Reliability and Availability Simulation Krige Visser, Professor, University of Pretoria, South Africa
Content BACKGROUND DEFINITIONS SINGLE COMPONENTS MULTI-COMPONENT SYSTEMS AVAILABILITY SIMULATION CONCLUSION
BACKGROUND The main goal of maintenance is to provide capacity through availability Availability is a function of reliability and maintainability Availability, reliability and maintainability are often key performance indicators for a plant Unexpected failures of the total system is undesirable Reliability is a way to measure the risk of failure
4 Background Availability, reliability and maintainability are typically measured every month Systems with a low level of preventive maintenance have many random failures This could lead to greatly varying values for reliability and availability Simulation tools can be used to model complex systems A study of a 20-component system revealed some interesting results
DEFINITIONS Reliability The probability that a component (item or system) will fail after a specified time period Maintainability The probability that a repair/ replacement task will be performed in less than a specified time Availability - The probability that a system will, when used under specified conditions, operate satisfactorily and effectively
Graphical Representation of Reliability Probability Density Function (PDF) Complementary Cumulative Distribution Function (CCDF)
Graphical Representation of Maintainability Probability Density Function (PDF) Cumulative Distribution Function (CDF)
SINGLE COMPONENT Each component of a system has a unique failure characteristic Some standard failure patterns have been observed from failure data analysis Six failure patterns were defined by Nowlan and Heap For practical application, two failure types are of importance Random failures Wear-out failures
Six Failure Patterns
Single Component: Random Failures f ( t ) = h exp( ht ) R ( t ) = exp( ht )
Single Component: Wear-out Failure f(t) = NORMDIST(t,µ,σ,FALSE) R(t) = 1 - NORMDIST(t,µ,σ,TRUE)
MULTICOMPONENT SYSTEM Complex systems Systems with a large number of components and many interactions between these components There is a need for modeling the reliability and maintainability of such systems Two types of system configuration can be distinguished Series system: failure of one component causes system failure Parallel system: multiple failure is needed for system failure
Repairable System Running Total time, e.g. 1 month Uptime Stopped Downtime A = Uptime Uptime + Downtime Time
Reliability for Series and Parallel System Series System 1 2 3 Parallel System 1 2 3 = R system = 1 [( 1 R1 ) ( 1 R2 ) ( 1 R3 )] R system R 1 R2 R3 N R system = j = R 1 j
Inputs to Simulation Failure distribution for each component is modeled by: Normal, or Exponential Parameters of the specific distribution (mean and standard deviation) for each component are assumed Repair distribution is modeled by means of a normal distribution Parameters for repair distribution (mean and standard 15 deviation) is assumed
System Parameters The mean time to failure (MTTF) for 20 components was determined randomly Values were taken from a triangular distribution, RANDTRIANGULAR(2160, 8640, 25920) Risksim add-in for MS Excel was used to generate 20 values of MTTF using the randtriangular function Risksim, www.treeplan.com
Analysis of 20-component System 1 2 3 4 1 1 2 0 1 2 3 4 5 6 7 8 9 1 0 2 0 1 2 3 4 5 6 7 8 9 1 0 2 0 S E No Redundancy S E 5 6 7 8 9 1 0 E S 20% Redundancy 50% Redundancy
System Reliability: Wear-out
System Reliability: Random Failures
AVAILABILITY SIMULATION Average availability over a certain time period can be determined with Excel Monte Carlo simulation is better to model availability of a complex system Various commercial software packages are available, e.g. AvSim+, Relex, Raptor Not all simulation software can provide dynamic availability values Some results using Raptor are given (www.arinc.com)
Availability for Series System 1 2 3 N A = system j = A 1 j A A A A system = 1 2 3 A N
System Availability: Effect of Random Failures
System Availability: Effect of Redundancy
Dynamic Availability Maintenance manager is interested in actual availability Availability is measured over constant periods, e.g. weekly, monthly, 3-monthly What is the variation over time? Is any action taken if availability decreases over a number of periods? Is it worthwhile to measure and compare availability every month?
1 2 3 4 5 Hand Simulation 20 comp s 6 7 8 9 10 11 12 13 14 15 16 17 18 19 Sys 5 9 16 7 9 0 1000 3000 5000 7000 9000 11000 13000 15000 17000 System Time (h)
Dynamic Availability
Availability vs. Time
Reliability vs. Time
CONCLUSION Dynamic simulation of a complex system shows that availability and reliability can vary significantly Comparing availability of a plant from month to month might not be useful for management Availability over 3 months or 4 months should be compared with monthly values Actual failure data for components of subsystems should be obtained and used for modeling