Exact Reliability for a Consecutive Circular k-out-of-r-from-n: F System with Equal and Unequal Component Probabilities

2019 ◽  
Vol 27 (01) ◽  
pp. 2050003 ◽  
Author(s):  
Y. Amirian ◽  
A. Khodadadi ◽  
O. Chatrabgoun
Keyword(s):  
Closed Form ◽  
Reliability Analysis ◽  
Numerical Results ◽  
Innovative Program ◽  
Circular Component ◽  
Extensive Class ◽  
Exact Amount ◽  
F System

A consecutive linear (circular) [Formula: see text]-out-of-[Formula: see text]-from-[Formula: see text]: F system consists of [Formula: see text] linear (circular)-ordered components such that the system fails if and only if there exists a set of [Formula: see text] consecutive linear (circular) component that contains at least [Formula: see text] failed components. Consecutive linear (circular) [Formula: see text]-out-of-[Formula: see text]-from-[Formula: see text]: F systems attract tremendous attention for researchers of reliability analysis. Recent efforts in this area have focused on simple situations or approximation bands for their reliability but closed form and exact amount not gained. In this paper, we designed an innovative algorithm and an innovative program to obtain the exact reliability for an extensive class of consecutive circular [Formula: see text]-out-of-[Formula: see text]-from-[Formula: see text]: F system with particular emphasis for equal and unequal component probabilities. Finally, we reviewed an applied example and applied comparative and numerical results and calculated the exact reliability of this strategic system.

Exact Reliability for a Multi-State Consecutive Linear (Circular) k-out-of-r-from-n:F System

2020 ◽  
pp. 2150014
Author(s):  
Y. Amirian ◽  
A. Khodadadi
Keyword(s):  
Closed Form ◽  
Real World ◽  
Numerical Results ◽  
State Probability ◽  
Complete Failure ◽  
State Models ◽  
First Time ◽  
Exact Amount

The multi-state consecutive linear (circular) [Formula: see text]-out-of-[Formula: see text]-from-[Formula: see text] system consists of [Formula: see text] linear (circular) ordered multi-state components. Both the system and its components can have [Formula: see text] different states: from complete failure (zero state) up to perfect functioning (([Formula: see text]1) state). In this paper we suggest, for the first time, exact reliability for these models. The system is at state below [Formula: see text] if and only if at least [Formula: see text] components out of any [Formula: see text] consecutive are in state below [Formula: see text] [Formula: see text]. Recent efforts in these branches have focused on simple situations or approximation bands for their reliability in two-state or multi-state models but closed form and exact amount not gained. In the continuation, there are the matlab programs of linear (circular) reliability system and [Formula: see text] state probability for [Formula: see text] in system. In the following, we applied comparative and numerical results and calculated the exact reliability of this strategic systems. Finally, we calculated the exact reliability for two real-world practical examples.

Modeling and Exact Reliability for a Consecutive Linear (k1,k2,…,kn−r+1)-Out-of-r-from-n: F System and Consecutive Circular (k1,k2,…,kn)-Out-of-r-from-n: F System

2021 ◽  
pp. 2150029
Author(s):  
Y. Amirian ◽  
A. Khodadadi
Keyword(s):  
Linear System ◽  
Order Statistic ◽  
Failed State ◽  
Time Modeling ◽  
Linear Formula ◽  
State Formula ◽  
Extensive Class ◽  
Circular System ◽  
First Time ◽  
F System

The consecutive linear [Formula: see text]-out-of-[Formula: see text]-from-[Formula: see text]:F system consists of [Formula: see text] linear ordered components and the consecutive circular [Formula: see text]-out-of-[Formula: see text]-from-[Formula: see text]:F system consists of [Formula: see text] circular ordered components. In this paper, we suggest, for the first time, modeling and exact reliability for these models. The linear system fails if and only if there exists a [Formula: see text]-order statistic of [Formula: see text]-consecutive [Formula: see text] [Formula: see text] of components in the failed state, [Formula: see text], [Formula: see text]; and the circular system fails if and only if there exists a [Formula: see text]-order statistic of [Formula: see text]-consecutive [Formula: see text] [Formula: see text] of components in the failed state, [Formula: see text], [Formula: see text]. In this paper, we designed an innovative algorithm to obtain the exact reliability for an extensive class of consecutive linear and circular systems. In continuation, there are the MATLAB Programs of exact reliability for consecutive linear and circular systems. In the following, we applied comparative and numerical results and calculated the exact reliability of this strategic systems. Finally, we calculated the exact reliability for two real-world practical examples.

scholarly journals Optimal Investment of DC Pension Plan under Incentive Schemes and Loss Aversion

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Yinghui Dong ◽  
Wenxin Lv ◽  
Siyuan Wei ◽  
Yeyang Gong
Keyword(s):  
Closed Form ◽  
Loss Aversion ◽  
Pension Plan ◽  
Optimal Investment ◽  
Numerical Results ◽  
Managerial Compensation ◽  
Incentive Schemes ◽  
Terminal Wealth ◽  
Portfolio Problem ◽  
Form Representation

We investigate the DC pension manager’s portfolio problem when the manager is remunerated through two schemes for DC pension managerial compensation under loss aversion and minimum guarantee. We apply the concavification technique and a static Lagrangian technique to solve the problem and derive the closed-form representation of the optimal wealth and portfolio processes. Theoretical and numerical results show that the incentive schemes can significantly impact the distribution of the optimal terminal wealth.

Stiffness of Annular Bonded Rubber Flanged Bushes

2006 ◽  
Vol 79 (2) ◽  
pp. 233-248 ◽  
Author(s):  
J. M. Horton ◽  
G. E. Tupholme
Keyword(s):  
Closed Form ◽  
Finite Length ◽  
Classical Theory ◽  
Theory Of Elasticity ◽  
Numerical Results ◽  
Torsional Stiffness ◽  
Radial Stiffness ◽  
Physical Data

Abstract Closed-form expressions are derived for the torsional stiffness, radial stiffness and tilting stiffness of annular rubber flanged bushes of finite length in three principal modes of deformation, based upon the classical theory of elasticity. Illustrative numerical results are deduced with realistic physical data of typical flanged bushes.

On the Contact Problem of Thin Circular Rings

1965 ◽  
Vol 32 (1) ◽  
pp. 11-20 ◽  
Author(s):  
Chien-Heng Wu ◽  
Robert Plunkett
Keyword(s):  
Contact Problem ◽  
Closed Form ◽  
Constant Curvature ◽  
Complete Solution ◽  
Elliptic Functions ◽  
Numerical Results ◽  
Elastic Contact ◽  
Flat Plates ◽  
Circular Rings

It is well known that the solution of an elastica subjected to end loads can be obtained in terms of elliptic functions. In the present paper, the combined problem of elastic contact between uniform circular rings or cylinders is reduced to a set of end-loaded elasticas. The approach is demonstrated by finding the complete solution in closed form for two unequal rings pressed between rigid anvils of constant curvature. Numerical results are obtained for the set of problems of two rings with equal stiffness but unequal radii compressed between two rigid flat plates.

Asymmetrical Bending of a Cylindrically Aeolotropic Tapered Disk

1956 ◽  
Vol 23 (1) ◽  
pp. 11-14
Author(s):  
E. S. Baclig ◽  
H. D. Conway
Keyword(s):  
Closed Form ◽  
Isotropic Material ◽  
Numerical Results ◽  
Simple Solution ◽  
Thickness Variation ◽  
Plate Bending ◽  
Small Deflection ◽  
Asymmetrical Bending

Abstract Variations of thickness, anisotropy, and asymmetry of loading usually tend to increase the mathematical difficulty of obtaining solutions to the small-deflection problems of plate bending. However, for the bending of a cylindrically aeolotropic disk twisted about its diameter and having a certain thickness variation, it is possible to obtain a relatively simple solution in closed form. This solution is presented here, numerical results being given for oak and for isotropic material.

scholarly journals Relativistic symmetries of Schioberg and general Manning-Rosen potentials and the effects of tensor coupling

2013 ◽  
Vol 37 (1) ◽  
pp. 1-17
Author(s):  
A. N. Ikot ◽  
E. Maghsoodi ◽  
C. N. Isonguyo ◽  
S. Zarrinkamar ◽  
H. Hassanabadi
Keyword(s):  
Dirac Equation ◽  
Potential Energy ◽  
Closed Form ◽  
Bound State ◽  
Tensor Interaction ◽  
Numerical Results ◽  
Wave Functions ◽  
Tensor Coupling ◽  
Energy Equations ◽  
Rosen Potential

Abstract In this paper we solve the Dirac equation with Schioberg and general Manning- Rosen potentials including the Coulomb-like tensor interaction. The approximate analytical bound state solutions of the Dirac equation with the Schioberg and Manning-Rosen potential, energy equations and the corresponding unnormalized wave functions are obtained in a closed form using SUSYQM. We have also reported the numerical results to show the effect of the tensor interaction.

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