4 Reliability Theory
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• the failure rate is increasing (wear out)—e.g. mechanical components are
subjected to abrasion, etc.
• the failure rate is decreasing (infant mortality)—e.g. software, as bugs are
discovered and fixed during early stages.
4.3 System Reliability
One of the typical attributes of the contemporary world is its complexity. Every
device and service available to us provides us with a building block, an opportunity
to use it for constructing a new system with its own objectives. As a consequence,
many of the devices and services that we rely upon are practically composed of
many interconnected smaller subsystems. We can reflect this by our mathematical
models and use the tools of probability theory to deduce the probability model
for the system behaviour from the probability models for the behaviour of its
components and their mutual interconnection. Exploiting the system structure also
leads to significant savings of resources. If we were to assess the reliability of a
complex system, like a space shuttle, by standard statistical methods, we would
have to design an experiment in which we test (break) multiple copies of the same
system. This would clearly lead to a vast waste of resources in the system design
process. Identifying the system components will, instead, allow us to carry out
cheaper experiments separately for those and even utilise our past experience with
them. Nevertheless, the separate experiments would not allow us to learn about
dependencies among the failure modes of components (common cause failures,
cascading failures) which have to be addressed separately.
The way we carry out inference about complex systems may be decomposed into
three major stages:
• Construct a model of the system consisting of components (subsystems) reflecting dependencies between states of the components and the state of the system
as a whole.
• Gather data and carry out inference about components, based on, for example,
statistical methods or expert elicitation procedures.
• Integrate the acquired models of the components behaviour with the model of
their influence on the system behaviour in order to obtain a model for TTF of the
whole system.
The first stage is a domain of engineers who have to specify the system topology
and carry out risk analyses to identify potential modes of failure and describe how
the system operates. Component models can be obtained by statistical methods and
are also often included in the component specification in the case of sub-contracting,
although, often, only partial specifications are available, in this case like first and
second moments of the component failure laws. In this section, we will further
focus on the first and the third part of the inference process, on how to integrate
the acquired information.
117
• the failure rate is increasing (wear out)—e.g. mechanical components are
subjected to abrasion, etc.
• the failure rate is decreasing (infant mortality)—e.g. software, as bugs are
discovered and fixed during early stages.
4.3 System Reliability
One of the typical attributes of the contemporary world is its complexity. Every
device and service available to us provides us with a building block, an opportunity
to use it for constructing a new system with its own objectives. As a consequence,
many of the devices and services that we rely upon are practically composed of
many interconnected smaller subsystems. We can reflect this by our mathematical
models and use the tools of probability theory to deduce the probability model
for the system behaviour from the probability models for the behaviour of its
components and their mutual interconnection. Exploiting the system structure also
leads to significant savings of resources. If we were to assess the reliability of a
complex system, like a space shuttle, by standard statistical methods, we would
have to design an experiment in which we test (break) multiple copies of the same
system. This would clearly lead to a vast waste of resources in the system design
process. Identifying the system components will, instead, allow us to carry out
cheaper experiments separately for those and even utilise our past experience with
them. Nevertheless, the separate experiments would not allow us to learn about
dependencies among the failure modes of components (common cause failures,
cascading failures) which have to be addressed separately.
The way we carry out inference about complex systems may be decomposed into
three major stages:
• Construct a model of the system consisting of components (subsystems) reflecting dependencies between states of the components and the state of the system
as a whole.
• Gather data and carry out inference about components, based on, for example,
statistical methods or expert elicitation procedures.
• Integrate the acquired models of the components behaviour with the model of
their influence on the system behaviour in order to obtain a model for TTF of the
whole system.
The first stage is a domain of engineers who have to specify the system topology
and carry out risk analyses to identify potential modes of failure and describe how
the system operates. Component models can be obtained by statistical methods and
are also often included in the component specification in the case of sub-contracting,
although, often, only partial specifications are available, in this case like first and
second moments of the component failure laws. In this section, we will further
focus on the first and the third part of the inference process, on how to integrate
the acquired information.