4 Reliability Theory
135
As indicated in the ALT Sect. 4.4.2, higher stress upon a component might lead to
its faster deterioration. If we introduce another component which takes on part of the
original component’s function, we may be able to achieve increased lifetimes of both
components due to decreased stress, and, even without decrease in load, increased
system lifetime due to the fact that upon the failure of one of these components, the
other can still fulfil the functionality by taking the load of the other (if the system
fails only when all these components fail).
The dependency of lifetime on stress may be examined, for example, by the
proportional hazard model (Sect. 4.4.3) or by an inferred model from accelerated life
tests (Sect. 4.4.2) and taken into account in the system model. Due to the introduced
redundancy, the component together with the introduced support systems may be
modelled as a macro-component with a new TTF given by
TTF load share system = max{TTF 1 , . . . , TTF n },
(4.4)
where n is a number of components in this load-share system and TTF i their
respective TTFs (which might be possibly influenced by the failures of other subcomponents by the increase of the remaining components failure rate functions).
In contrast to the load-sharing setting, we can also introduce spares, stand-by
components which do not operate (and we assume that they also do not deteriorate)
until the original component fails, and then they replace its function. This new
configuration of N components may again be viewed as a macro-component itself
with new TTF
TTF system with spares =
N
i=1
TTF i ,
(4.5)
where TTF i denotes the TTF of the ith sub-component.
Figure 4.8 depicts how different scenarios of load sharing influence the system
reliability. Stand-by components are not considered there. We consider a system
with single component with exponentially distributed lifetime and compare its survival function (the curve “Original”) with scenarios where a redundant component
is introduced in the system assuming that the load share:
• does not influence components’ lifetime, so the overall TTF is given by Eq. (4.4)
with the original component TTFs (the curve “Same stress”),
• increases the lifetime of components by decreasing its failure rate and a failure of
one component does not influence the failure rate of the other, so the overall TTF
is given by Eq. (4.4) with TTFs with decreased failure rate (the curve “Decreased
stress”),
• increases the lifetime of components, as in the previous case, but a failure of one
of the components increases stress on the other by imposing the original failure
rate for the rest of its life (the curve “Change of stress”).
135
As indicated in the ALT Sect. 4.4.2, higher stress upon a component might lead to
its faster deterioration. If we introduce another component which takes on part of the
original component’s function, we may be able to achieve increased lifetimes of both
components due to decreased stress, and, even without decrease in load, increased
system lifetime due to the fact that upon the failure of one of these components, the
other can still fulfil the functionality by taking the load of the other (if the system
fails only when all these components fail).
The dependency of lifetime on stress may be examined, for example, by the
proportional hazard model (Sect. 4.4.3) or by an inferred model from accelerated life
tests (Sect. 4.4.2) and taken into account in the system model. Due to the introduced
redundancy, the component together with the introduced support systems may be
modelled as a macro-component with a new TTF given by
TTF load share system = max{TTF 1 , . . . , TTF n },
(4.4)
where n is a number of components in this load-share system and TTF i their
respective TTFs (which might be possibly influenced by the failures of other subcomponents by the increase of the remaining components failure rate functions).
In contrast to the load-sharing setting, we can also introduce spares, stand-by
components which do not operate (and we assume that they also do not deteriorate)
until the original component fails, and then they replace its function. This new
configuration of N components may again be viewed as a macro-component itself
with new TTF
TTF system with spares =
N
i=1
TTF i ,
(4.5)
where TTF i denotes the TTF of the ith sub-component.
Figure 4.8 depicts how different scenarios of load sharing influence the system
reliability. Stand-by components are not considered there. We consider a system
with single component with exponentially distributed lifetime and compare its survival function (the curve “Original”) with scenarios where a redundant component
is introduced in the system assuming that the load share:
• does not influence components’ lifetime, so the overall TTF is given by Eq. (4.4)
with the original component TTFs (the curve “Same stress”),
• increases the lifetime of components by decreasing its failure rate and a failure of
one component does not influence the failure rate of the other, so the overall TTF
is given by Eq. (4.4) with TTFs with decreased failure rate (the curve “Decreased
stress”),
• increases the lifetime of components, as in the previous case, but a failure of one
of the components increases stress on the other by imposing the original failure
rate for the rest of its life (the curve “Change of stress”).