scholarly journals Some reliability characteristics of a linear consecutive 2-out-of-4 system connected to 2-out-of-4 supporting device for operation

2018 ◽  
Vol 7 (1) ◽  
pp. 135
Author(s):  
Yusuf Ibrahim ◽  
Bashir Yusuf ◽  
Mansur Babagana ◽  
Baffa Sani ◽  
Muhammad Auwal Lawan
Keyword(s):  
Busy Period ◽  
Repairable System ◽  
Profit Function ◽  
Order Linear Differential Equation ◽  
System Parameters ◽  
First Order ◽  
Reliability Characteristics ◽  
Linear Differential ◽  
Supporting Device ◽  
System Operating

This paper presents the Markov model for the reliability analysis of a linear consecutive 2-out-of-4 repairable system operating with the help of a linear consecutive 2-out-of-4 external supporting device. The system is analyzed using first order linear differential equation to develop the explicit expression for steady-state availability, busy period and profit function. Based on assumed numerical values given to system parameters, graphical illustrations are given to highlight important results. In addition, the effect of failure and repair on availability and profit are researched.

Availability evaluation of repairable system requiring two types of supporting device for operations

2017 ◽  
Vol 6 (1) ◽  
pp. 14
Author(s):  
Nura Jibrin Fagge ◽  
Ibrahim Yusuf ◽  
U.A. Ali
Keyword(s):  
Single Unit ◽  
Modern Science ◽  
Repairable System ◽  
System Parameters ◽  
First Order ◽  
Unit System ◽  
The Impact ◽  
Availability Assessment ◽  
Supporting Device ◽  
First Order Differential Equations

With advancement of modern science and technology, complex systems connected to an external supporting device for their operations have been manufactured to meet the demand of industries, economic growth and populace in general. Companies and organizations heavily rely on these systems to conduct their business. This study presents the availability assessment of a single unit system connected to two types of an external supporting device for its operation. Each type of supporting device has two copies I and II. First order differential equations method is used to obtain the explicit expression for the steady-state availability. Based on assumed numerical values given to system parameters, graphical illustrations are given to highlight important results. Comparisons are performed to highlight the impact of unit failure and repair rates.

scholarly journals Oscillation of first order linear differential equations with several non-monotone delays

2018 ◽  
Vol 16 (1) ◽  
pp. 83-94
Author(s):  
E.R. Attia ◽  
V. Benekas ◽  
H.A. El-Morshedy ◽  
I.P. Stavroulakis
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Linear Differential Equation ◽  
Linear Differential Equations ◽  
Order Linear Differential Equation ◽  
Order Linear ◽  
First Order ◽  
Linear Differential

AbstractConsider the first-order linear differential equation with several retarded arguments$$\begin{array}{} \displaystyle x^{\prime }(t)+\sum\limits_{k=1}^{n}p_{k}(t)x(\tau _{k}(t))=0,\;\;\;t\geq t_{0}, \end{array} $$where the functions pk, τk ∈ C([t0, ∞), ℝ+), τk(t) < t for t ≥ t0 and limt→∞τk(t) = ∞, for every k = 1, 2, …, n. Oscillation conditions which essentially improve known results in the literature are established. An example illustrating the results is given.

scholarly journals Availability Analysis of Hybrid Systems Consisting of Main Units and Cold Standby Processors

2021 ◽  
Author(s):  
Ibrahim Yusuf ◽  
Nafisatu Muhammad Usman ◽  
Saminu Iliyasu Bala
Keyword(s):  
Hybrid Systems ◽  
Numerical Experiments ◽  
Rank Correlation ◽  
Correlation Coefficients ◽  
Critical Parameters ◽  
System Parameters ◽  
First Order ◽  
Availability Analysis ◽  
Linear Differential ◽  
Partial Rank Correlation

The present paper studies availability of four hybrid systems configured as series-parallel systems. Each system or configuration consisting of main units and their corresponding processors. Configuration I consist of three processors is a 2-out-of-3 unit connected to 2-out-of-3 processors, Configuration II is a 2-out-of-3 unit connected to 2-out-of-4 processors, Configuration III is a 2-out-of-4 unit connected to 2-out-of-4 processors while Configuration IV is a 2-out-of-4 unit connected to 2-out-of-3 processors. The failure and repair times of units and their processors are assumed to be exponentially distributed. Explicit expressions for steady state availability are developed for each system using first order linear differential difference equations and validated by performing numerical experiments. Analysis of the effect of various system parameters on availability was performed. Graphical illustrations are given to highlight important results. The systems are ranked based on their availability and found that Configuration IV is better. Sensitivity analysis on the model’s outcomes are performed using partial rank correlation coefficients (PRCC) to determine the most critical parameters leading to increase (decrease) in the value of availability.

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