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BEERS was developed at the Institute
for Reliability and Risk Analysis, and forms part of a suite of
programs designed to work in the Microsoft Windows environment.
OVERVIEW
On many occasions, we wish to assess the reliability of a large group of
different but related items. For example, in the nuclear power industry,
electrical diesel generators are found in every power station, and these
generators are similar in many respects: similar design, similar construction,
similar operating conditions.
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For
items such as these, that tend to be highly reliable, we typically have
very limited data on failures for the individual items. Therefore,
standard statistical techniques will typically provide estimators of
reliability with high variance. A worrying feature is that if we observe
no failures for a particular unit, our estimate of reliability will be
one, representing perfect reliability.
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Due in part to these problems, we have developed an alternative approach to
reliability assessment. Instead of treating every item seperately,
we assume that there is some weak dependence between the reliability of the
different items. In this way, data on one item will influence our opinion
as to the reliability of the other items. The techniques used are Bayesian
in nature. We elicit the views of an expert concerning the reliability of a
generic item, and then let the observed data update these views. In this
way, estimates can be obtained even for small amounts of data; however, if
we are fortunate enough to have large quantities of data, the estimates
will be determined to the most part by the data, and not the prior beliefs
of the expert. This technique is a coherent and useful method of analysis.
The results of the approach are encouraging. It reduces the variance of
reliability estimators considerably. Furthermore, estimates for the
unreliability of items with zero recorded failures are no longer zero, and
estimates of unreliability for items with a large number of failures are
shrunk from their previously high values.
DATA INPUT
When the software is run, a window appears as shown above. To conduct an
analysis, the user must enter two pieces of information. To start, he must
enter failure data for the items considered. The failure data is binomial,
meaning that we record the number of times the item is tested, and the
number of times that it fails. To enter the data, the user clicks on the
grid in the main window. In response, an input box will appear, in which
the user enters the relevent details for the
selected item. This procedure is repeated until all data is entered. The
data can then be saved using the save feature of the program and reloaded at
a later time using the file open procedure.
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In
addition to entering failure data, the user must enter his prior beliefs
about the unreliability of the items. This is done in the window
displayed on the left. We are essentially specifying a single parameter,
and there are two ways of doing this. If one knows the value of this
parameter, one simply enters it in the box at bottom-right. However, if
one does not know the value of the parameter, one can adjust the graphs
until they suitably represent the beliefs. By dragging the red button
around, the graphs dynamically move.
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ANALYSIS
Once a data set has been input, we wish to calculate estimates of all the relevent parameters. The way these estimates are
calculated is through sampling from probability distributions. The results
we obtain improve as we sample. To start an analysis, one clicks on the
circular icon or selects run. While the program is running, we can view
various graphs, and these are dynamically updated as we collect more data.
RESULTS
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The
results of an analysis can be displayed in many ways. One option is to
show the point estimates of the unreliabilities
for the various items. Alternatively, one can view various
"item" reliabilites - the prior and
posterior under independence or dependence assumptions. Finally, one can
display the overall reliability of the items (as shown at left). This
represents our prior beliefs about the reliability of another item picked
at random.
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OTHER FEATURES
The program has all the usual features of a Windows-based program,
including full file management facilities and the facility to print the
results either in tabular or graphical form.
REFERENCE
Chen J. and Singpurwalla N. D., 'Composite
Reliability and its Hierarchical Bayes
Estimation' Journal of the American Statistical Association, 91,
436: 1474-1484.
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