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In order to obtain maintenance system reliability and availability, preventive replacements according to the age of elements and subsystems are introduced into the maintenance system. Age-replacements have been known for a long time, e.g. [2]. This problem was examined through development of preventive age-replacement for various individual cases. In particular, in the papers [3, 4, 10, 12] whole range of important analytical results was obtained. However, the methods of age-replacement for technical objects with valid manufacturer’s warranty were developed much later. Currently, manufacturer’s warranty is a basic element of modern market. The basic role of a warranty is an offer including a list of actions the customer must undertake when the product is damaged during warranty period. Manufacturer’s warranty for the product creates an incentive for the customer to make various commitments, improving the reputation of the manufacturer, and influencing the market share as well as potential profit. A detailed discussion and overview of the results connected to various approaches to product warranty is included in the following papers [5, 6, 7]. In particular, the warranty policy for non-repairable products was discussed in the paper [5]. The warranty policy analyzed in this paper is carried out through the strategy of damaged element replacement within the period of warranty by a new element with full warranty. The mathematical model and cost analysis for such strategy were developed in the papers [1, 8, 13]. In the paper [14] the criteria function defining the costs connected to carrying out preventive replacements of non-repairable elements with a warranty when time before failure has distribution with increasing failure rate function. In the quoted paper the criteria function depends on the distribution of time before failure, repair and preventive replacement costs as well as the length of warranty period. It is assumed that the times of repair and preventive replacement are negligible. In this paper the criteria function discussed is more general than in the paper [14], taking into consideration non-zero times of repair and times of preventive replacements. The set-up of the criteria function g(x) was based on the limit values of semi–Markov processes. The aim of this work is to formulate the conditions for existence of minimum function g(x) defining losses in maintenance system.

optimal age-replacement policy for non-repairable technical objects with warranty