Using Duty Cycles in
System Reliability Analysis
Components of a system may not operate
continuously during a systems mission, or may be subjected to loads greater
or lesser than the rated loads during system operation. To model this, a
factor called the "duty cycle" is used. The duty cycle can also be used to
account for changes in environmental stress, such as temperature changes,
that may affect the operation of a component. The use of duty cycles in
reliability modeling, especially in system reliability modeling and
analysis, provides additional flexibility for the analyst. This article
explains how to perform analysis using duty cycles in
Analysis with Duty Cycles
The duty cycle is a positive value, with a default value of 1 representing
continuous operation at rated load. Any values other than 1 represent other
load values with respect to the rated load value (or total operating time).
The value of the duty cycle depends on the
Life-Stress Relationship (LSR) of the component. If a linear LSR can be
assumed, the duty cycle is simply the ratio of the load on the component (V2)
to the rated load (V1), i.e. dc = (V2/V1).
For an inverse power LSR, dc = (V2/V1)n.
A duty cycle value higher than 1 indicates a load in excess of the rated
value. A duty cycle value lower than 1 indicates that the component is
operating at a load lower than the rated load or not operating continuously
during the systems mission. For instance, a duty cycle of 0.5 may be used
for a component that operates only half of the time during the systems
The reliability metrics for a component with a
duty cycle are calculated as follows. Let dc represent the
duty cycle during a particular mission of the component, t represent
the mission time and t' represent the accumulated age. Then:
t' = dc t
The reliability equation for the component is:
R(t') = R(dc t)
The component pdf is:
Example 1: Components with Intermittent Usage
The use of duty cycles in BlockSim allows you to specify the blocks usage as
a percentage of the system usage. A component with intermittent usage, such
as the CD drive in a computer, may accumulate only 18 minutes of usage for
every hour the computer operates, and would have a duty cycle (usage rate)
Consider a computer system with three
components in series: a processor, a hard drive and a CD drive, as shown in
the next reliability block diagram (RBD).
Assume that all three components follow a
Weibull failure distribution and that under normal operating conditions the
parameters are β1
= 1.5 and η1 = 5000 days for the processor,
β2 = 2.5 and η2 = 3000 days for the
hard drive and β3 = 2 and
η3 = 4000 days for the CD drive. The CD drive is used only
30% of the time.
The failure distribution for the CD drive
is entered as follows:
The other components' distributions are
entered in the same fashion.
The duty cycle for the CD drive is
specified in the Block Properties window as follows:
The reliability of the computer system
after one year (365 days) of operation, assuming that the CD drive is used
only 30% of the time, is estimated to be 0.9747, as shown next.
Example 2: Stressed Components
Duty cycles can also be used to model components that are over-stressed (dc
> 1) or under-stressed (dc < 1). Assume that under certain
elevated stress conditions of temperature and humidity, the components of
the above RBD are stressed by a dc
factor of 1.5. The dc properties of the blocks would be
entered as follows:
Notice that the CD drive's dc factor reflects the
combination of the stressed environment and the usage rate (i.e. dc
= 0.3 1.5 = 0.45).
The reliability of the computer system
after one year (365 days) of operation under the elevated conditions and
assuming that the CD drive is used only 30% of the time is estimated to be
0.9492, as shown next.
Example 3: Changing Usage Rates/Stress Factors over Different Phases of an
All components of a system may be collectively subjected to different
operating conditions as the system goes through different phases of its
mission. Such a scenario may be modeled by assigning a duty cycle value for
each phase of the system. For example, the load on an aircrafts components
may be different during taxiing (e.g. dc = 1),
take-off (e.g. dc = 1.5), cruising (e.g.
= 1.1) and landing (e.g. dc = 1.3).
Phase diagrams will be discussed in future
articles. For more information about reliability phase diagrams, see
System Analysis Reference.