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

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 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

The distribution of the maximum of a random number of random variables with applications

1973 ◽  
Vol 10 (01) ◽  
pp. 122-129 ◽  
Author(s):  
Janos Galambos
Keyword(s):  
Service Time ◽  
Joint Distribution ◽  
Random Number ◽  
Random Variables ◽  
Stochastic Independence ◽  
Fixed Integer ◽  
Number Of Components ◽  
Distribution Of The Maximum ◽  
Distribution Of Elements ◽  
Mild Assumption

The asymptotic distribution of the maximum of a random number of random variables taken from the model below is shown to be the same as when their number is a fixed integer. Applications are indicated to determine the service time of a system of a large number of components, when the number of components to be serviced is not known in advance. A much slighter assumption is made than the stochastic independence of the periods of time needed for servicing the different components. In our model we assume that the random variables can be grouped into a number of subcollections with the following properties: (i) the random variables taken from different groups are asymptotically independent, (ii) the largest number of elements in a subgroup is of smaller order than the overall number of random variables. In addition, a very mild assumption is made for the joint distribution of elements from the same group.

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.

The distribution of the maximum of a random number of random variables with applications

1973 ◽  
Vol 10 (1) ◽  
pp. 122-129 ◽  
Author(s):  
Janos Galambos
Keyword(s):  
Service Time ◽  
Joint Distribution ◽  
Random Number ◽  
Random Variables ◽  
Stochastic Independence ◽  
Fixed Integer ◽  
Number Of Components ◽  
Distribution Of The Maximum ◽  
Distribution Of Elements ◽  
Mild Assumption

The asymptotic distribution of the maximum of a random number of random variables taken from the model below is shown to be the same as when their number is a fixed integer. Applications are indicated to determine the service time of a system of a large number of components, when the number of components to be serviced is not known in advance. A much slighter assumption is made than the stochastic independence of the periods of time needed for servicing the different components. In our model we assume that the random variables can be grouped into a number of subcollections with the following properties: (i) the random variables taken from different groups are asymptotically independent, (ii) the largest number of elements in a subgroup is of smaller order than the overall number of random variables. In addition, a very mild assumption is made for the joint distribution of elements from the same group.

Reliability evaluation of m-consecutive- k, l-out-of-n: F system subjected to shocks

2021 ◽  
pp. 1748006X2110489
Author(s):  
Fahrettin Özbey
Keyword(s):  
Random Number ◽  
Shock Model ◽  
Number Of Components ◽  
Optimal Replacement ◽  
Long Run ◽  
Time Problem ◽  
Phase Type ◽  
Phase Type Distributions ◽  
Replacement Time ◽  
F System

In this paper, we propose a shock model for an m-consecutive- k, l-out-of- n: F system. This paper presents a reliability analysis of an m-consecutive- k, l-out-of- n: F system subjected to shocks that destroy a random number of components. One of the main random variables is the number of components affected by successive shocks. Phase-type distributions have been used to model the intervals between successive shocks. The main objective of this study is to show how phase-type distributions can be used to determine the reliability of m-consecutive- k, l-out-of- n: F systems subjected to shocks, which destroy a random number of components. Consideration is given to the optimal replacement time problem, which addresses the minimization of the total long-run average cost per unit time.

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