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Reliability Estimation
Product reliability estimation is concerned with
modeling the life distribution so that estimates of
various aspects of the time to failure can be made. The
theoretical population models used to describe product
lifetimes are known as “life distributions”. The
“product” is a generic reference to a component, an
assembly, a complete product or a system comprised of
multiple products. The basic information needed for
reliability estimation is time-to-failure data on a
representative set of products from the population of
all products of interest.
Reliability is defined as the probability a product
survives a certain length of time. The instantaneous
failure rate is the rate of failure at a particular
point in the product lifetime. Typically product
lifetimes follow the so-called “bath tub curve”. This
“U-shaped” curve depicts the tendency for products to
have a decreasing failure rate early in life, a stable
failure rate during the useful life of the product, and
an increasing failure rate as the product wears out and
approaches the end of life. Reliability estimation
methods can model any portion of the bath tub curve or
even the combination of the different stages in the
product’s lifetime. Reliability estimates are useful
for many purposes including the estimation of warranty
cost, identifying the weakest component in a system, and
determining the number of spare parts to carry in
inventory.
Many
of the standard reliability methods are intended for
non-repairable systems. Here, when the component,
subassembly or system fails, it is not returned to
service. The Weibull distribution and other well-known
distributions which effectively describe the time to
failure assume the failures are “terminal”. That is,
the whole system is replaced. In contrast, repairable
systems may fail multiple times during their lifetimes
and this results in “recurrent events” in which system
components may be repaired or replaced to bring the
system back on line. In this case, a single system
actually has multiple ages. That is, components which
have been repaired or replaced are “younger” than the
rest of the system. Reliability data comprised of
recurrent events should be analyzed differently than
time-to-failure data from non-repairable systems.
Time-to-repair data from a warranty data base are an
application of a repairable system. Modeling this
system provides estimates of warranty cost over time and
can be used to answer questions regarding the length of
the warranty period.
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