An iterative method for solving a minimization problem of unconstrained optimization is presented. This multistep curve search method uses the specific form of iteration with two direction parameters, the approximation of Hessian by appropriately constructed diagonal matrix, and the inexact line search procedure. It is proved that constructed numerical process is well defined under some assumptions. Considering certain conditions, the method is linearly convergent for uniformly convex and strictly convex quadratic functions. Numerical results arising from defined algorithms are also presented and analyzed.

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A reduction of the originally double step size iteration into the single step length scheme is derived under the proposed condition that relates two step lengths in the accelerated double step size gradient descent scheme. The proposed transformation is numerically tested. Obtained results confirm the substantial progress in comparison with the single step size accelerated gradient descent method defined in a classical way regarding all analyzed characteristics: number of iterations, CPU time, and number of function evaluations. Linear convergence of derived method has been proved.

A stochAstic model for estimAtion of repAir rAte for system operAting under performAnce bAsed logistics stochAstyczny model do szAcowAniA intensywności nAprAw dlA systemu dziAłAjącego w wArunkAch logistyki wydAjnościowej Performance Based Logistics (PBL) concept has an aim to improve the system availability and it has been extensively researched in the recent years. These researches showed that inventory level does not impact system availability as much as component reliability and repair time in repairable system operating under PBL contract. Based on that, in this paper, we propose a new stochastic model for determination of annual repair rate for critical aircraft components in such system in order to achieve desired availability. The result obtained could be used for planning of base stock level and capacity of repair facilities. Keywords: repair rate, availability, stochastic model, performance based logistic. Koncepcja Logistyki Opartej na Wydajności (Performance Based Logistics, PBL), której celem jest poprawa gotowości systemów, została w ostatnich latach szeroko zbadana. Badania te wykazały, że w przypadku systemów działających w warunkach PBL, poziom zapasów nie wpływa na gotowość systemu w tak dużym stopniu jak niezawodność elementów składowych oraz czasy napraw. Opierając się na tej obserwacji, w niniejszym artykule proponujemy nowy model stochastyczny do określania rocznej intensywności napraw krytycznych elementów samolotu tworzących system tego typu. Model ten pozwala na osiągnięcie pożądanej gotowości. Uzyskany model może być wykorzystany do planowania bazowego poziomu zapasów oraz przepustowości zakładów remontowych.Słowa kluczowe: intensywność napraw, gotowość, model stochastyczny, logistyka oparta na wydajności.KoNtrec N, PANić S, Petrović M, Milošević H. A stochastic model for estimation of repair rate for system operating under performance based logistics. eksploatacja i Niezawodnosc - Maintenance and reliability 2018; 20 (1): 68-72, http://dx.doi.org/10.17531/ein.2018.1.9. Eksploatacja i NiEzawodNosc -MaiNtENaNcE aNd REliability Vol. 20, No. 1, 2018 69 sciENcE aNd tEchNology availability as much as reliability and repair rate. The authors advise to focus on the component reliability and repair system efficiency to improve system availability.Based on the aforesaid research, the model presented in this paper observes the repair rate as a stochastic process and has an aim to determine this parameter for preferred level of availability. The need for stochastic modeling of repairable systems has been justified and explained in paper [1]. Model for assessment of expected time to repairIn this paper we are observing system that alternates between two states -system is operative at certain time and non-operative otherwise. In the literature, this approach is known as alternating renewal process [4]. We assumed that at the start system is operative. It remains in that state for a period of time T (failure time), then it stops operating for time R (repair time) and after being repaired system is...