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Based on the extended geometric process, a repair replacement model of a degradation system is studied, in which the delayed repair time depends on the working time after the last repair. Replacement and repair thresholds describe when the system will be replaced and when the system can be repaired, respectively. Two kinds of replacement policies are studied. One policy is jointly determined by the moment of the Nth failure and the first hitting time of the working time after the last repair for the replacement threshold, and the system is replaced, whichever occurs first; the other is the special case of the first policy, and the system is replaced when the working time after the last repair first hits the replacement threshold. The exact expressions of the long-run average cost rate are obtained. The optimal policies exist and can be ascertained by numerical methods. Finally, numerical examples are presented to demonstrate the application of the results obtained in the paper. [ABSTRACT FROM AUTHOR]

In this article, by considering both a limited number of failure replacements and a limited number of random working cycles as warranty terms, a hybrid warranty (HW) is designed from the manufacturer's point of view to warrant the product that does successive projects at random working cycles. The warranty cost produced by HW is derived and analyzed. By defining that HW warrants the product, two types of post-warranty replacement models are investigated from the consumer's point of view to ensure the reliability of the product through HW, i.e., customized post-warranty replacement and uniform post-warranty replacement. Depreciation expense is integrated into each post-warranty replacement. The expected cost rate model is presented for each post-warranty replacement and some special cases are obtained by setting parameters in the expected cost rate. Finally, sensitivities on both HW and post-warranty replacements are analyzed in numerical experiments. It is shown that when a limited number of failure replacements or/and a limited number of random working cycles are introduced to a warranty, the warranty cost can be reduced; and the performance of the uniform post-warranty replacement is superior to the customized post-warranty replacement. [ABSTRACT FROM AUTHOR]