The use of the doubly exponential distribution for tensile strength of rubbers

The doubly exponential (Fisher-Tippett Type 1) distribution has been assumed widely to represent the distribution of strength measurements and its use for tensile strength is recommended in BS 5324: 1976. This standard also recommends the use of a ‘mode’, calculated on this assumption, as the ‘most important measure of central tendency’ and indicates methods, previously described elsewhere in the literature, for calculating this mode.

In the present paper a much simpler and mathematically more rigorous method for calculating the ‘mode’ is described.

The use of the mode as a measure of central tendency is, however, debatable. The median conforms better with a key principle of control theory, namely equality of risk between manufacturer and purchaser. The median, unlike the mode, can also be estimated without bias directly from a comparatively small sample of measurements without any assumptions as to the population distribution.

Practical and theoretical evidence for the lack of general applicability of the doubly exponential distribution to strength measurements is presented.