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Times to intermittent and to permanent failures as Brownian crossing times

Published online by Cambridge University Press:  14 July 2016

Arthur Nádas
Arthur Nádas*
Affiliation:
IBM Corporation, Hopewell Junction, N. Y.
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Extract

Consider a device which begins operating at time t = 0 and then operates continuously in time. The operation of the device is satisfactory so long as a physical parameter X(t) of the device remains less than a critical value c > 0 (X(0) = 0). The device does not operate satisfactorily (i.e., it is “failed”) at a time t if X(t) ≧ c. Suppose that X(t) is a random variable with mean EX(t) = ta (a> 0), i.e., the device parameter X drifts with a linear rate a.

Type
Short Communications
Information
Journal of Applied Probability , Volume 8 , Issue 4 , December 1971 , pp. 838 - 840
Copyright
Copyright © Applied Probability Trust 1971 

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References

[1] Breiman, L. (1968) Probability. Addison-Wesley, Reading, Mass.Google Scholar
[2] Takács, L. (1967) Combinatorial Methods in the Theory of Stochastic Processes. J. Wiley and Sons, New York.Google Scholar