scholarly journals Optimization Problem in Series Systems with Random Number of Components from the Family of Power Series Distributions

2022 ◽  
Vol 15 (2) ◽  
pp. 481-504
Author(s):  
Motahare ZaeamZadeh ◽  
Jafar Ahmadi ◽  
Bahareh Khatib Astaneh ◽  
◽  
◽  
...  
Keyword(s):  
Power Series ◽  
Optimization Problem ◽  
Random Number ◽  
Number Of Components ◽  
The Family ◽  
In Series ◽  
Power Series Distributions ◽  
Series Systems

COMBINED SERIES AND PARALLEL SYSTEMS SUBJECT TO INDIVIDUAL VERSUS OVERARCHING DEFENSE AND ATTACK

2013 ◽  
Vol 30 (02) ◽  
pp. 1250056 ◽  
Author(s):  
KJELL HAUSKEN
Keyword(s):  
Parallel Systems ◽  
Series System ◽  
Number Of Components ◽  
Unit Costs ◽  
Special Cases ◽  
In Series ◽  
Individual Protection ◽  
Overarching Protection ◽  
Series Systems ◽  
Analytical Expressions

A system of components can be in series, parallel, or combined series/parallel. The components and system are protected individually and overarchingly by a defender, and attacked individually and overarchingly by an attacker. Both layers of protection have to be breached for an attack to be successful. Each component, and the system as a whole, have vulnerabilities determined by individual and overarching protection and attack. The agents choose their effort variables simultaneously and independently to maximize their utilities. Each component and the system have unit costs of protection and attack, and a contest intensity. We show for both the parallel and series systems that the defender always prefers overarching and individual protection and attack, while the attacker always prefers individual protection and attack. Analytical expressions are developed for the agents' effort variables, each individual component's vulnerability, and the system vulnerability. The expenditure ratio, between individual protection and attack, and overarching protection and attack, is shown to increase in the number of components for the parallel system, and decrease in the number of components for the series system. Special cases are considered and interpreted. Comparisons are made with only individual protection and attack. The model is applicable to determine how the defender and attacker should strike the balance between choosing efforts to protect and attack components individually versus overarchingly.

scholarly journals Preservation properties of stochastic orders by transformation to Harris family

2018 ◽  
Vol 38 (2) ◽  
pp. 441-458
Author(s):  
Somayeh Abbasi ◽  
Mohammad Hossein Alamatsaz
Keyword(s):  
Random Number ◽  
Stochastic Orders ◽  
Stochastic Comparisons ◽  
Number Of Components ◽  
Lifetime Analysis ◽  
Reliability Systems ◽  
Series Systems

Stochastic comparisons of lifetime characteristics of reliability systems and their components are of common use in lifetime analysis. In this paper, using Harris family distributions, we compare lifetimes of two series systems with random number of components, with respect to several types of stochastic orders. Our results happen to enfold several previous findings in this connection. We shall also show that several stochastic orders and ageing characteristics, such as IHRA, DHRA, NBU, and NWU, are inherited by transformation to Harris family. Finally, some refinements are made concerning related existing results in the literature.

scholarly journals A class of regression models for parallel and series systems with a random number of components

Statistics ◽  
2016 ◽  
Vol 51 (2) ◽  
pp. 294-313
Author(s):  
Alice L. Morais ◽  
Silvia L. P. Ferrari
Keyword(s):  
Regression Models ◽  
Random Number ◽  
Number Of Components ◽  
Series Systems

scholarly journals Max Weibull-G Power Series Distributions

2021 ◽  
pp. 15-29
Author(s):  
Munteanu Bogdan Gheorghe
Keyword(s):  
Probability Distribution ◽  
Power Series ◽  
Probability Distributions ◽  
Random Variables ◽  
Random Variable ◽  
Independent Random Variables ◽  
New Family ◽  
The Family ◽  
Distribution Family ◽  
Power Series Distributions

Based on the Weibull-G Power probability distribution family, we have proposed a new family of probability distributions, named by us the Max Weibull-G power series distributions, which may be applied in order to solve some reliability problems. This implies the fact that the Max Weibull-G power series is the distribution of a random variable max (X1 ,X2 ,...XN) where X1 ,X2 ,... are Weibull-G distributed independent random variables and N is a natural random variable the distribution of which belongs to the family of power series distribution. The main characteristics and properties of this distribution are analyzed.

Some aging properties of parallel and series systems with a random number of components

2014 ◽  
Vol 61 (3) ◽  
pp. 238-243 ◽  
Author(s):  
Nil Kamal Hazra ◽  
Asok K. Nanda ◽  
Moshe Shaked
Keyword(s):  
Random Number ◽  
Number Of Components ◽  
Aging Properties ◽  
Series Systems

INAR(1) Processes with Inflated-parameter Generalized Power Series Innovations

2020 ◽  
Vol 12 (2) ◽  
Author(s):  
Tito Lívio ◽  
Marcelo Bourguignon ◽  
Fernando Nascimento
Keyword(s):  
Power Series ◽  
Transition Probability ◽  
Innovation Process ◽  
Real Data ◽  
Generalized Power Series ◽  
The Family ◽  
New Models ◽  
Power Series Distributions ◽  
Conditional Maximum ◽  
Mean Variance

AbstractIn this paper, new models are studied by proposing the family of generalized power series distributions with inflated parameter (IGPSD) for the innovation process of the INAR(1) model. The main properties of the process were established, such as mean, variance, autocorrelation and transition probability. The methods of estimation by Yule–Walker and the conditional maximum likelihood were used to estimate the parameters of the models. Two particular cases of the INAR$\left(1\right)$ model with IGPSD innovation were studied, named IPoINAR$\left(1\right)$ and IGeoINAR$\left(1\right)$. Finally, in the real data example, a good performance of the proposed new models was observed.

Binomial subsampling

2006 ◽  
Vol 462 (2068) ◽  
pp. 1181-1195 ◽  
Author(s):  
Carsten Wiuf ◽  
Michael P.H Stumpf
Keyword(s):  
Mathematical Biology ◽  
Power Series ◽  
Generating Functions ◽  
Binomial Distribution ◽  
Random Variable ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
The Family ◽  
Necessary And Sufficient ◽  
Finite Moments

In this paper, we discuss statistical families with the property that if the distribution of a random variable X is in , then so is the distribution of Z ∼Bi( X ,  p ) for 0≤ p ≤1. (Here we take Z ∼Bi( X ,  p ) to mean that given X = x ,  Z is a draw from the binomial distribution Bi( x ,  p ).) It is said that the family is closed under binomial subsampling. We characterize such families in terms of probability generating functions and for families with finite moments of all orders we give a necessary and sufficient condition for the family to be closed under binomial subsampling. The results are illustrated with power series and other examples, and related to examples from mathematical biology. Finally, some issues concerning inference are discussed.

Some new results on redundancy allocation in series systems

2021 ◽  
pp. 1-18
Author(s):  
Yinzhao Wei ◽  
Sanyang Liu ◽  
Xiaoliang Ling
Keyword(s):  
Redundancy Allocation ◽  
In Series ◽  
Series Systems
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