

MILHDBK338B: Electronic Reliability Design Handbook 
 

6.4.4.2.4.2 Monte Carlo Simulation Method
6.4.4.2.4.2 Monte Carlo
Simulation Method
Monte Carlo simulation may be used to synthesize a system
reliability prediction from a reliability block diagram by means of random
sampling. Monte Carlo simulation is employed in instances where individual
equipment probabilities (or equivalent reliability parameter) are known but the mission reliability model is exceedingly
complex to derive a general equation for solution. The method does not result
in a general probability of success equation but computes the system
probability of success from the individual equipment probabilities and the
reliability block diagram. Monte Carlo simulation is performed by computer due
to the large number of repetitive trials and calculations required to obtain a
significant result. Monte Carlo simulation is applicable to single functioned
and multifunctioned systems.
Monte Carlo simulation determines
the distribution of a function of one or more variables from the distribution
of the individual variables. The method involves random sampling from the
distributions of all variables and inserting the values so obtained in the
equation for the function of interest. Suppose the function whose probability
of success distribution is to be estimated is, P(x_{1} . . . ,
x_{n}) and that the x_{1}, x_{2} . . . , xn are
independent random variables whose distributions are presumed to be known. The
procedure is to pick a set of x’s randomly from the distributions of the x’s,
calculate P for that set, and store that value of P. This is repeated many
times until enough values of P are obtained. From this sample of P values, its
distribution and parameters can be estimated.
Monte Carlo simulation is based on
several principles of probability and on the techniques of probability
transformation. One underlying principle is the law of large numbers, which
states that the larger the sample the more certainly the sample mean will be a
good estimate of the population mean.
Software tools for simulation
modeling include (see the RAC Web Site; the URL is http://rac.iitri.org/DATA/RMST):
(1) 
AvSim, Availability Simulator allows the user to
predict and optimize system and component performance. Uses Monte
Carlo simulation techniques. 
(2) 
CARE, ComputerAided Reliability
Estimation helps estimate the reliability of complex, redundant, or
faulttolerant systems. Capable of modeling very large systems that
incorporate some form of system management strategy which controls
hardware/software resources in the presence of multiple faults or
errors. 
(3) 
ETARA, Event Time Availability,
Reliability Analysis is an interactive event driven simulation
program. The program simulates the behavior of a system over a
specified period of time using Monte Carlo methods to generate block
failure and repair times as a function of exponential or Weibull
distributions. 
(4) 
REST, (RADC Reliability Simulation
Tool, is a Monte Carlo simulation used to evaluate reliability figures
of merit for fault tolerant systems. Given a fault tolerant system
configuration component MTBF’s and repair
rates, the program calculates the system MTBCF, MTTR, reliability and
availability. REST also synthesizes reliability demonstration plans
for fault tolerant systems. Can be used to model systems with full,
standby, or partial standby redundancy. 
(5) 
RAPTOR, The Rapid Availability
Prototyping for Testing Operational Readiness (RAPTOR) software tool
was developed by Headquarters Air Force Operational Test and
Evaluation Center, Logistics Studies and Analysis Team (HQ
AFOTEC/SAL). Its primary purpose is Reliability, Maintainability &
Availability (RM&A) analysis of systems undergoing Operational
Test and Evaluation (OT&E). Other applications include test
planning, requirements definition, reliability prediction and
sensitivity analysis. It can be downloaded over the
Internet
(URL: http://www.afotec.af.mil/sa/safrmset.htm). 




 
 