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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.

In recent times, spare parts inventory systems have been extensively researched, but most inventory models were not fully adequate due to the stochastic nature of inventory environment. This paper proposes an approach that supports decision making process in planning and controlling of spare parts in aircraft maintenance systems. Reliability characteristics of aircraft consumable parts were analyzed in order to substantiate this approach. Moreover, the proposed reliability model was used to evaluate characteristics of subassemblies and/or assemblies these parts belong to. Finally, an innovative approach for determining the total amount of parts required in inventory and underage costs, based on observing the total unit time as a stochastic process, is presented herein.

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...

Stochastic models for spare parts forecasting have not been widely researched in scientific literature from the aspect of their reliability. In this chapter, the authors present models which analyze standard reliability parameters of technical systems' parts/components. By analyzing system reliability and failure rate, we estimate the required number of spare parts in the moment of expected failure or when reliability falls below the predefined level. Two different approaches based on data availability are presented herewith.

The Gaussian Q-function has considerable applications in numerous areas of science and engineering. However, the fact that a closed-form expression for this function does not exist encourages finding approximations or bounds of the Q-function. In this paper, we determine analytically two novel interval upper bound Q-function approximations and show that they could be used efficiently not only for the symbol error probability (SEP) estimation of transmission over Nakagami-m fading channels, but also for the average symbol error probability (ASEP) evaluation for two modulation formats. Specifically, we determine analytically the composition of the upper bound Q-function approximations specified at disjoint intervals of the input argument values so as to provide the highest accuracy within the intervals, by utilizing the selected one of two upper bound Q-function approximations. We show that a further increase of the accuracy, achieved in the case with two upper-bound approximations composing the interval approximation, can be obtained by forming a composite interval approximation of the Q-function that assumes another extra interval and by specifying the third form for the upper-bound Q-function approximation. The proposed analytical approach can be considered universal and widely applicable. The results presented in the paper indicate that the proposed Q-function approximations outperform in terms of accuracy other well-known approximations carefully chosen for comparison purposes. This approximation can be used in numerous theoretical communication problems based on the Q-function calculation. In this paper, we apply it to estimate the average bit error rate (ABER), when the transmission in a Nakagami-m fading channel is observed for the assumed binary phase-shift keying (BPSK) and differentially encoded quadrature phase-shift keying (DE-QPSK) modulation formats, as well as to design scalar quantization with equiprobable cells for variables from a Gaussian source.

We present a hybridization of the accelerated gradient method with two vector directions. This hybridization is based on the usage of a chosen three-term hybrid model. Derived hybrid accelerated double direction model keeps preferable properties of both included methods. Convergence analysis demonstrates at least linear convergence of the proposed iterative scheme on the set of uniformly convex and strictly convex quadratic functions. The results of numerical experiments confirm better performance profile in favor of derived hybrid accelerated double direction model when compared to its forerunners.

This paper, based on the extensive research of relevant professional literature, will present and elaborate possible aspects of influence which information-communications technologies (ICT) have on educational process. Contemporary information-communications technologies and their use in teaching process resulted in numerous enhancements of teaching process altering traditional methods of learning and teaching. With the aim of confirming theoretical postulates researches were conducted on candidates with specific educational degrees in various forms of traditional teaching and teaching with educational software. The survey was conducted on a control and experimental group, on a sample of 1542 candidates. The candidates were observed in a period of approximately five months. The results of this research indicate that the candidates taught by use of educational software have shown far greater level of achieved knowledge and significantly higher motivation for learning. The participants of the experimental group actively participated in the acquisition of their competences. The contribution of this paper is in the new methodological approach to the organization of education, which significantly improves the teaching process, its goals and outcomes.