scholarly journals Stochastic Analysis of a Computer System with Unit Wise Cold Standby Redundancy and Failure of Service Facility

2020 ◽  
Vol 5 (3) ◽  
pp. 529-543
Author(s):  
R. K. Yadav ◽  
S. C. Malik
Keyword(s):  
Computer System ◽  
Probability Density Functions ◽  
Software Components ◽  
Treatment Rate ◽  
Repair Rate ◽  
Service Facility ◽  
Negative Exponential Distribution ◽  
Cold Standby ◽  
Negative Exponential ◽  
Similar Unit

Here, we analyze stochastically a computer system by taking one more similar unit (called computer system) in cold standby redundancy. The computer system consists of hardware and software components together. The provision of a single service facility has been made for repairing hardware and up-grading the software. The failure of the service facility is considered which resumes the jobs with full efficiency as new after availing treatment. The failure rates of hardware and software components as well as failure rate of the service facility are taken as constant and thus follow negative exponential distribution. The treatment rate of the service facility, repair rate of the hardware and up-gradation rate of the software follow arbitrary distributions with different probability density functions. Efforts have been made to determine reliability measures in steady state by using SMP and RPT. The behavior of MTSF, availability and also the profit function is observed graphically for some particular situations of the parameters.

The Comparison Between the Bayes Estimator and the Maximum Likelihood Estimator of the Reliability Function for Negative Exponential Distribution

2018 ◽  
pp. 439
Author(s):  
Hazim Mansour Gorgees ◽  
Bushra Abdualrasool Ali ◽  
Raghad Ibrahim Kathum
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Exponential Distribution ◽  
Reliability Function ◽  
Bayes Estimator ◽  
Likelihood Estimator ◽  
Monte Carlo Simulation Technique ◽  
Negative Exponential Distribution ◽  
Negative Exponential ◽  
Better Than

     In this paper, the maximum likelihood estimator and the Bayes estimator of the reliability function for negative exponential distribution has been derived, then a Monte –Carlo simulation technique was employed to compare the performance of such estimators. The integral mean square error (IMSE) was used as a criterion for this comparison. The simulation results displayed that the Bayes estimator performed better than the maximum likelihood estimator for different samples sizes.

Ehrenfest urn models

1965 ◽  
Vol 2 (02) ◽  
pp. 352-376 ◽  
Author(s):  
Samuel Karlin ◽  
James McGregor
Keyword(s):  
Exponential Distribution ◽  
Continuous Time ◽  
Random Variables ◽  
Independent Random Variables ◽  
Urn Models ◽  
Time Intervals ◽  
Negative Exponential Distribution ◽  
Negative Exponential ◽  
Random Times

In the Ehrenfest model with continuous time one considers two urns and N balls distributed in the urns. The system is said to be in stateiif there areiballs in urn I, N −iballs in urn II. Events occur at random times and the time intervals T between successive events are independent random variables all with the same negative exponential distributionWhen an event occurs a ball is chosen at random (each of theNballs has probability 1/Nto be chosen), removed from its urn, and then placed in urn I with probabilityp, in urn II with probabilityq= 1 −p, (0 <p< 1).

scholarly journals Traffic Characteristics for A Freeway Normal Section at Baghdad City

2018 ◽  
Vol 7 (4.20) ◽  
pp. 283
Author(s):  
Jalal T. S. Al-Obaedi ◽  
Muhanad Al-temimy ◽  
Amal Ali
Keyword(s):  
Traffic Flow ◽  
Research Work ◽  
Distribution Data ◽  
Lane Changing ◽  
Traffic Characteristics ◽  
Traffic Lane ◽  
Video Recordings ◽  
Negative Exponential Distribution ◽  
Headway Distribution ◽  
Negative Exponential

Traffic characteristics at highway sections are usually varying based on many factors including type of highways, geometric design and drivers’ behavior at a given area (country).  This paper focuses on finding the characteristics for traffic on selected normal freeway section at Baghdad city.  Video recordings and speed gun are used to collect data from a basic freeway section within Mohammed Al-Qassim freeway that represents the busiest freeway at the city.  The estimated characteristics include the distribution of traffic among the available lanes, desired speed of traffic, lane-changing frequency, and headway distribution.  For traffic distribution, it is found that traffic concentrates more in off side lane compared with other lanes for moderate to high flow rates.  Regression models have been developed based on the available lane distribution data.  The lane found to be increased with the increasing of traffic flow and the desired speeds found to be normally distributed.  Examining the headway data shows that the shifted negative exponential distribution can be used to represent the headway distribution for low to intermediate traffic flow only.  The findings of this work provides a good database for traffic characteristics for Iraqi highways as little effort has been given in previous research work.  

A characterization of the negative exponential distribution with application to reliability theory

1981 ◽  
Vol 18 (3) ◽  
pp. 652-659 ◽  
Author(s):  
M. J. Phillips
Keyword(s):  
Exponential Distribution ◽  
Random Variables ◽  
Reliability Theory ◽  
The Other ◽  
Independent Random Variables ◽  
System Availability ◽  
Failure Times ◽  
Negative Exponential Distribution ◽  
Negative Exponential

The negative exponential distribution is characterized in terms of two independent random variables. Only one of the random variables has a negative exponential distribution whilst the other can belong to a wide class of distributions. This result is then applied to two models for the reliability of a system of two modules subject to revealed and unrevealed faults to show when the models are equivalent. It is also shown, under certain conditions, that the system availability is only independent of the distribution of revealed failure times in one module when unrevealed failure times in the other module have a negative exponential distribution.

An exponential Markovian stationary process

1980 ◽  
Vol 17 (04) ◽  
pp. 1117-1120 ◽  
Author(s):  
L. Valadares Tavares
Keyword(s):  
Exponential Distribution ◽  
Autocorrelation Function ◽  
Stationary Process ◽  
Autoregressive Process ◽  
Exact Distribution ◽  
Markovian Process ◽  
Negative Exponential Distribution ◽  
Negative Exponential

A new markovian process {X i : i = 0, 1, 2, ·· ·} following a negative exponential distribution and with the same autocorrelation function as the lag-1 autoregressive process is proposed and studied in this paper. The exact distribution of the maxima and of the minima of n consecutive Xi values are obtained and the exact expected upcrossing interval is given for any crossing level.

A characterization of the negative exponential distribution with application to reliability theory

1981 ◽  
Vol 18 (03) ◽  
pp. 652-659 ◽  
Author(s):  
M. J. Phillips
Keyword(s):  
Exponential Distribution ◽  
Random Variables ◽  
Reliability Theory ◽  
The Other ◽  
Independent Random Variables ◽  
System Availability ◽  
Failure Times ◽  
Negative Exponential Distribution ◽  
Negative Exponential

The negative exponential distribution is characterized in terms of two independent random variables. Only one of the random variables has a negative exponential distribution whilst the other can belong to a wide class of distributions. This result is then applied to two models for the reliability of a system of two modules subject to revealed and unrevealed faults to show when the models are equivalent. It is also shown, under certain conditions, that the system availability is only independent of the distribution of revealed failure times in one module when unrevealed failure times in the other module have a negative exponential distribution.

scholarly journals Strong convergence of multivariate maxima

2020 ◽  
Vol 57 (1) ◽  
pp. 314-331
Author(s):  
Michael Falk ◽  
Simone A. Padoan ◽  
Stefano Rizzelli
Keyword(s):  
Strong Convergence ◽  
Higher Dimensions ◽  
Convergence Result ◽  
Common Distribution ◽  
Convergence Results ◽  
Negative Exponential Distribution ◽  
Common Distribution Function ◽  
Variation Distance ◽  
Negative Exponential ◽  
Variational Distance

AbstractIt is well known and readily seen that the maximum of n independent and uniformly on [0, 1] distributed random variables, suitably standardised, converges in total variation distance, as n increases, to the standard negative exponential distribution. We extend this result to higher dimensions by considering copulas. We show that the strong convergence result holds for copulas that are in a differential neighbourhood of a multivariate generalised Pareto copula. Sklar’s theorem then implies convergence in variational distance of the maximum of n independent and identically distributed random vectors with arbitrary common distribution function and (under conditions on the marginals) of its appropriately normalised version. We illustrate how these convergence results can be exploited to establish the almost-sure consistency of some estimation procedures for max-stable models, using sample maxima.

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