scholarly journals On the Survival Time of a Duplex System: A Sokhotski-Plemelj Problem

2008 ◽  
Vol 2008 ◽  
pp. 1-13
Author(s):  
Edmond J. Vanderperre
Keyword(s):  
Survival Time ◽  
Survival Function ◽  
Solution Procedure ◽  
Security Level ◽  
Duplex System ◽  
Coupled Partial Differential Equations ◽  
System A ◽  
Risk Criterion ◽  
The Laplace Transform ◽  
Warm Standby

We analyze the survival time of a renewable duplex system characterized by warm standby and subjected to a priority rule. In order to obtain the Laplace transform of the survival function, we employ a stochastic process endowed with time-dependent transition measures satisfying coupled partial differential equations. The solution procedure is based on the theory of sectionally holomorphic functions combined with the notion of dual transforms. Finally, we introduce a security interval related to a prescribed security level and a suitable risk criterion based on the survival function of the system. As an example, we consider the particular case of deterministic repair. A computer-plotted graph displays the survival function together with the security interval corresponding to a security level of 90%.

scholarly journals Reliability of an engineering system characterized by hot and cold standby: A compound boundary value problem

2021 ◽  
pp. 16-16
Author(s):  
Edmond Vanderperre ◽  
Stanislav Makhanov
Keyword(s):  
Boundary Value Problem ◽  
Survival Time ◽  
Boundary Value ◽  
Survival Function ◽  
Holomorphic Functions ◽  
Engineering System ◽  
Entire System ◽  
Duplex System ◽  
Cold Standby ◽  
Auxiliary Unit

We analyse the reliability (survival function) of a duplex system characterized by hot standby and sustained by an auxiliary unit in cold standby. The entire system is attended by two heterogeneous repairmen. Our methodology is based on the theory of sectionally holomorphic functions combined with the notion of dual transforms. Finally, we also study the total occupational time of the repairman responsible for the repair of the failed priority unit during the survival time of the system.

scholarly journals Cox proportion hazard model for patients with hepatitis disease in Iraq

2009 ◽  
Vol 6 (3) ◽  
pp. 612-617
Author(s):  
Baghdad Science Journal
Keyword(s):  
Regression Model ◽  
Survival Time ◽  
Cox Regression ◽  
Survival Function ◽  
Hazard Model ◽  
Cox Regression Model ◽  
Hepatic Diseases ◽  
Kaplan Meier

Cox regression model have been used to estimate proportion hazard model for patients with hepatitis disease recorded in Gastrointestinal and Hepatic diseases Hospital in Iraq for (2002 -2005). Data consists of (age, gender, survival time terminal stat). A Kaplan-Meier method has been applied to estimate survival function and hazerd function.

WAITING TIME ANALYSIS OF MULTI-CLASS QUEUES WITH IMPATIENT CUSTOMERS

2013 ◽  
Vol 27 (3) ◽  
pp. 333-352 ◽  
Author(s):  
Vahid Sarhangian ◽  
Bariş Balciog̃lu
Keyword(s):  
Waiting Time ◽  
Delay Systems ◽  
Single Server ◽  
Impatient Customers ◽  
Preemptive Priority ◽  
System A ◽  
Virtual Waiting Time ◽  
The Laplace Transform ◽  
Time Requirements ◽  
Priority Policy

In this paper, we study three delay systems where different classes of impatient customers arrive according to independent Poisson processes. In the first system, a single server receives two classes of customers with general service time requirements, and follows a non-preemptive priority policy in serving them. Both classes of customers abandon the system when their exponentially distributed patience limits expire. The second system comprises parallel and identical servers providing the same type of service for both classes of impatient customers under the non-preemptive priority policy. We assume exponential service times and consider two cases depending on the time-to-abandon distribution being exponentially distributed or deterministic. In either case, we permit different reneging rates or patience limits for each class. Finally, we consider the first-come-first-served policy in single- and multi-server settings. In all models, we obtain the Laplace transform of the virtual waiting time for each class by exploiting the level-crossing method. This enables us to compute the steady-state system performance measures.

APPROXIMATION OF SURVIVAL FUNCTION FOR HETEROGENEOUS POPULATIONS

2011 ◽  
Vol 162 (4) ◽  
pp. 342-358
Author(s):  
Stanisława OSTASIEWICZ
Keyword(s):  
Survival Time ◽  
Survival Function ◽  
Polish Population ◽  
Survival Functions ◽  
Heterogeneous Populations ◽  
Long Time ◽  
General Survival

For a long time demographers and actuaries have been deliberating the issue of the laws of life. A number of proposed survival functions turned out to be unsatisfactory when they were applied empirically. One of the ways to overcome the difficulties is to modify the general survival functions by introducing an additional formula characterizing the frailty of individuals. Another way is to use a mixture of appropriate distributions. In this contribution the latter approach to determine the survival time of men in the Polish population in 2009 is applied.

A functional equation related to a repairable system subjected to priority rules

2016 ◽  
Vol 28 (1) ◽  
pp. 123-140
Author(s):  
E. J. VANDERPERRE ◽  
S. S. MAKHANOV
Keyword(s):  
Functional Equation ◽  
Survival Time ◽  
Function Theory ◽  
Complex Function ◽  
Priority Rules ◽  
Complex Function Theory ◽  
Duplex System ◽  
Repair Facility ◽  
Parameter Dependent ◽  
Auxiliary Unit

We analyse the survival time of a general duplex system sustained by an auxiliary cold standby unit and subjected to priority rules. The duplex system is attended by two general repairmenRpandRh. RepairmanRphas priority in repairing failed units with regard to repairmanRhprovided that both repairmen are jointly idle. Otherwise, the priority is overruled. The auxiliary unit has its own repair facility. The duplex system has overall, break-in priority (often called pre-emptive priority) in operation and in standby with regard to the auxiliary unit. The analysis of the survival time is based on advanced complex function theory (sectionally holomorphic functions). The main problem is to convert a functional equation into a (parameter dependent) Sokhotski–Plemelj problem.

An Analytical Solution of the Generalized Phase-Lagging Equation for Ultra-Fast Heat Transfer in One-Dimensional Semi-Infinite Domain

2012 ◽  
Author(s):  
Vladimir Kulish ◽  
Kirill V. Poletkin
Keyword(s):  
Analytical Solution ◽  
Domain Boundary ◽  
Integral Form ◽  
Solution Procedure ◽  
Generalized Derivatives ◽  
Infinite Domain ◽  
One Dimensional ◽  
Confluent Hypergeometric Functions ◽  
The Laplace Transform ◽  
Derivatives Of

The paper presents an integral solution of the generalized one-dimensional phase-lagging heat equation with the convective term. The solution of the problem has been achieved by the use of a novel technique that involves generalized derivatives (in particular, derivatives of non-integer orders). Confluent hypergeometric functions, known as Whittaker’s functions, appear in the course of the solution procedure, upon applying the Laplace transform to the original transport equation. The analytical solution of the problem is written in the integral form and provides a relationship between the local values of the temperature and heat flux. The solution is valid everywhere within the domain, including the domain boundary.

Aeroelastic Flutter of Continuous Systems: A Generalized Laplace Transform Method

2016 ◽  
Vol 83 (8) ◽  
Author(s):  
Arion Pons ◽  
Stefanie Gutschmidt
Keyword(s):  
Laplace Transform ◽  
Continuous Systems ◽  
Laplace Transform Method ◽  
Aeroelastic System ◽  
Transform Method ◽  
Wing Model ◽  
System A ◽  
Aeroelastic Flutter ◽  
The Laplace Transform ◽  
Eigenvalue Parameter

This paper presents a generalization of the Laplace transform method (LTM) for determining the flutter points of a linear ordinary-differential aeroelastic system—a linear system involving a spatial derivative as well as a time-eigenvalue parameter. Current implementations of the LTM have two major problems: they are unable to solve systems of arbitrary size, order, and boundary conditions, and they require certain key operations to be performed by hand or with symbolic manipulation libraries. Our generalized method overcomes both these problems. We also devise a new method for solving and visualizing the algebraic system that arises from the LTM procedure. We validate our generalized LTM and novel solution method against both the Goland wing model and a large system of high differential order, as a demonstration of their effectiveness for solving such systems.

scholarly journals Random Communication System Based on Skewed Alpha-Stable Levy Noise Shift Keying

2017 ◽  
Vol 16 (03) ◽  
pp. 1750024 ◽  
Author(s):  
Areeb Ahmed ◽  
F. Acar Savaci
Keyword(s):  
Communication System ◽  
Secure Communication ◽  
Signal To Noise Ratio ◽  
Additive White Gaussian Noise ◽  
Security Level ◽  
System A ◽  
Shift Keying ◽  
Digital Communication System ◽  
Noise Sequence ◽  
Stable Noise

The digital communication system is based on the skewed alpha-stable ([Formula: see text]-stable) noise sequence which is chosen as the random carrier to modulate the binary message at the transmitter side. Antipodal characteristic of the skew parameter beta ([Formula: see text]) is exploited for decoding information at the receiver side to obtain a secure communication system. A fast estimator used in this paper is based on Modified Extreme Value Method (MEVM) to extract the binary message from the signal received through the Additive White Gaussian Noise (AWGN) channel. Our proposed receiver is achieving better bit error rate (BER) versus Mixed Signal to Noise Ratio (MSNR) than previously introduced receivers which are based on Sinc and Logarithmic estimators. MEVM estimator is indeed less complex compared to the Sinc and Logarithmic estimators and hence more fast. Additionally, the criterion to measure the security level of random communication system, which is based on [Formula: see text]-stable noise sequence, has also been introduced.

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