Reliability HotWire |
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Reliability Basics | |||||||||||||||||||||||

Some accelerated life tests may use a
time-varying stress application (such as step-stress or ramp-stress) to
assure the observation of failures more quickly in order to shorten the
product development cycle. Likewise, some products are expected to be
operated under normal use conditions where the stress exposure varies with
time. When performing data analysis for these types of situations, the
life-stress relationship model must take into account the cumulative effect
of the applied stresses. Such a model is commonly referred to as a
cumulative damage or "cumulative exposure" model. ReliaSoft's
ALTA PRO software
supports the use of the cumulative damage model for data with time-varying
stresses and with the recent release of Version 7, the software is now
capable of analyzing data with
- Cumulative damage Arrhenius relationship (for analysis involving one time-varying stress)
- Cumulative damage power relationship (for analysis involving one time-varying stress)
- Cumulative damage exponential relationship (for analysis involving one time-varying stress)
- Cumulative damage general log-linear relationship (for analysis involving multiple time-varying stresses)
These relationships are combined with the different distributions to create the "complete" model to be used for analyzing accelerated life test data with time-varying stresses. The following is a summary of these models. It should be noted that there is more uncertainty in the results from such time-varying stress tests than from traditional constant stress tests of the same length and sample size.
This relationship is typically used when the stress type is thermal in
nature (
Combining the cumulative damage Arrhenius relationship with an underlying life distribution assumption leads to the following models:
where:
and:
This relationship is typically used when the stress type is non-thermal in
nature (
Combining the cumulative damage power relationship with an underlying life distribution assumption leads to the following models:
where:
and:
This relationship can be used when the stress is a categorical type that can
take on discrete values, such as the lot designation for products from
different manufacturing lots or made of different materials, etc. It is also
sometimes used when the stress type is corrosion (humidity) or voltage.
Given a time-varying stress
Combining the cumulative damage exponential relationship with an underlying life distribution assumption leads to the following models:
where:
and:
This relationship is used when analyzing accelerated life data where
multiple stress types are applied simultaneously and the application of one
or more of those stresses varies with time. It is based on the
general log-linear relationship. Given
X,...,
_{2}(t)X, the cumulative damage general log-linear
relationship is given by: _{n}(t)
Combining the cumulative damage general log-linear relationship with an underlying life distribution assumption leads to the following models:
where:
The
The stress profiles are set
up in ALTA 7 PRO as follows (by selecting
The failure times obtained in
the test, as entered in ALTA PRO, are shown in the next figure, where the
labels in the
The components failure behavior is assumed to follow a Weibull distribution. For the temperature stress, the Arrhenius relationship is used. For the voltage stress, the power relationship is used. These relationships are specified in the Stress Transformation window, as shown next.
The estimated model parameters are shown next. The use level reliability plot is shown in the next figure.
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