Optimal replacement policy for obsolete components with general failure rates

Abstract

Identical components are considered, which become obsolete once new-type ones are available, more reliable and less energy consuming. We envision different possible replacement strategies for the old-type components by the new-type ones: either purely preventive, where all old-type components are replaced as soon as the new-type ones are available; either purely corrective, where the old-type ones are replaced by new-type ones only at failure; or a mixture of both strategies, where the old-type ones are first replaced at failure by new-type ones and next simultaneously preventively replaced after a fixed number of failed old-type components.To evaluate the respective value of each possible strategy, a cost function is considered, which represents the mean total cost on some finite time interval [0, t]. This function takes into account replacement costs, with economical dependence between simultaneous replacements, and also some energy consumption (and/or production) cost, with a constant rate per unit time.A full analytical expression is provided for the cost function induced by each possible replacement strategy. The optimal strategy is derived in long-time run. Numerical experiments conclude the paper. fixed time, say time 0, some new components appear in the market, issued from a new technology, which makes them more reliable, less energy consuming and more performing. Such new-type of components may be substituted to the older ones with no problem of compatibility. There is no stocking of old-type components and after time 0, no old-type component is available anymore (or the industrialist is not allowed to use old-type components anymore, e.g. for safety reasons). After time 0, any failed component, either old-type or new-type, is then instantaneously replaced by a new-type one. At time 0, each old-type component is in use since some random time, with some random remaining lifetime. If the new-type components are much less energy consuming than the older ones and if the period of interest is very long, it may then be expedient to remove all old-type components immediately at time 0 and replace them by new-type ones, leading to some so-called purely preventive replacement strategies. On the contrary, in case there is no much improvement between both technologies and if the period of interest is short, it may be better to wait until the successive failures of the old-type components and replace them by new-type ones only at failure, leading to some purely corrective replacement strategy. More generally, some mixture of both strategies, preventive and corrective, may also be envisioned and may lead to lower costs, as can be seen later. The point of the present paper is to look for the optimal replacement strategy among the purely preventive one, the purely corrective one and the mixtures of both strategies envisioned here. To evaluate the respective value of each possible strategy, a cost function is considered, which represents the mean total cost on some finite time interval [0, t]. This function takes into a...

Algorithms for asset replacement under limited technological forecast

“…In addition, the impact of uncertainty on the replacement policy is of primary importance (Mercier, 2008, Nguyen et al, 2013, Richardson et al, 2013.We leave these issues for a future study.…”

“…(IH) The infinite-horizon minimization of the present value of the total replacement cost chooses the infinite sequence of the future lifetimes of a sequentially replaced asset (Elton and Gruber, 1976;Sethi and Chand, 1979;Bethuyne, 1998;Regnier et al, 2004;Yatsenko and Hritonenko, 2005, 2008, 2010. (EL) The economic Life method minimizes the asset's total equivalent annual cost by choosing the optimal replacement time of current asset (Thuesen and Fabrycky, 1993;Newman et al, 2004;Hartman, 2007).…”

Maintaining a system subject to uncertain technological evolution

“…Moreover, as mentioned previously, the new technology is assumed to be more attractive than the old one (A1). This assumption that management is no longer interested in the old technology and will invest directly in new technology after its appearance on the market is also used in many references [9,14,6,7].…”

Optimal maintenance and replacement decisions under technological change with consideration of spare parts inventories

“…The authors examine the effects of obsolescence on costs under several different conditions: constant obsolescence risk and no shortages are allowed; varying obsolescence risk and no shortages are allowed and finally varying obsolescence risk with shortages. 7 parts inventory and On the end of the spectrum, models devoted to maintenance optimization involving technological change do not consider the spare part inventory impact (Borgonovo et al, 2000;Labeau, 2009a, 2009b;Dogramaci and Fraiman, 2004;Hopp and Nair, 1994;Karsak and Tolga, 1998;Mercier, 2008). This gap in the literature motivates us to develop an appropriate model to meet management's requirements: optimization of maintenance cost while simultaneously updating information on technological development and considering the impact of spare parts inventory levels to make sound investment decisions.…”