scholarly journals On the Consecutive k1 and k2-out-of-n Reliability Systems

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 630
Author(s):  
Ioannis S. Triantafyllou
Keyword(s):  
Generating Function ◽  
Recurrence Relations ◽  
Reliability Function ◽  
Numerical Results ◽  
Reliability Study ◽  
Distributed Components ◽  
Signature Vector ◽  
Reliability Systems ◽  
Independent And Identically Distributed

In this paper we carry out a reliability study of the consecutive-k1 and k2-out-of-n systems with independent and identically distributed components ordered in a line. More precisely, we obtain the generating function of the structure’s reliability, while recurrence relations for determining its signature vector and reliability function are also provided. For illustration purposes, some numerical results and figures are presented and several concluding remarks are deduced.

scholarly journals Reliability Study of Systems: A Generating Function Approach

2020 ◽  
Vol 6 (1) ◽  
pp. 44-65 ◽  
Author(s):  
Ioannis S. Triantafyllou
Keyword(s):  
Generating Function ◽  
Recurrence Relations ◽  
Reliability Function ◽  
Numerical Results ◽  
Function Approach ◽  
Reliability Study ◽  
Distributed Components ◽  
Signature Vector ◽  
Independent And Identically Distributed

In this paper we carry out a reliability study of the <n, f, 2> systems with independent and identically distributed components ordered in a line. More precisely, we obtain the generating function of structure’s reliability, while recurrence relations for determining its signature vector and reliability function are also provided. For illustration purposes, several numerical results are presented and some figures are constructed and appropriately commented.

scholarly journals Mixture Representations of Inactivity Times of Conditional Coherent Systems and their Applications

2010 ◽  
Vol 47 (03) ◽  
pp. 876-885 ◽  
Author(s):  
Zhengcheng Zhang
Keyword(s):  
Order Statistics ◽  
Reliability Function ◽  
Coherent System ◽  
Coherent Systems ◽  
Distributed Components ◽  
Inactivity Time ◽  
Independent And Identically Distributed

In this paper we obtain several mixture representations of the reliability function of the inactivity time of a coherent system under the condition that the system has failed at time t (&gt; 0) in terms of the reliability functions of inactivity times of order statistics. Some ordering properties of the inactivity times of coherent systems with independent and identically distributed components are obtained, based on the stochastically ordered coefficient vectors between systems.

A Note on the Mixture Representation of the Conditional Residual Lifetime of a Coherent System

2013 ◽  
Vol 50 (02) ◽  
pp. 475-485 ◽  
Author(s):  
Xiuying Feng ◽  
Shuhong Zhang ◽  
Xiaohu Li
Keyword(s):  
Order Statistics ◽  
Stochastic Ordering ◽  
Reliability Function ◽  
Residual Lifetime ◽  
Coherent System ◽  
Distributed Components ◽  
Residual Lifetimes ◽  
Independent And Identically Distributed

This paper builds a mixture representation of the reliability function of the conditional residual lifetime of a coherent system in terms of the reliability functions of conditional residual lifetimes of order statistics. Some stochastic ordering properties for the conditional residual lifetime of a coherent system with independent and identically distributed components are obtained, based on the stochastically ordered coefficient vectors.

scholarly journals Mixture Representations of Inactivity Times of Conditional Coherent Systems and their Applications

2010 ◽  
Vol 47 (3) ◽  
pp. 876-885 ◽  
Author(s):  
Zhengcheng Zhang
Keyword(s):  
Order Statistics ◽  
Reliability Function ◽  
Coherent System ◽  
Coherent Systems ◽  
Distributed Components ◽  
Inactivity Time ◽  
Independent And Identically Distributed

In this paper we obtain several mixture representations of the reliability function of the inactivity time of a coherent system under the condition that the system has failed at time t (> 0) in terms of the reliability functions of inactivity times of order statistics. Some ordering properties of the inactivity times of coherent systems with independent and identically distributed components are obtained, based on the stochastically ordered coefficient vectors between systems.

scholarly journals A Note on the Mixture Representation of the Conditional Residual Lifetime of a Coherent System

2013 ◽  
Vol 50 (2) ◽  
pp. 475-485 ◽  
Author(s):  
Xiuying Feng ◽  
Shuhong Zhang ◽  
Xiaohu Li
Keyword(s):  
Order Statistics ◽  
Stochastic Ordering ◽  
Reliability Function ◽  
Residual Lifetime ◽  
Coherent System ◽  
Distributed Components ◽  
Residual Lifetimes ◽  
Independent And Identically Distributed

This paper builds a mixture representation of the reliability function of the conditional residual lifetime of a coherent system in terms of the reliability functions of conditional residual lifetimes of order statistics. Some stochastic ordering properties for the conditional residual lifetime of a coherent system with independent and identically distributed components are obtained, based on the stochastically ordered coefficient vectors.

scholarly journals Some new results on stochastic comparisons of coherent systems using signatures

2020 ◽  
Vol 57 (1) ◽  
pp. 156-173
Author(s):  
Ebrahim Amini-Seresht ◽  
Baha-Eldin Khaledi ◽  
Subhash Kochar
Keyword(s):  
Likelihood Ratio ◽  
Hazard Rate ◽  
Sufficient Conditions ◽  
Coherent Systems ◽  
Stochastic Comparisons ◽  
Numerical Examples ◽  
Distributed Components ◽  
Signature Vector ◽  
Theoretical Results ◽  
Independent And Identically Distributed

AbstractWe consider coherent systems with independent and identically distributed components. While it is clear that the system’s life will be stochastically larger when the components are replaced with stochastically better components, we show that, in general, similar results may not hold for hazard rate, reverse hazard rate, and likelihood ratio orderings. We find sufficient conditions on the signature vector for these results to hold. These results are combined with other well-known results in the literature to get more general results for comparing two systems of the same size with different signature vectors and possibly with different independent and identically distributed component lifetimes. Some numerical examples are also provided to illustrate the theoretical results.

scholarly journals On the Lifetime and Signature of Constrained (k, d)-out-of-n: F Reliability Systems

2020 ◽  
Vol 6 (1) ◽  
pp. 66-78 ◽  
Author(s):  
Ioannis S. Triantafyllou
Keyword(s):  
Multivariate Distribution ◽  
Residual Lifetime ◽  
Reliability Study ◽  
Conditional Mean ◽  
Mean Residual Lifetime ◽  
Signature Vector ◽  
Reliability Systems

In the present paper we carry out a reliability study of the constrained (k, d)-out-of-n: F systems with exchangeable components. The signature vector is computed by the aid of the proposed algorithm. In addition, explicit signature-based expressions for the corresponding mean residual lifetime and the conditional mean residual lifetime of the aforementioned reliability system are also provided. For illustration purposes, a well-known multivariate distribution for modelling the lifetimes of the components of the constrained (k, d)-out-of-n: F structure is considered.

Algorithms and Formulae for Conversion Between System Signatures and Reliability Functions

2015 ◽  
Vol 52 (02) ◽  
pp. 490-507
Author(s):  
Jean-Luc Marichal
Keyword(s):  
System Reliability ◽  
Reliability Function ◽  
Efficient Algorithms ◽  
System Designs ◽  
Independent And Identically Distributed

The concept of a signature is a useful tool in the analysis of semicoherent systems with continuous, and independent and identically distributed component lifetimes, especially for the comparison of different system designs and the computation of the system reliability. For such systems, we provide conversion formulae between the signature and the reliability function through the corresponding vector of dominations and we derive efficient algorithms for the computation of any of these concepts from any other. We also show how the signature can be easily computed from the reliability function via basic manipulations such as differentiation, coefficient extraction, and integration.

scholarly journals On the p,q-Humbert Functions from the View Point of the Generating Function Method

2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Ayman Shehata
Keyword(s):  
Generating Function ◽  
Generating Functions ◽  
Function Method ◽  
Recurrence Relations ◽  
View Point ◽  
Starting Point ◽  
Explicit Representations

The main object of the present paper is to construct new p,q-analogy definitions of various families of p,q-Humbert functions using the generating function method as a starting point. This study shows a class of several results of p,q-Humbert functions with the help of the generating functions such as explicit representations and recurrence relations, especially differential recurrence relations, and prove some of their significant properties of these functions.

Distribution of the Time of the First k-Record

1997 ◽  
Vol 11 (3) ◽  
pp. 273-278 ◽  
Author(s):  
Ilan Adler ◽  
Sheldon M. Ross
Keyword(s):  
Generating Function ◽  
Random Variables ◽  
Recursive Formula ◽  
Finite Set ◽  
Independent And Identically Distributed

We compute the first two moments and give a recursive formula for the generating function of the first k-record index for a sequence of independent and identically distributed random variables that take on a finite set of possible values. When the random variables have an infinite support, we bound the distribution of the index of the first k-record and show that its mean is infinite.

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