Reliability optimization for non-repairable series-parallel systems with a choice of redundancy strategies and heterogeneous components: Erlang time-to-failure distribution

2020 ◽  
pp. 1748006X2095257
Author(s):  
Meisam Sadeghi ◽  
Emad Roghanian ◽  
Hamid Shahriari ◽  
Hassan Sadeghi
Keyword(s):  
Lower Bound ◽  
Closed Form ◽  
System Reliability ◽  
Parallel Systems ◽  
Closed Form Expression ◽  
Erlang Distribution ◽  
Time To Failure ◽  
Form Expression ◽  
Integrodifference Equation ◽  
Cold Standby

The redundancy allocation problem (RAP) of non-repairable series-parallel systems considering cold standby components and imperfect switching mechanism has been traditionally formulated with the objective of maximizing a lower bound on system reliability instead of exact system reliability. This objective function has been considered due to the difficulty of determining a closed-form expression for the system reliability equation. But, the solution that maximizes the lower bound for system reliability does not necessarily maximize exact system reliability and thus, the obtained system reliability may be far from the optimal reliability. This article attempts to overcome the mentioned drawback. Under the assumption that component time-to-failure is distributed according to an Erlang distribution and switch time-to-failure is exponentially distributed, a closed-form expression for the subsystem cold standby reliability equation is derived by solving an integrodifference equation. A semi-analytical expression is also derived for the reliability equation of a subsystem with mixed redundancy strategy. The accuracy and the correctness of the derived equations are validated analytically. Using these equations, the RAP of non-repairable series-parallel systems with a choice of redundancy strategies is formulated. The proposed mathematical model maximizes exact system reliability at mission time given system design constraints. Unlike most of the previous formulations, the possibility of using heterogeneous components in each subsystem is provided so that the active components can be of one type and the standby ones of the other. The results of an illustrative example demonstrate the high performance of the proposed model in determining optimal design configuration and increasing system reliability.

Reliability optimization for non-repairable series-parallel systems with a choice of redundancy strategies: Erlang time-to-failure distribution

2017 ◽  
Vol 231 (5) ◽  
pp. 587-604
Author(s):  
Meisam Sadeghi ◽  
Emad Roghanian
Keyword(s):  
Closed Form ◽  
System Reliability ◽  
High Performance ◽  
Parallel Systems ◽  
Erlang Distribution ◽  
Time To Failure ◽  
Allocation Model ◽  
Design Problems ◽  
Proposed Model ◽  
Engineering Design Problems

This article deals with a new redundancy allocation model for non-repairable series-parallel systems with multiple strategy choices. The proposed model simultaneously determines the type of components, number of active and standby components to maximize system reliability subject to design constraints. Traditionally, due to complexity and difficulty in obtaining the closed form version of system reliability, a convenient lower-bound on system reliability has been widely applied to approximate it. Assuming that switching mechanism time-to-failure is exponentially distributed, the closed form version of the reliability of subsystems with cold standby redundancy is derived analytically for the first time. This is successfully performed using Markov process and solving the relevant set of differential-difference equations. With respect to the obtained formulation, a semi-analytical expression for the reliability of subsystems with mixed redundancy strategy is also extracted. Component time-to-failure is assumed to follow an Erlang distribution which is suitable for most engineering design problems. The presented model is linear and in the form of standard zero-one integer programs and thus using integer programming algorithms guarantees optimal solutions. The computational results of solving a well-known example indicate the high performance of the proposed model in improving system reliability.

A closed-form equation for steady-state availability of cold standby repairable k-out-of-n

2019 ◽  
Vol 37 (1) ◽  
pp. 145-155
Author(s):  
Afshin Yaghoubi ◽  
Seyed Taghi Akhavan Niaki ◽  
Hadi Rostamzadeh
Keyword(s):  
Steady State ◽  
Closed Form ◽  
Design Methodology ◽  
Closed Form Expression ◽  
System Failure ◽  
Exponential Distributions ◽  
Form Expression ◽  
Content Type ◽  
Cold Standby ◽  
Markov Method

Purpose The purpose of this paper is to derive a closed-form expression for the steady-state availability of a cold standby repairable k-out-of-n system. This makes the availability calculation much easier and accurate. Design/methodology/approach Assuming exponential distributions for system failure and repair, the Markov method is employed to derive the formula. Findings The proposed formula establishes an easier and faster venue and provides accurate steady-state availability. Research limitations/implications The formula is valid for the case when the probability density function of the component failure and the repair is exponential. Originality/value The Markov method has never been used in the literature to derive the steady-state availability of a cold standby repairable k-out-of-n: G system.

scholarly journals Secrecy capacity optimization artificial noise: the ergodic secrecy capacity lower bound and optimal power allocation

2020 ◽  
Author(s):  
Yebo Gu ◽  
Zhilu Wu ◽  
Zhendong Yin ◽  
Bowen Huang
Keyword(s):  
Lower Bound ◽  
Channel Estimation ◽  
Closed Form ◽  
Power Allocation ◽  
Estimation Error ◽  
Closed Form Expression ◽  
Artificial Noise ◽  
Secrecy Capacity ◽  
Capacity Optimization ◽  
Form Expression

Abstract The secure transmission problem of MIMO wireless system in fading channels is studied in this paper. We add a secrecy capacity optimization artificial noise(SCO-AN) to the transported signal for improving the security performance of the system. The closed-form expression of secrecy capacity's lower bound is obtained. Base on the closed-form expression of secrecy capacity's lower bound, We optimize the power allocation between the information-bearing signal and the SCO-AN. By calculating, the optimal ratio of power alloation betwenn the information-bearing signal and the SCO-AN is obtained. Through simulation, the results shows the secrecy capacity increases with more receiving antennas and less eavesdropping antennas.And more power should be allocated to the SCO-AN with the increase of the colluding eavedroppers.More over, we study the effect of channel estimation error on power allocation between information-bearing signal and SCO-AN and find that more power should be allocated to decrease eavesdroppers capacity if the channel estimation is not perfect.

scholarly journals Synthesizing of Planar and Conformal Double-Sided Parallel-Cross Dipoles FSS Based on Closed-Form Expression

IEEE Access ◽  
2021 ◽  
pp. 1-1
Author(s):  
Yassine Zouaoui ◽  
Larbi Talbi ◽  
Khelifa Hettak ◽  
Naresh K. Darimireddy
Keyword(s):  
Closed Form ◽  
Closed Form Expression ◽  
Form Expression

Distribution of Consensus in a Broadcasting-based Consensus-forming Algorithm

2021 ◽  
Vol 48 (3) ◽  
pp. 91-96
Author(s):  
Shigeo Shioda
Keyword(s):  
Distribution Function ◽  
Probability Density Function ◽  
Closed Form ◽  
Probability Density ◽  
Infinite Number ◽  
Stable Distribution ◽  
Random Variable ◽  
Cauchy Distribution ◽  
Closed Form Expression ◽  
Form Expression

The consensus achieved in the consensus-forming algorithm is not generally a constant but rather a random variable, even if the initial opinions are the same. In the present paper, we investigate the statistical properties of the consensus in a broadcasting-based consensus-forming algorithm. We focus on two extreme cases: consensus forming by two agents and consensus forming by an infinite number of agents. In the two-agent case, we derive several properties of the distribution function of the consensus. In the infinite-numberof- agents case, we show that if the initial opinions follow a stable distribution, then the consensus also follows a stable distribution. In addition, we derive a closed-form expression of the probability density function of the consensus when the initial opinions follow a Gaussian distribution, a Cauchy distribution, or a L´evy distribution.

scholarly journals Colored HOMFLY-PT for hybrid weaving knot $$ {\hat{\mathrm{W}}}_3 $$(m, n)

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Vivek Kumar Singh ◽  
Rama Mishra ◽  
P. Ramadevi
Keyword(s):  
Closed Form ◽  
Topological Strings ◽  
Chebyshev Polynomials ◽  
Fibonacci Numbers ◽  
Infinite Family ◽  
Closed Form Expression ◽  
Two Dimensional ◽  
Laurent Polynomials ◽  
Form Expression ◽  
Torus Knots

Abstract Weaving knots W(p, n) of type (p, n) denote an infinite family of hyperbolic knots which have not been addressed by the knot theorists as yet. Unlike the well known (p, n) torus knots, we do not have a closed-form expression for HOMFLY-PT and the colored HOMFLY-PT for W(p, n). In this paper, we confine to a hybrid generalization of W(3, n) which we denote as $$ {\hat{W}}_3 $$ W ̂ 3 (m, n) and obtain closed form expression for HOMFLY-PT using the Reshitikhin and Turaev method involving $$ \mathrm{\mathcal{R}} $$ ℛ -matrices. Further, we also compute [r]-colored HOMFLY-PT for W(3, n). Surprisingly, we observe that trace of the product of two dimensional $$ \hat{\mathrm{\mathcal{R}}} $$ ℛ ̂ -matrices can be written in terms of infinite family of Laurent polynomials $$ {\mathcal{V}}_{n,t}\left[q\right] $$ V n , t q whose absolute coefficients has interesting relation to the Fibonacci numbers $$ {\mathrm{\mathcal{F}}}_n $$ ℱ n . We also computed reformulated invariants and the BPS integers in the context of topological strings. From our analysis, we propose that certain refined BPS integers for weaving knot W(3, n) can be explicitly derived from the coefficients of Chebyshev polynomials of first kind.

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