Calculation Methods for RAMS

When designing critical products / systems, Reliability, Availability, Safety, and Maintainability (RAMS) aspects have to be accounted for.
Standards were defined for RAMS analyses in many industries, for example: RAIL [1] [2] [3], aerospace [4], defense [5], automotive [6] and medical devices [7].
The standards define the type of analyses that have to be carried out. The following table presents common analyses:

Topic Analysis Meaning
MTBF Mean Time Between Failure Calculate component and assembly MTBF, accounting for environment and operation profile.
MTBF calculations are the basis for safety, reliability and maintainability analyses.
Safety Failure Mode, Effects, and Criticality Analysis (FMECA) [8] Analyze the consequences of single failure modes (frequency, severity, and risk)
Safety Fault Tree Analysis [9] (FTA) Calculate the occurrence rate and probability of safety events that result from complex combinations of sub-events
Reliability and Availability Reliability Block Diagram [10] (RBD) Calculate reliability, availability, Mean Time Between Failure (MTBF) and Mean Time To Restore (MTTR) of complex systems, depending on the minimal required functionalities that allow the system to operate.
Reliability and Availability Markov chains [11] Markov chains allow to analyze complex systems by modelling each possible system state, and transition rates between the states.
Maintainability Spare parts availability at stock Calculate the probability that a spare is available in the stock on demand.
Maintainability Spare parts effect on operational availability Calculate system operational availability accounting for increased restoration time due to shortage of spare parts.
Maintainability Testability Analysis [12] Design a Built In Test (BIT) plan for high coverage of failure modes, and quick failure isolation.

Table 1: key RAMS analyses


FMECA deals with effects of a single failure mode event, therefore this calculation is quite straightforward.

Other calculations can become quite complex because of inter-dependence between the states of components of the analyzed system.
A central stock provides spare parts for two helicopters. When one helicopter consumes a spare part, the availability of spare parts for the second helicopter is reduced.

There are two types of methods for calculating behavior of complex systems:

  • Analytic – using equations and numeric integration
  • Monte Carlo Simulation – simulating many possible scenarios triggered by random events

Each method has advantages and disadvantages that dictate when each method should be used.

The following table summarizes the advantages, deficiencies, and uses of each method:


  Analytic Simulation
Advantages When the analytic algorithm is carefully designed [13], high accuracy can be obtained in a very short calculation time.For example: requirement of failure probability lower than 10-9 per flight hour can be easily verified. Simulation can be very flexible, allowing to model highly complex systems with minimal assumptions.
Disadvantages Approximations often have to be employed in order to allow analytic calculation. For safety analysis, approximations have to be “worst case” i.e. provide upper bound to failure probability. In order to achieve high accuracy, many simulations have to be carried out and averaged. This may require a lot of computation resources and time.
Uses Safety

Fault Tree Analysis is often used for occurrence probability of safety events. Analytic calculation allows for fast and accurate analysis.


Spare optimization

The goal of spare optimization is to find the cheapest combination of spare parts that will provide the required system availability. Using fast analytic calculations allows to quickly scan many sparing options. When coupled with a smart optimization engine, the optimal spare parts combination can be achieved.



Steady state availability (system availability after sufficiently long time, when correlations between system components decay) can be calculated quickly and accurately.


Life Cycle Cost

Upper bound on the mean life cycle cost and mean cost components for each life year can be quickly calculated.

Availability and Reliability

Monte Carlo simulations can provide the point availability and reliability (a curve of availability / reliability over time), accounting for correlations between operational age of components.


Life Cycle Cost

By attaching a cost to all events, the life cycle cost can be calculated, including a curve showing how the expenses accumulate over time.

Table 2: comparing analytic calculations to Monte Carlo simulations


BQR provides a complete solution for RAMS analyses, covering a wide variety of analytic and Monte Carlo simulation software

MTBF prediction

  • Support all standards
  • Reusable libraries
  • Web or desktop
Screenshot of MTBF prediction software
Calculation summary view


  • Support all standards
  • Failure modes libraries
Risk Matrix, screenshot of FMECA software
Risk Matrix


  • Support common causes
  • Cut-sets
  • Sensitivity analysis
FTA traditional view
FTA traditional view

Testability / Diagnostics Analysis

  • Detection and Isolation analyses
  • Tests Library
  • Detailed reports
BIT and test lists


  • Supports RBD networks
  • Monte Carlo simulation
  • Equipment library
RAM analysis - Reliability Block Diagram Software
Network Reliability Block Diagram
Reliability Block Diagram Software - Monte Carlo simulation
Monte Carlo simulation results for two pumps operating in standby model

Markov chain

  • Load sharing
  • Spare parts availability
  • RAID failure probability
Reliability Block Diagram Software - Markov Models
Markov model

Spare Parts Optimization and Life Cycle Cost

  • Supports multi – tier logistics
  • Shared and exclusive stocks
  • Accounts for system reliability model
Spare Parts Availability Model


[1] EN 50126:2017 Railway Applications. The Specification and Demonstration of Reliability, Availability, Maintainability and Safety (RAMS). Generic RAMS Process.
[2] EN 50128:2011 Railway applications. Communication, signalling and processing systems. Software for railway control and protection systems.
[3] EN 50129:2018 Railway applications. Communication, signalling and processing systems. Safety related electronic systems for signalling.
[5] MIL-STD-882E:2012 System Safety.
[6] ISO 26262:2018 Road vehicles Functional safety.
[7] ISO 14971:2007 Medical devices – Application of risk management to medical devices.
[8] IEC 60812:2018 Failure modes and effects analysis (FMEA and FMECA).
[9] IEC 61025:2007 Fault tree analysis (FTA).
[10] IEC 61078:2016 Reliability block diagrams.
[11] IEC 61165:2006 Application of Markov techniques.
[13] A. S. &. Y. Bot, “Fault Tree Analysis, How accurate is it?,” in ESREL 2017, 2017.