Abstract
In this paper, we introduce and study the geometric process which is a sequence of independent non-negative random variablesX 1,X 2,... such that the distribution function ofX n isF (a n−1 x), wherea is a positive constant. Ifa>1, then it is a decreasing geometric process, ifa<1, it is an increasing geometric process. Then, we consider a replacement model as follows: the successive survival times of the system after repair form a decreasing geometric process or a renewal process while the consecutive repair times of the system constitute an increasing geometric process or a renewal process. Besides the replacement policy based on the working age of the system, a new kind of replacement policy which is determined by the number of failures is considered. The explicit expressions of the long-run average costs per unit time under each replacement policy are then calculated, and therefore the corresponding optimal replacement policies can be found analytically or numerically.
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Lin, Y.(.Y. Geometric processes and replacement problem. Acta Mathematicae Applicatae Sinica 4, 366–377 (1988). https://doi.org/10.1007/BF02007241
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DOI: https://doi.org/10.1007/BF02007241