Software

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.

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.

Due in part to these problems, we have developed an alternative approach to reliability assessment. Instead of treating every item separately, 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 relevant 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.

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.


Analysis

Once a data set has been input, we wish to calculate estimates of all the relevant 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

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.


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.