January 16, 2012

Reliability Availability Estimation - PA-11

Calculate the probabilities of the product operating properly

A. Scope

Electronic reliability analysis aims to assess the probability of a product functioning correctly over a given time interval. For example, the reliability of a satellite may be 0.8 to 3 years.

The document "RNC-CNES-Q-HB-30-504 Evaluation prévisionnelles de fiabilité en électronique" sets out the different methods for assessing the reliability of a product.

For non-electronic systems, other methods for assessing reliability may be used, for example such as the stress/strength method described in the document "RNC-CNES-Q-HB-30-506 Evaluation de la fiabilité de systèmes non élctroniques (méthode contrainte résistance)".

Instantaneous availability is the capacity of a product to perform its function at a given moment. The average availability (which may be measured a posterior) is often assessed as the ratio of correct functioning time over total mission time. For example, the availability of a network service can be 95%. The document "RNC-ECSS-Q-ST-30-09 Availability analysis" sets out the various possible methods for assessing the availability of a product.

The concepts of reliability and availability must be distinguished from the concept of lifetime. This concept characterises the length of time for which a product is sized and qualified.

B. Principles of preparation

The (reliability or availability) assessment of a product is based on the use of a modelling method, combined with a processing method.



The modelling method must be adapted to the problem encountered. There is no generic, universal method. It must be rich enough to represent the product correctly and as simple as possible in order to be validated.

The processing methods are essentially limited to analytical calculation, solving differential equations (Markovian process) or Monte-Carlo simulation.

I. Reliability

Only Reliability Block Diagram modelling (RBD) is presented in this paragraph, with analytical processing for systems showing constant failure rates (exponential laws for calculating the reliability of electronic elements). Readers looking for further details on the other methods are referred to the standards mentioned above.

The reliability R(t) of an electronic element is expressed by:

R(t) = e-λtWhere λ: element failure rate (expressed as h-1 or fit (failure in time) equivalent to 10-9 h-1) and t the time under consideration.


The Reliability Block Diagram (RBD) is a representation of the elements that participate in performing the different functions of a product, in the form of serial or parallel blocks.



Functioning is ensured as long as the chain represented is not broken by the failure of one or more blocks. The reliability (or the availability) of a product represented in this way can be simply calculated as indicated below:



RBD representation is particularly simple, but it is not appropriate for describing the functioning of a complex product. Its symbology may however be enriched in order to improve its expressive capacity as illustrated in the figure below:



The following may then be represented (amongst other things):

Active redundancy M from N: The N elements in redundancy function simultaneously but only M elements are necessary for providing the expected service.

Passive redundancy M from N: N-M elements are used as spare for remedying the loss of active elements. The reconfiguration on a spare element can be accompanied by a transition time period "tr" during which service is not provided.

Hot/cold redundancy: The terms hot and cold are used to characterise the energy status of the spare elements in passive redundancy (active redundancy is always hot). In fact, the failure rate of an element is often considered lower in its cold status than in its hot status (λoff = λon/10 is one hypothesis which is often used for electronic components).

The reliability of a redundancy M from N for non-reparable elements can be expressed in the following manner:

In the case of active redundancy M from N:



In the case of passive redundancy (λ* = λoff):



II. Availability

The availability of a non-reconfigurable and non-repairable system is equal to its reliability.

The availability of a reconfigurable and non-repairable system (satellite) is lower than the reliability because of the length of non-availability due to the reconfiguration (if the service is not provided during this time).

The availability of a repairable system (ground facilities) is characterised by a short transitory phase if the system functions at the initial instant, then by a steady state.

The functioning of a reconfigurable or reparable product can be represented in accordance with the time by the following diagram (product functioning = high state; functioning interrupted = low state):



The following terms are defined thus:

MTTF (Mean Time To Failure): Average duration of correct functioning before the first failure.

MUT (Mean Up Time): Average duration of correct functioning.

MDT (Mean Down Time): Average duration of unavailability.

MTTR (Mean Time To Repair): Average duration of repair (MTTR ≤ MDT).

MTBF (Mean Time Between Failure): Average time between two consecutive failures.

The average availability is equal to the asymptotic availability and can be expressed in the following way:



The sources of unavailability encountered in orbit can be:

  • Deterministic: orbital manoeuvres with service interruption, calibration of instruments, periodic occultation of sensors or instruments for certain orbital positions, etc.
  • Random: reconfigurable failures, radiation events (SEU, passive latch-up), etc.


Activities / documentation

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