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.
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
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.
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.
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
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.
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 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.
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.
Chen J. and Singpurwalla N. D., 'Composite Reliability and its Hierarchical
Bayes Estimation' Journal of the American Statistical Association,
91, 436: 1474-1484.