also comments on the provisional evaluation, given by students from the Faculty of Mathematics and Informatics, Sofia University, of a developed WWW-based distance education course: Management Support Systems, implementing the outlined technique.
Cost assessment related to age of multiple components is discussed. We use definitions of equival... more Cost assessment related to age of multiple components is discussed. We use definitions of equivalent ages in multi-dimensional life, to illustrate how cost characteristics should be fairly assessed. Pricing of used items with residual value, and assigning warranty for used items as a function of item's age are the subjects of our study. Numeric examples based on correlated Bivariate normal distribution for two life components illustrate our concepts.
In this paper we illustrate several aspects of art databases, such as: the spread of the multimed... more In this paper we illustrate several aspects of art databases, such as: the spread of the multimedia art images; the main characteristics of art images; main art images search models; unique characteristics for art image retrieval; the importance of the sensory and semantic gaps. In addition, we present several interesting features of an art image database, such as: image indexing; feature extraction; analysis on various levels of precision; style classification. We stress color features and their base, painting analysis and painting styles. We study also which MPEG-7 descriptors are best for fine painting images retrieval. An experimental system is developed to see how these descriptors work on 900 art images from several remarkable art periods. On the base of our experiments some suggestions for improving the process of searching and analysis of fine art images are given.
In this paper a new method for image retrieval using high level color semantic features is propos... more In this paper a new method for image retrieval using high level color semantic features is proposed. It is based on extraction of low level color characteristics and their conversion into high level semantic features using Johannes Itten theory of color, Dempster-Shafer theory of evidence and fuzzy production rules.
We explore an idea of transferring some classic measures of global dependence between random vari... more We explore an idea of transferring some classic measures of global dependence between random variables Χ1, Χ2, L, Χn into cumulative measures of dependence relative at any point (χ1, χ2, L, χn) in the sample space. It allows studying the behavior of these measures throughout the sample space, and better understanding and use of dependence. Some examples on popular copula distributions are also provided.
Two renewal processes, known in reliability maintenance as minimal repair and replacement policy,... more Two renewal processes, known in reliability maintenance as minimal repair and replacement policy, arc considered. Their properties are studied in the case where the generating random sequence has a distribution with periodic failure rate. A characterization theorem establishes necessary and sufficient conditions for a non-stationary Poisson process to have a periodic failure rate. Applications in risk theory are shown.
A general model for describing, evaluation and control of most common reliability characteristics... more A general model for describing, evaluation and control of most common reliability characteristics of multi-stage systems with gradual failures and repairs of the whole system is proposed. The steady state probabilities and the Laplace transform of the reliability function are calculated. *
BOYAN DIMITROVt, STEFANKA CHUKOVAt, AND DAVID GREEN, JR.t Abstract. Periodic random environments ... more BOYAN DIMITROVt, STEFANKA CHUKOVAt, AND DAVID GREEN, JR.t Abstract. Periodic random environments and mechanisms of their effect on imbedded random variables are discussed. The variables under consideration represent either waiting time until some event occurs ...
Two renewal processes, known in reliability maintenance as minimal repair and replacement policy,... more Two renewal processes, known in reliability maintenance as minimal repair and replacement policy, arc considered. Their properties are studied in the case where the generating random sequence has a distribution with periodic failure rate. A characterization theorem establishes necessary and sufficient conditions for a non-stationary Poisson process to have a periodic failure rate. Applications in risk theory are shown.
ABSTRACT A concept of the lack-of-memory property at a given time point c > 0 is introduce... more ABSTRACT A concept of the lack-of-memory property at a given time point c > 0 is introduced. It is equivalent to the concept of the almost-lack-of-memory (ALM) property of the random variables. A representation theorem is given for the cumulative distribution function of such random variables as well as for corresponding decompositions in terms of independent random variables. It is shown that a periodic failure rate for a random variable is equivalent to the ALM property. In addition some properties of the service time of an unreliable server are observed.On introduit la propriété d'ètre “sans mémoire” en un instant donné c > 0. Ceci est équivaleut au concept de variable aléatoire “presque sans mémoire”. On démontre un théorème de représentation pour la function de répartition de telles variables aléatoires ainsi que pour les décompositions correspondantes en variables aléatoires indépendantes. Il est démonré qu'un taux de panne périodeque est une condition néccessaire et suffisante pour qu'une variable aléatoire soit “presque sans mémoire” Finalement, on étudie quelques propriétés des temps de service d'un serveur non fiable.
A new characterization of the exponential distribution via an invariant property of probability d... more A new characterization of the exponential distribution via an invariant property of probability distributions of the execution time in queuing models with an unreliable server, and no more than two interruptions of service, is discussed. The original conditions of known similar characterizations have been weakened.
We consider a MAP/Mj2/K queueing model in which messages should leave the system in the order in ... more We consider a MAP/Mj2/K queueing model in which messages should leave the system in the order in which they entered into the system. In the case of infinite resequencing buffer, the steady-state probability vector is shown to be of matrix-geometric type. The total sojourn time of an admitted message into the system is shown to be of phase type. Efficient algorithmic procedure:; for computing various performance measures are given, and some interesting numerical examples are discussed. 0 1998 Elsl:vier Science B.V.
Journal of Applied Mathematics and Stochastic Analysis, 1993
... Flint, MI 850-898 USA J.-P. DION Universite du Quebec a Montreal Case postale 8888, succursal... more ... Flint, MI 850-898 USA J.-P. DION Universite du Quebec a Montreal Case postale 8888, succursale "A" Montreal (QC) H3C 3P3 CANADA ABSTCT ... [4], and Lau and Rao [7] are obtMned under weakened conditions and the proofs are s}mplfied. ...
An age-dependent repair model is proposed. The notion of the "age" of the product and the degree ... more An age-dependent repair model is proposed. The notion of the "age" of the product and the degree of repair are used to define the virtual age of the product. The virtual failure rate function and the virtual hazard function related to the lifetime of the product are discussed. Under a non-homogeneous Poisson process scenario the expected warranty costs for repairable products associated with linear pro-rata, non-renewing free replacement and renewing free replacement warranties are evaluated. Illustration of the results is given by numerical and graphical examples.
Communications in Statistics - Theory and Methods, 1996
Page 1. COMMUN. STATIST.-THEORY METH., 25(3), 609-630 (1996) SOME MOMENT PROPERTIES AND LIMIT THE... more Page 1. COMMUN. STATIST.-THEORY METH., 25(3), 609-630 (1996) SOME MOMENT PROPERTIES AND LIMIT THEOREMS OF THE REVERSED GENERALIZED LOGISTIC DISTRIBUTION WITH APPLICATIONS Ferris State ...
The paper introduces a technique for designing WWW-based distance education courses. It also comm... more The paper introduces a technique for designing WWW-based distance education courses. It also comments on the provisional evaluation, given by students from the Faculty of Mathematics and Informatics, Sofia University, of a developed WWW-based distance education course: Management Support Systems, implementing the outlined technique.
Cost assessment related to age of multiple components is discussed. We use definitions of equival... more Cost assessment related to age of multiple components is discussed. We use definitions of equivalent ages in multi-dimensional life, to illustrate how cost characteristics should be fairly assessed. Pricing of used items with residual value, and assigning warranty for used items as a function of item's age are the subjects of our study. Numeric examples based on correlated Bivariate normal distribution for two life components illustrate our concepts.
In this paper we illustrate several aspects of art databases, such as: the spread of the multimed... more In this paper we illustrate several aspects of art databases, such as: the spread of the multimedia art images; the main characteristics of art images; main art images search models; unique characteristics for art image retrieval; the importance of the sensory and semantic gaps. In addition, we present several interesting features of an art image database, such as: image indexing; feature extraction; analysis on various levels of precision; style classification. We stress color features and their base, painting analysis and painting styles. We study also which MPEG-7 descriptors are best for fine painting images retrieval. An experimental system is developed to see how these descriptors work on 900 art images from several remarkable art periods. On the base of our experiments some suggestions for improving the process of searching and analysis of fine art images are given.
In this paper a new method for image retrieval using high level color semantic features is propos... more In this paper a new method for image retrieval using high level color semantic features is proposed. It is based on extraction of low level color characteristics and their conversion into high level semantic features using Johannes Itten theory of color, Dempster-Shafer theory of evidence and fuzzy production rules.
We explore an idea of transferring some classic measures of global dependence between random vari... more We explore an idea of transferring some classic measures of global dependence between random variables Χ1, Χ2, L, Χn into cumulative measures of dependence relative at any point (χ1, χ2, L, χn) in the sample space. It allows studying the behavior of these measures throughout the sample space, and better understanding and use of dependence. Some examples on popular copula distributions are also provided.
Two renewal processes, known in reliability maintenance as minimal repair and replacement policy,... more Two renewal processes, known in reliability maintenance as minimal repair and replacement policy, arc considered. Their properties are studied in the case where the generating random sequence has a distribution with periodic failure rate. A characterization theorem establishes necessary and sufficient conditions for a non-stationary Poisson process to have a periodic failure rate. Applications in risk theory are shown.
A general model for describing, evaluation and control of most common reliability characteristics... more A general model for describing, evaluation and control of most common reliability characteristics of multi-stage systems with gradual failures and repairs of the whole system is proposed. The steady state probabilities and the Laplace transform of the reliability function are calculated. *
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