Tag Archives: Modelica

Availability Reliability Requirements Engineering

[007] Amending Item Models by MTTR and Availability Computation

Item model with parameters MTBF and MTTR and associated item Availability, displyed as simple block icon

In this post we’re going to amend the existing library blocks by the quantities and arithmetics introduced in post [006] and see how this can facilitate the computation of the availability of a system.

What we need in the first step are the required variable and parameter slots, assigned to each individual item. For the time being we assume that the Mean Time To Repair MTTR is given as a known parameter for each item with the default unit of hours.[more…]

In the Modelica modeling language, parameters are quantities whose value has to be assigned prior to a simulation run, i.e. they will not be calculated. In that aspect the parameter type differs from normal variables. We plan to consider also other ways to determine and represent the MTTR and will describe this in future posts.

Cartoon, Maintenance and Lubrication, Improving Mean Time Between Failures MTBFSince the Mean Time Between Failures MTBF has been introduced in a similar parametric way in the default item, the local availability A of this particular item may immediately be calculated according to the arithmetics in post [006]. So if the pre-assigned parameter values of MTBF is 10000 hours and the Mean Time To Repair is 1 hour, this results in a local item availability of 0.9999 or 99.99%. In case we want to achiev 99.999% i.e. five nines, we would have to modify e.g. MTTR to 0.1 hour – i.e. speed up the repair action – or increase MTBF to 100000 hours – i.e. get higher-quality parts. Since such modifications can be done interactively “on the fly”, this might help the system engineer to specify the quality requirements.

We may specify in the item graphics, that these parameter values shall be displayed besides the visual icon, along with the individual name (see intro figure).

As the modeling approach follows an object-oriented concept, all item models are derived from one general item class and we need to do these declarations only at a single spot in the library. The next figure shows how this new functionality can be implemented very quickly in a few lines of code in the internal modeling language. Its only a reference to the GeneralItem master model, the equations for A and N and the declaration of the mttr parameter in a one-liner:

Amending the base class by parameters and arithmetics to compute the Availability and Non-Availability of an item

Before we proceed, it’s important to understand what we really have achieved now. We have just added the parameter MTTR to the master item description in the library. Such an item might represent various things like

  • a certain technical hardware unit within a machine,
  • a process step within a bigger procedure,
  • an adminstrative item within an organisation
  • or any other kind of element in a bigger context.

Further links:


Together with the already existing parameter MTBF this allowed us to compute the also newly introduced availability quantity A. However, this item availability value is rather a theoretical value, describing a statistical value of this “box” in a standalone view, assuming that it is properly supplied.

In a real system, such an item almost never exists isolated. Instead, it will be connected to and interacting with its neighbors in a more or less complex environment. So in order to compute the actual service availability at the output of this box, we have to consider also the individual supply situation at its input. This will be the topic of post [008], then allowing us to efficiently compute the service availability of the power supply system from post [005]. And the good message is: this is possible without having to touch the overall system model!

Thanks for sharing this article!

Availability RAMS Reliability

[006] Computing the Availability of a System, some Basics

Cartoon Maintenance, Computing the Availability of a system, five ninesSimilar to the concept of Reliability computation introduced in post [003], we also would like to support the computation of system Availability with the model blocks. However, before talking about the availability arithmetics, again we have to clarify its meaning.

So what is system availability? – Basically, a system can be “up” and operating, i.e. providing the required service, or “down” and non-operating, i.e. not providing the service. Being in downtime can be planned (e.g. scheduled maintenance) or unplanned (e.g. irregular failure of system parts). Dependent on the required work effort, the need and delivery time of spare parts, the qualification of the repair and maintenance team etc. it takes more or less time to repair the system and get it back into the desired “Up”-mode..[more…]


Further links:


While Reliability is used to express, how probable it is that a certain desired functionality of a system fails within a given period of time, the feature of Availability quantifies the operating time within such a period. Simply put, Wikipedia summarizes Availability being “the proportion of time a system is in a functioning condition”. (If interested, please look up more explanations there.)

Besides the already mentioned MTBF, important additional calculation symbols in this context are:

  • A: the symbol denoting the Availability of the respective part, item or service with theoretical values between 0 and 1, but practically usually being close to one, e.g. in high availability systems the magic “five nines” like 0.99999 or in percent this value is 99.999%, meaning 5 minutes per year (!);
  • N: the symbol denoting the Non-Availability of the respective part, item or service and the complement to A, i.e. the sum of A and N is always 1;
  • MTTR: the symbol denoting the Mean Time To Repair, the time needed to repair the system and get it back to service. To be correct, this time is not only needed for repair, but often is used to represent the complete downtime period, including fault detection and reporting, parts ordering (and delays), assembling, testing, start-up etc.

With these variables and stochastical parameters, the basic equations to compute the availability of a system item is:

A = MTBF / (MTBF + MTTR).

Although this maybe looks like a quite familiar equation, it is important to have a clear picture, to what these quantities really relate. Ok, MTBF and MTTR are kind of statistical parameters that have been estimated or gathered from the field and clearly can be associated to individual components. But with respect to A, we referred to certain services or functions of an item, that shall be available.

As long as we talk about system items providing only one single service, this distinction between components and their provided functions might appear artificial and not be so obvious: we can clearly observe it being Up or Down and there is a 1:1-mapping between the hardware and the functionality.

But as soon as we consider hierarchical systems or sub-systems that provide more than one single service or function, it is important to have proper and separated variable slots for the availability of system components and system functions, according to the orthogonal view we introduced earlier.

In terms of building-blocks of the SmartRAMDependencies of component output availability on inputs, MTBF and MTTRS-library in the “Availability layer” we need to provide MTBF and MTTR parameter slots only once for each component. However, concerning availability, variable slots have to be provided for each interacting service, the outgoing and the incoming ones, as illustrated in the picture. Thanks to the modular port-concept of Modelica, extending the already existing interfaces – or ports – by an additional variable for A is a matter of just one single model statement.

This were some basic thoughts about the required variable slots. Adding also the required arithmetics to the existing model classes and demonstrating it along the emergency power system that we used in the risk assessment example will be topic of post [007] .