Geodesic
The life time of a~random binary sequence (coherent system)
Diskretnaya Matematika, Tome 22 (2010) no. 2, pp. 51-59.

Voir la notice de l'article provenant de la source Math-Net.Ru

We introduce and investigate a probabilistic model of a coherent system which consists of $m$ elements and is intended for fulfilment of homogeneous tasks. On the first stage, one task out of the total number $n$ of tasks enters each element of the system. The result of work of an element is either a fulfilment of the task or a failure of the element. In the case of the failure of an element, it is excluded from the system, and the task which is not fulfilled returns to the queue of those waiting for fulfilment. On the second stage, $m_1$ tasks are sent to the system, where $m_1$ is the number of elements of the system remained operable after the first stage, and so on. In the paper, a detailed analysis of the suggested model is realised in the case where each element of the system fulfils tasks with the same probability independently of the rest of the elements. 
@article{DM_2010_22_2_a3,
     author = {V. N. Surikov},
     title = {The life time of a~random binary sequence (coherent system)},
     journal = {Diskretnaya Matematika},
     pages = {51--59},
     publisher = {mathdoc},
     volume = {22},
     number = {2},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2010_22_2_a3/}
}
TY  - JOUR
AU  - V. N. Surikov
TI  - The life time of a~random binary sequence (coherent system)
JO  - Diskretnaya Matematika
PY  - 2010
SP  - 51
EP  - 59
VL  - 22
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DM_2010_22_2_a3/
LA  - ru
ID  - DM_2010_22_2_a3
ER  - 
%0 Journal Article
%A V. N. Surikov
%T The life time of a~random binary sequence (coherent system)
%J Diskretnaya Matematika
%D 2010
%P 51-59
%V 22
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DM_2010_22_2_a3/
%G ru
%F DM_2010_22_2_a3
V. N. Surikov. The life time of a~random binary sequence (coherent system). Diskretnaya Matematika, Tome 22 (2010) no. 2, pp. 51-59. http://geodesic.mathdoc.fr/item/DM_2010_22_2_a3/

[1] Ronzhin A. F., Surikov V. N., “O vremeni polnogo perebora”, Obozrenie prikladnoi i promyshlennoi matematiki, 14:4 (2007), 506–508

[2] Samaniego F. J., “On closure of the IFR class under formation of coherent systems”, IEEE Trans. Reliab., 34 (1985), 69–72 | DOI | Zbl

[3] Navarro J., Balakrishnan N., Samaniego F. J., “Mixture representations of residual lifetimes of used systems”, J. Appl. Probab., 45:4 (2008), 1097–1112 | DOI | MR | Zbl

[4] Navarro J., Rychlik T., “Reliability and expectation bounds for coherent systems with exchangeable components”, J. Multivariate Anal., 98 (2007), 102–113 | DOI | MR | Zbl

[5] Spizzichino F., “Ageing and positive dependence”, Encyclopaedia of Statistics for Quality and Reliability, Wiley, Chichester, 2007, 82–95

[6] Sedyakin N. M., “Ob odnom fizicheskom printsipe teorii nadezhnosti”, Izvestiya AN SSSR. Tekhnicheskaya kibernetika, 1966, no. 3, 80–87

[7] Bagdonavichyus V. B., “Statisticheskaya proverka modeli additivnogo nakopleniya povrezhdenii”, Teoriya veroyatnostei i ee primeneniya, 23:2 (1978), 403–408 | MR | Zbl

[8] Prokhorov Yu. V. (red.), Veroyatnost i matematicheskaya statistika, Entsiklopediya, Bolshaya Rossiiskaya Entsiklopediya, M., 1999 | MR

[9] Ronzhin A. F., “Tochnye formuly dlya veroyatnostnykh kharakteristik vremeni vykhoda nakaplivayuschikhsya summ iskhodov bernullievskoi posledovatelnosti za pryamolineinye granitsy i ikh primenenie k opredeleniyu srednei informatsionnoi skorosti odnogo sposoba skrytoi peredachi informatsii”, Obozrenie prikladnoi i promyshlennoi matematiki, 14:4 (2007), 593–597 | Zbl

[10] Ouen D. B., Sbornik statisticheskikh tablits, VTs AN SSSR, Moskva, 1966 | MR

[11] Bahadur R. R., “Some approximations to the binomial distribution”, Ann. Math. Statist., 3:1 (1960), 43–54 | DOI | MR

[12] Feller V., Vvedenie v teoriyu veroyatnostei i ee prilozheniya, Mir, Moskva, 1964 | Zbl

[13] Kolchin V. F., Sluchainye otobrazheniya, Nauka, Moskva, 1984 | MR | Zbl