Abstract
The case is considered of a single two-state unit which undergoes a symmetric alternating process of failure and restoration. It is admitted that under general circumstances aging may be described in terms of total elapsed calendar-time, total accumulated on-time (or down-time) and, possibly, upon the number of transitions. Thus it is of utmost importance to be able to calculate and find explicit analytic expressions for the p.d.f. of total on-time (or total down-time) at a given time instant. The solution of the problem relies upon a set of integral equations. This set can be easily reduced to a set of partial differential equations. The solutions appear to be rather simple and manageable for a number of cases of practical interest. Finally, relations are established with the Chapman-Kolmogorov equations describing the non-homogeneous Markov repair process.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
D.L. Snyder, “Random point processes”, J. Wiley and Sons, New York, N.Y. (1975).
S. Garribba, G. Reina and G. Volta, “Availability of repairable units when failure and restoration rates age in real time”, IEEE Trans, on Reliability, R-25: 88 (1976).
A. Bendell and S. Humble, “Operating history and failure and degradation tendencies”, IEEE Trans, on Reliability, R-27: 75 (1976).
G.W. Parry and D.H. Worledge, "The use of regeneration diagrams to solve component reliability problems, Nucl. Engng. and Design, 45: 271 (1978).
D.G. Kendall, “On the generalized birth-and-death process”, Ann. Math. Statist., 19: 1 (1948).
L. Takács, “On certain sojourn time problems in the theory of stochastic processes”, Acta Math. Acad. Sci. Hung., 8: 169 (1957).
B.V. Gnedenko, Yu. K. Belyayev and A.D. Solovyev, “Mathematical methods of reliability theory”, Academic Press, New York, N.Y. (1969) (transl. of “Matematicheskiye Metody v Teorii Nadezhnosti”, Nauka Press, Moscow (1965)).
G.W. Parry and D.H. Worledge, “The downtime distribution in reliability theory”, Nucl. Engng. and Design, 49: 295 (1978).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1980 Plenum Press, New York
About this chapter
Cite this chapter
Para, A.F., Garribba, S. (1980). Reliability Analysis of a Repairable Single Unit Under General Age-Dependence. In: Apostolakis, G., Garribba, S., Volta, G. (eds) Synthesis and Analysis Methods for Safety and Reliability Studies. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-3036-3_12
Download citation
DOI: https://doi.org/10.1007/978-1-4613-3036-3_12
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-3038-7
Online ISBN: 978-1-4613-3036-3
eBook Packages: Springer Book Archive