A language is necessary for discussing reliability. The NFPA standards use a Weibull analysis graph to plot results and describe conclusions. The Weibull method is commonly used for analyzing data from reliability testing because of its versatility in modeling various statiscial distributions. However, the complexity of the equations means they are most readily solved using software. An example is shown in the graph.

In the graph, failure data (test specimens that have reached a threshold) are shown as green dots in the plot. The horizontal axis is the time (in this case, cycles) to reach termination, and the vertical axis is a probability number, which is obtained from a table. It represents the fraction of the population (not just the test unit) that has failed on a cumulative basis.

The most immediate observation is that failures do not occur all at the same time. Thus, the first dot, at 7,260,000 cycles, represents that about 8.4% of the population would have failed by this point. This is based on the sample of eight specimens (one specimen was suspended during the test and does not appear on the plot).

Therefore, some term must be used to explain that products will reach the end of their life progressively. The term most commonly used is the life at which 10% of the population has reached failure — the B10 life.

Examining test elements
The straight blue line in the graph is a best fit representation of the data. But will these same data occur again if the test is repeated with another sample of eight specimens? How about several repeated tests? The answer, of course, is almost certainly not.

Additional test results will yield more blue lines that will lie between the green curved lines. These green lines — called confidence bounds — form the limits for subsequent test data. Typically they are calculated for a 95% lower limit (on the left), and a 5% upper limit (on the right). So if the test is repeated many times, the data will lie within these bounds 90% of the time. Only 5% will fall outside either confidence bound.

The Weibull graph also shows two B10 life values. The first occurs at the intersection of the blue line with the 10% cumulative failure, at a life of 10.1 million cycles. However, this results from just one test. There will be several blue lines to examine when the test is repeated many times, and the ones of interest will be at the lower values of life. Therefore, choosing the green curved line at the left would yield a 95% confidence that the B10 life would be at least 4.1 million cycles.That leaves 90% of the population still operating satisfactorily. Therefore, another parameter, characteristic life, is also used. This point is at the 63.2% level because it results in a fixed value regardless of the slope of the blue line for a given set of test data.

In there-peated test concept, the slope of the blue (best fit) line can also vary — which is why the confidence bounds (green lines) containing them are curved. Each set of such test data has a best fit line that is a compromise of its slope and its distance from each data point. But regardless of the compromise, all possible curves for one test will cross through the 63.2% level at the same value of life. It is a characteristic of the mathematics of a Weibull distribution, which is why it is called the characteristic life. Characteristic life is usually associated with the blue line from the test data, and in this example it is 51.8 million cycles.

The last consideration is the slope of the blue line, which is 1.43 for this example. Values between 1.0 and 2.0 (sometimes to 3.0) are typical for fluid power components. A lower number indicates that the resulting spread of life from a test is smaller; higher values indicate a greater spread. A value of 3.6 often corresponds to a normal distribution, and values higher than 10 should be suspect of poor test results.

For more information, contact the author at jberninger@parker.com. This article is based on a paper presented by the author and contains extensive references to additional information. the document can be viewed or downloaded from the June 2009 issue archived on our website, at www.hydraulicspneumatics.com.