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    Extremal Nature of Dielectric Breakdown—Effect of Sample Size


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    Data are commonly gathered to furnish information regarding the distribution of the quality characteristics of a material, usually for a specific purpose such as the establishment of a quality standard or the determination of confonnance with a specified quality standard. In 1933, a “Manual on Presentation of Data” (7) was published by the ASTM to make available some of the principles of efficient presentation of data and to recommend practices for the American Society for Testing Materials.” In this manual, consideration is given particularly to “a series of n observations representing single measurements of the same quality characteristic of n similar things.” The two distribution parameters said to be the most important are arithmetic average, and standard deviation, σ. Practically no mention is made of individual extreme values. Little attention was paid to skewed distributions and that little only to skewed normal distributions. It has become apparent in recent years that the normal law is not a good approximation to the distribution of values obtained from the operation of a process which is “weak-link” in character, that is, dielectric breakdown or mechanical rupture tests. A fundamental objection is that it does not obey the stability postulate. This means that only the reference distribution can be normal. Furthermore, it requires that the standard deviation as well as the mean decrease with increase in sample size. Types of distributions which do obey the stability postulate were presented by E. J. Gumbel (1) in a recent publication of the National Bureau of Standards. It is the aim of this paper to call attention to recent work which shows close conformity of dielectric breakdown data, for both liquids and solids, with one of Gumbel's “extreme-value” distributions. The consequences of this conformity on the rate of decrease of minimum breakdown values with increase in sample size or area are then discussed.

    Author Information:

    Endicott, H. S.
    General Electric Co., Schenectady, N. Y.

    Weber, K. H.
    General Electric Co., Pittsfield, Mass.

    Committee/Subcommittee: D09.19

    DOI: 10.1520/STP46274S