The
reliability of a product/component constitutes an important aspect
of product quality. Of particular interest is the quantification
of product reliability, so that one can derive estimates of the product expected
useful life. Knowing the probability of product/ component failures at different
stages of its life can be very useful to make a decision about when to replace or
overhaul the component.
A useful general distribution for describing failure time data is the Weibull
distribution named after the Swedish professor Waloddi Weibull (1887-1979),
who demonstrated the appropriateness of this distribution for modeling a wide variety
of different data sets.
It is often meaningful to consider the function that describes the probability of
failure during a very small time increment (assuming that no failures have occurred
prior to that time). This function is called the hazard function (or, sometimes,
also the conditional failure, intensity, or force of mortality function), and is
generally defined as:
h(t) = f(t)/(1-F(t))
where h(t) stands for the hazard function (of time t), and f(t) and F(t) are the
probability density and cumulative distribution functions, respectively. The hazard
(conditional failure) function for most components or devices can best be described
in terms of the "bathtub" curve: Very early during the life of a device,
the rate of failure is relatively high (so-called Infant Mortality Failures); after
all components settle, and the electronic parts are burned in, the failure rate
is relatively constant and low. Then, after some time of operation, the failure
rate again begins to increase (Wear-out Failures), until all components or devices
will have failed.
The Weibull distribution is flexible enough for modeling the key stages of this
typical bathtub-shaped hazard function.
Weibull distribution is very useful in reliability because of its ability in modelling
increasing and decreasing failure rate functions.
SoHaR solution fully supports Weibull analysis as part of its approach to failure
analysis, understanding and prevention.
By utilizing Weibull distribution SoHaR team can understand the reasons for failure
causes and establish a lasting preventive action.
RAM Commander Weibull Module
RAM Commander reliability software provides Weibull module
allowing input/import of failure statistics (time to failure) and calculation of
Weibull distribution parameters (Shape and Scale):
Weibull parameters calculation algorithm takes into consideration "censored"
data too, e.g. not only failures but also times at which equipment was tested and
appeared to be operational.
After the calulation user may generate Weibull reports and graphs like PDF
(Probability Density Function), CDF (Cumulative Distribution Function),
FR(t), number of failures till time t etc.
to predict failures, plan warranty times etc.:
Distribution parameters can be used in sustem reliability analysis using
Reliability Block Diagrams module of RAM Commander.
See also:
SoHaR Reliability and Safety Software Overview
Reliability&Safety Analysis Software Download
SoHaR Reliability, Safety and Quality Services
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