A general formula for the downtime distribution of a parallel system

1996 ◽  
Vol 33 (3) ◽  
pp. 772-785 ◽  
Author(s):  
Harald Haukås ◽  
Terje Aven
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Time Distribution ◽  
Life Time ◽  
Exact Formula ◽  
Parallel System ◽  
System Failure ◽  
System Failures ◽  
Failure Scenario ◽  
Common Situation

In this paper we study the problem of computing the downtime distribution of a parallel system comprising stochastically identical components. It is assumed that the components are independent, with an exponential life-time distribution and an arbitrary repair time distribution. An exact formula is established for the distribution of the system downtime given a specific type of system failure scenario. It is shown by performing a Monte Carlo simulation that the portion of the system failures that occur as described by this scenario is close to one when we consider a system with quite available components, the most common situation in practice. Thus we can use the established formula as an approximation of the downtime distribution given system failure. The formula is compared with standard Markov expressions. Some possible extensions of the formula are presented.

A general formula for the downtime distribution of a parallel system

1996 ◽  
Vol 33 (03) ◽  
pp. 772-785
Author(s):  
Harald Haukås ◽  
Terje Aven
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Time Distribution ◽  
Life Time ◽  
Exact Formula ◽  
Parallel System ◽  
System Failure ◽  
System Failures ◽  
Failure Scenario ◽  
Common Situation

In this paper we study the problem of computing the downtime distribution of a parallel system comprising stochastically identical components. It is assumed that the components are independent, with an exponential life-time distribution and an arbitrary repair time distribution. An exact formula is established for the distribution of the system downtime given a specific type of system failure scenario. It is shown by performing a Monte Carlo simulation that the portion of the system failures that occur as described by this scenario is close to one when we consider a system with quite available components, the most common situation in practice. Thus we can use the established formula as an approximation of the downtime distribution given system failure. The formula is compared with standard Markov expressions. Some possible extensions of the formula are presented.

Monte Carlo simulation of the renewal function

1981 ◽  
Vol 18 (2) ◽  
pp. 426-434 ◽  
Author(s):  
Mark Brown ◽  
Herbert Solomon ◽  
Michael A. Stephens
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Renewal Process ◽  
Time Distribution ◽  
Interarrival Time ◽  
Renewal Function ◽  
Expected Number ◽  
Unbiased Estimators ◽  
Monte Carlo Estimation ◽  
Naive Estimator

The problem of Monte Carlo estimation of M(t) = EN(t), the expected number of renewals in [0, t] for a renewal process with known interarrival time distribution F, is considered. Several unbiased estimators which compete favorably with the naive estimator, N(t), are presented and studied. An approach to reduce the variance of the Monte Carlo estimator is developed and illustrated.

Modeling and Specification of Time-Limited Dispatch Categories for Commercial Aircraft

2008 ◽  
Vol 130 (2) ◽  
Author(s):  
D. R. Prescott ◽  
J. D. Andrews
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Control System ◽  
System Failure ◽  
Failure Rates ◽  
Simulation Approach ◽  
Commercial Aircraft ◽  
Modeling Systems ◽  
Certification Requirements ◽  
Reduced State

Time-limited dispatch allows the degraded redundancy dispatch of aircraft. Aircraft can be dispatched with certain control system faults and fault combinations for specified periods of time if the failure rates from those configurations meet certification requirements. The various system faults and fault combinations are assigned to dispatch categories according to these failure rates. This gives the dispatch criteria for the system. The overall failure rate of the system can then be calculated according to the dispatch criteria. Dispatch criteria are allocated to a small example system, and the system is subsequently modeled using a reduced-state Markov approach currently recommended in SAE ARP5107. An alternative method of setting dispatch criteria and modeling systems, using Monte Carlo simulation, is proposed in this paper, and this technique is also applied to the example system. Dispatch criteria applied to the different models are seen to differ, as are the system failure rates calculated using the different models. A method for setting the dispatch criteria for a system using a Monte Carlo simulation approach is introduced. The method is applied to a simple system, giving auditable results that exhibit the expected behavior for such a system. Because restrictive assumptions in the mathematics are unnecessary with Monte Carlo simulation, it is expected to give more accurate results in comparison to Markov approaches. Also, the results of the reduced-state Markov model appear to be largely dependent on failure rates, which are very difficult to determine.

CHARACTERIZING FAILURE DURATION IN 2-TERMINAL NETWORK PROBLEMS

2001 ◽  
Vol 08 (02) ◽  
pp. 137-158
Author(s):  
PETER J. SMITH ◽  
HOWARD W. SILBY ◽  
YU HAYAKAWA ◽  
CHRIS CARLISLE
Keyword(s):  
Monte Carlo ◽  
Importance Sampling ◽  
Analytical Method ◽  
Failure Time ◽  
System Failure ◽  
System Failures ◽  
Network Problems ◽  
Great Relevance ◽  
Component Failures ◽  
Failure Time Distributions

To characterize the "reliability" or "robustness" of a network, more information is required than simply the system failure rate. In particular the length of the downtimes can be of great relevance. Hence, in this paper we present two methods for computing the system downtime distribution in 2-terminal network problems. The first method is an importance sampling simulation which allows simulations to capture the tail of the distribution with much greater precision than simple Monte Carlo methods. Hence the statistics of unusually long failures can be investigated by simulation. The second method is an approximate analytical method whereby system failures due to 1 or 2 or … or N component failures are characterized exactly. The error in using N=2 and neglecting greater than three simultaneous component failures is shown to be negligible in many cases of interest. This method can be extended to handle N>2 component failures but the resulting calculations escalate rather quickly and are omitted here. This technique makes it possible to provide approximate failure time distributions very rapidly for arbitrary networks.

Estimation of System Reliability by Monte Carlo Simulation

2009 ◽  
Author(s):  
A. Naess ◽  
B. J. Leira ◽  
O. Batsevych
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Reliability Analysis ◽  
Failure Probability ◽  
Failure Criterion ◽  
System Reliability ◽  
Substantial Reduction ◽  
Structural Systems ◽  
System Failure ◽  
Simulation Monte Carlo

A new method for estimating the reliability of structural systems is proposed. The method is based on the use of Monte Carlo simulation. Monte Carlo based methods for system reliability analysis has several attractive features, the most important being that the system failure criterion is usually relatively easy to check almost irrespective of the complexity of the system. The disadvantage of such methods is the amount of computational efforts that may be involved. However, by reformulating the reliability problem to depend on a parameter and exploiting the regularity of the failure probability as a function of this parameter, it is shown that a substantial reduction of the computational efforts involved can be obtained.

PAUSING-TIME DISTRIBUTION OF ANOMALOUS DIFFUSION OF HYDROGEN WITH RANDOM ENERGY

2014 ◽  
Vol 28 (05) ◽  
pp. 1450042 ◽  
Author(s):  
HARUMI HIKITA ◽  
KAZUO MORIGAKI
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Random Walk ◽  
Power Law ◽  
Time Distribution ◽  
Fractal Structure ◽  
Analytical Calculation ◽  
Disordered System ◽  
Random Energy ◽  
Diffusion Of Hydrogen

It has been empirically known that the disordered system exhibits a power-law behavior. We show from calculation the power law t-1-α for the pausing-time distribution of thermal diffusion of hydrogen in the exponential density of states. This power law of the pausing-time distribution is examined by the Monte Carlo simulation. The results agree with those obtained by analytical calculation. We discuss the power law in terms of random walk in fractal structure (Cantor ensemble).

Monte Carlo simulation of the renewal function

1981 ◽  
Vol 18 (02) ◽  
pp. 426-434 ◽  
Author(s):  
Mark Brown ◽  
Herbert Solomon ◽  
Michael A. Stephens
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Renewal Process ◽  
Time Distribution ◽  
Interarrival Time ◽  
Renewal Function ◽  
Expected Number ◽  
Unbiased Estimators ◽  
Monte Carlo Estimation ◽  
Naive Estimator

The problem of Monte Carlo estimation of M(t) = EN(t), the expected number of renewals in [0, t] for a renewal process with known interarrival time distribution F, is considered. Several unbiased estimators which compete favorably with the naive estimator, N(t), are presented and studied. An approach to reduce the variance of the Monte Carlo estimator is developed and illustrated.

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