br By substituting the semi Markov kernels from

By substituting the semi-Markov kernels from Table 2 into Eqs. (5), we shall obtain the following:
By changing the variables and substituting φ1(t) into the dopamine receptors for φ0(t) in system (6), we obtain:
By transforming Eq. (7), we obtain: where * is the convolution operator. Let us introduce notations
Then expression (8) shall take the form
Then expression (9) shall take the form
By iterating, we obtain: where ;
The obtained distribution function (11) describes the system\'s mean time between failures. Let us find the distribution function for the system\'s recovery time using Eq. (4):
Since and , the distribution function (12) takes the form
Discussion of the obtained results Let us compare the mathematical expectation values of the function (11) we obtained and the mathematical expectation found using the expression [16]:
The mathematical expectation value of the distribution function we obtained is while the one found by the authors of Ref. [16] is
Nevertheless, using primitive flows to describe failures is acceptable in many cases. Any TM is a complex technical system consisting of a great number of nodes and components. Failure flow of an individual mechanical component is expressed, as a rule, by an exponent. The law of the behavior of the mean time between failures for a TM consisting of nodes and components whose mean times between failures follow the exponent will also be expressed by an exponent [22]. In the case when any flow turns out to be ordinary and stationary, the Khinchin theorem can be used [23]. Khinchin once proved that if the flow is a superposition of stationary, ordinary and mutually independent flows, and λ is the rate of an ith flow, then the total flow will tend to the simplest flow with the rate if n is large enough. This poses the question how high the n value should be for the TM\'s failure flow to be taken as exponential. Let us construct an imitation model to assess this value using the GPSS world system. Let us accept the generalized Erlang law of the second order as the law for the mean time between failures. The program listing for a TM consisting of two nodes is shown in Fig. 4. The modeling was performed for a TM comprising between 2 and 6 nodes. Some MTBF histograms are shown in Fig. 5. It can be seen from the modeling results that the hypothesis of the exponential distribution of MTBF of the whole TM can be accepted starting from a TM consisting of 6 nodes (see Fig. 5(c)). Since a TM actually contains a far larger number of nodes and components, the assumption we made in the model is quite acceptable. Similar reasoning is valid for the MTBF of the SD.
Conclusion As a result of the study we have carried out, we have reached our goal of developing a semi-Markov model for the operational process of the ‘technological module–storage device’ structure. We obtained the expressions for determining the distribution functions of the mean times between failures and the mean times till recovery (see Eqs. (11) and (13), respectively). We compared the mathematical expectation values of MTBF determined using the distribution function we obtained and the one obtained from the formula given in Ref. [16]; as it turned out, the results coincided almost completely.
Acknowledgment
The studies were carried out with the financial support of the Ministry of Education and Science of the Russian Federation for the basic part of state task no. 2014/702 (project no. 3858) and with the support of the Russian Foundation for Basic Research no. 15-01-05840.
Introduction The alkaline earth chalcogenides such as MgSe, CaSe, SrSe, etc., have attracted the scientific community due to their potential applications in various optoelectronic devices, especially luminescent ones. Wang et al. [1] have studied the growth of MgSe films of zinc-blende structure on ZnTe substrates by the molecular beam epitaxy (MBE) method. The surface reconstructions of MgSe under different flux ratios and growth temperatures were studied. Rouff et al. [2] have studied MgSe using the energy dispersive X-ray diffraction to 202GPa and local density approximation to ultra-soft pseudo-potentials to 500GPa. It was reported that MgSe underwent continuous phase transformation from rocksalt to FeSi. Prete et al. [3] have reported growth and characterization of ZnMgSe and MgSe on (100) GaAs by low-pressure metallorganic vapour phase epitaxy (MOVPE). The crystallographic phases of as grown MgSe and ZnMgSe were investigated. Sahraoui et al. [4] have reported the structural and electric properties of MgSe at high hydrostatic pressure by the pseudo-potential plane wave method. Pendey and Sutjianto [5] have studied structural phase transition on MgSe from wurtzite zinc-blende to rocksalt phase by the periodic Hartree–Fock method. As compared to low pressure, the MOVPE and MBE methods used for the deposition of MgSe thin films, the spray pyrolysis method has many advantages, such as high deposition rate, control of various deposition parameters and low cost [6–12]. The spray method has been used for several decades in glass industry and in solar cell production to deposit electrically conducting electrodes. Thin film formation using this technique involves spraying a metal salt solution onto a heated substrate. The sprayed droplet reaching the hot substrate surface undergoes spyrolytic decomposition and forms the desired product. The other volatile by-products escape in the vapor phase. The quality and properties of the films depend largely on substrate temperature, precursor solution concentration, spray rate and substrate, etc. Previous studies have shown that very few reports are available on growth of MgSe films by solution growth [13, 14] by the metalorganic vapor chemical deposition (MOVCD) [5] and MBE [1] methods. The effect of triethanolamine (TEA) on the physical properties of MgSe thin films grown by the chemical bath deposition method has been reported in our earlier report [15]. The purpose of this work is to investigate the effect of the quantity of spray solution on the physical properties of MgSe thin films. This paper reports structural, electrical and optical properties of MgSe thin films prepared by varying the quantity of the spray solution from 5 to 30mL.