Knowledge gained in the study of the physics of failure has lead to more meaningful distributions of time to failure for components subject to failure. This work expands the application of this knowledge by developing mathematical models for failure based upon physical failure models. The form of the distribution of time to failure may then be derived under certain conditions. This model applies to components for which failure can be associated with some extreme random phenomenon such as the largest flaw or impurity, etc. The method is illustrated for two cases which are likely to be found in applications. In their simplest form these two cases reduce to distributions found empirically to be useful in reliability.
[1]
J. W. Cohen,et al.
Some ideas and models in reliability theory
,
1974
.
[2]
C. A. Krohn,et al.
Hazard Versus Renewal Rate of Electronic Items
,
1969
.
[3]
M. Shooman.
Reliability Physics Models
,
1968
.
[4]
E. J. Gumbel,et al.
Statistics of Extremes.
,
1960
.
[5]
G. Pólya,et al.
Über den zentralen Grenzwertsatz der Wahrscheinlichkeitsrechnung und das Momentenproblem
,
1920
.
[6]
H. Grimm.
Williamson, E., und M. H. Bretherton: Tables of the Negative Binomial Distribution. John Wiley & Sons, London, New York 1963. 275 S., Preis 90 s
,
1965
.