Reliability Availability and Maintainability (RAM) Study simulates the arrangement, operation, failure, and maintenance of a system throughout its mission duration. The study will provide statistical estimates of several parameters of the system, such as its availability, expected maintenance activities, and the overall reliability of the system. The key definition is as follows:
-
Reliability is defined as the ability of a system or component to perform its required functions under stated conditions for a specified period of time. It is expressed as a function of failure rate probability distribution and its mission duration. For a mature component or system, for a system reliability
-
Availability is the parameter that translates system reliability and maintainability characteristics into an index of effectiveness. It is defined as a measure of the degree to which an item is in an operable and committable state at the start of a mission when the mission is called for at a random point in time. Others factor outside the turbine that affect the operability of the turbine, such as weather is outside the scope of the availability study and should be taken into consideration in the risk analysis. The basic relationship model for availability is :
$$Availability = \frac{Uptime}{Uptime + Downtime}$$ Availability is time-related function, below figure illustrates the breakdown of total equipment time into its time-based elements.
| Item | Definition |
|---|---|
| TT | Total Time, total intended utilization period |
| Operating Time | Operating Time (Equipment in use) |
| Standby Time | Standby Time (not operating but assumed operable) in a specified period |
| Preventive Maintenance | Scheduled maintenance time per specified period |
| Preventive Maintenance | Corrective Maintenance, unscheduled maintenance per specified period |
| Delay | Administrative and Logistics Downtime, down time spent waiting for parts, administrative processing, maintenance personnel, or transportation per specified period |
| Off time | During this time, system operation is not required, hence it is excluded from availability analysis |
- Maintainability is defined as the ability of an item to be retained or restored to specified conditions when maintenance is performed by qualified personnel. For the purpose of the study the following maintenance assumptions is considered
A Reliability Block Diagram (RBD) is a a method to represent system configuration from reliability point of view. It represents the state of the system, in this case the functioning states of its components. A system can be modeled in series block configuration when all of the components within that system have to successfully function during the intended mission time of the system in order for the system to success, as a consequence if there is any components in the system fail, it results in the system failure as a whole. When there is redundancy of a particular component in the system, it can be modeled as a paralel block in RBD.
For more complex system reliability configuration that cannot be
easily represented by a combination of series-parallel block diagram,
cut set or path set methods can be used to determine the reliability of
such system.
Monte Carlo Simulation (MCS) uses pseudo random numbers generator and statistical models to simulate (imitate) reality. In the case of availability simulation, this approach is similar to a virtual experiment in which a random number is generated based on the failure rate characteristic of the evaluated system in order to represent its time to failure. The resulting time to failure from the simulation is then evaluated against the required mission time, where their failure occurrences and required reparation are recorded. The process is repeated for large number of times, each one behaving differently due to the stochastic characters of the component failure behavior. From the accumulative output, the mean availability and other information can be gathered. The accuracy of the simulation is depends on the accuracy of the probability distribution of the component failure and the numbers of repeated simulaton.
In MCS, the inverse transform method is one of the technique to generate
random numbers from any failure rate distribution type given its
cumulative distribution function (CDF). CDF is the unreliability
function of a component. Inverse transform method takes uniform samples
of a number U between 0 to 1, interpreted it as a CDF and then
inverting that function to have the time to failure of the component.
For component failure rate with exponential distribution type, the CDF
and its inverse transform method is expressed as:
CDF o**r Unreliability (U) = 1 − e( − λ.TtF)
where
The implementation of MCS in Reliability simulation utilizing Reliability Block Diagram as the basis of the simulation is explained below.
| Arrangement | Definition |
|---|---|
| Series Arrangement | In a series system, any fail components will results in system failure. During the MCS if the simulated time to failure of any of the component is below the mission duration, the system is considered to be failed |
| Hot Redundancy | For hot redundancy, where both component operational, the redundant system will fail if the highest simulated time to failure of one of the components in the redundant arrangement is lower than the mission duration. |
| Cold Redundancy | For cold redundancy, where one component is on stand-by, the redundant system will fail if the summation of the time to failure of the components in the redundant system fall below the mission duration |
The following figure illustrates the MCS procedure. For the first simulation, the component fails after 3 years of operation (1st TtF), then it undergoes a corrective maintenance.
In this illustration the total mission duration is 10 years. After
the restart, a new random number is generated to simulate the time to
failure of the component. The process is repeated until the accumulated
time surpass the mission time which is 10 years. For the first
simulation the component total time (TT) surpass the mission duration
with one failure. On the second simulation, through similar random
number generation process, the component fails twice throughout its
mission duration, whereas the third simulation the component does not
fail at all. For each iterations, the following informations are
recorded: - System reliability and availability - Total number of
repairs - Which components causing the failure and their time to failure
This procedure is then repeated for n times. In the end, the tidal turbine availability is estimated to be the mean availability value of the n simulation. The other parameters are also averaged from the n simulation.
🔗 Live Demo → manunk.shinyapps.io/wind_turbine_ram
This simulation is developed in R (Shiny) and hosted on shinyapps.io. It implements the RAM methodology described above as a fully interactive web application — no installation required to use the live version.
| Items | Remarks |
|---|---|
| components_input | Name of the system components to be included in the simulation. (Max = 10) |
| failure_rate | Failure rate per year for each component. If there is any redundancy, the redundant component will have identical failure rate. (Min = 0.1, Max = 10) |
| time_to_repair | Time to repair the component in hours. |
| redundancy | Redundancy options. There are three option, no redundancy, hot redundancy, and cold redundancy. |
| select | Option to include or exclude certain component in the simulation. |
| Generate RBD Button | Once the components information table is filled, click the generate RBD button in order to generate the RBD. In the event where components information table is modified after a simulation, click the generate RBD button again prior to starting a new simulation. |
| Mission Time Duration | Duration of the system (in year) to which the time to failure of the system is evaluated against. (Max = 10 years) |
| Simulations Number | Number of simulation iterations to be conducted (Max = 5000) |
| Output | Description |
|---|---|
| System reliability | Probability of surviving to mission end — equation vs. simulation curves plotted together |
| System availability | Mean uptime fraction across all iterations |
| Expected failure count | Probability distribution of failure occurrences |
| Failure cause breakdown | Which components drive system-level failures, as a percentage |
- R / Shiny — simulation engine and reactive web app framework
- rhandsontable — interactive spreadsheet-style component input table
- DiagrammeR / Mermaid — dynamic RBD diagram rendered from component configuration
- Plotly — interactive output charts
- hash — dictionary lookups for component repair time mapping
- purrr — functional iteration over simulation results
- dplyr / tidyr — data wrangling
# Install dependencies
install.packages(c("shiny", "shinydashboard", "rhandsontable",
"DiagrammeR", "plotly", "hash", "purrr",
"dplyr", "tidyr", "reshape2"))
# Clone the repo and run
shiny::runApp("path/to/RAM-Monte-Carlo-Simulation")
This repository forms the simulation foundation for Offshore-Wind-Farm-RAM-Simulation, which extends the engine with wind resource variability and maintenance vessel scheduling — factors critical to offshore wind farm availability analysis.
Manunggal Sukendro — Reliability engineer with a focus on offshore energy systems.
github.com/manunggal