Appendix - Breakdown statistics

The investigation of failures of manufactured components and systems, especially in the electronics and aerospace industries, has generated a variety of statistical models on which data analysis may be based. Each model uses a specific distibution of failure probabilities, and it is important to select a model that matches the actual distribution inherent in the product concerned. In the case of dielectric breakdown, where a large number of quite different modes of failure are known to occur, sometimes even together, the application of a particular statistical failure model must be approached with great caution. Nevertheless, one treatment, based on a Weibull distribution of failure probability, has taken root, and is most generally used in practice. For a dielectric, the Weibull failure probability function has the form 

Here Pf is the probability of failure and E is the applied electrical stress (field strength) that progressively increases and eventually causes the item to fail. (The stress could also be taken as the time to failure at constant applied voltage.) The parameters a and 3 define the scale and shape of the distribution in this they are analogous to the mean and standard deviation of the normal 

Although the scale parameter a is the primary characteristic value of failure in a set of samples, representing the applied field by which 63% of the samples have broken down, the shape parameter /3 is also extremely important. f3 is required in order to calculate when the first 1%, say, of samples will have failed - a more important parameter for a design engineer than the 63% figure. 

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Three reports have been issued containing IPRDS failure data. Information on pumps, valves, and major components in NPP electrical distribution systems has been encoded and analyzed. All three reports provide introductions to the IPRDS, explain failure data collections, discuss the type of failure data in the data base, and summarize the findings. They all contain comprehensive breakdowns of failure rates by failure modes with the results compared with WASH-1400 and the corresponding LER summaries. Statistical tables and plant-specific data are found in the appendixes. Because the data base was developed from only four nuclear power stations, caution should be used for other than generic application. 

In the following sections we discuss briefly the principal mechanisms of electrical breakdown in solid polymers and some of the consequences for the use of these as insulating materials. A brief outline of the statistical treatment of breakdown data is given in the appendix (Section 6.9). 

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