Geodesic
Adaptation of the Rosenblatt~--- Parzen method for the experimental evaluation of the computing system reliability
Prikladnaya Diskretnaya Matematika. Supplement, no. 14 (2021), pp. 148-153.

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The lack of initial information about the law of distribution of random variables and their realization at a time moment close to the beginning of the observation, as well as the presence of censored data, force us to adapt the nonparametric Rosenblatt — Parzen method. To compensate for the bias and eliminate the violation of the normalization condition, the method of mirroring the original data is considered. When constructing the distribution density of random variables, it is proposed to take into account censored data. The accuracy of the estimate shows a decrease in error when using the adapted Rosenblatt — Parzen method. The practical implementation of the adapted Rosenblatt — Parzen method is demonstrated by the example of an experimental assessment of the reliability indicators of a computing system. Plotting the density and the mean time between failures distribution function allows calculating the main indicators of the object's reliability: failure rate, probability of no-failure operation, mean time between failures. Calculated estimates of the reliability indicators of a computing system are necessary for making control decisions during operation and maintaining the facility's performance.
Keywords: experimental reliability analysis, small samples, computing systems, Rosenblatt — Parzen method. 
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     author = {V. S. Nikulin},
     title = {Adaptation of the {Rosenblatt~---} {Parzen} method for the experimental evaluation of the computing system reliability},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
     pages = {148--153},
     publisher = {mathdoc},
     number = {14},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDMA_2021_14_a33/}
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V. S. Nikulin. Adaptation of the Rosenblatt~--- Parzen method for the experimental evaluation of the computing system reliability. Prikladnaya Diskretnaya Matematika. Supplement, no. 14 (2021), pp. 148-153. http://geodesic.mathdoc.fr/item/PDMA_2021_14_a33/

[1] Polovko A. M., Gurov S. V., Osnovy teorii nadezhnosti, 2-e izd., BKhV-Peterburg, SPb., 2008

[2] Zakharov D. N., Nikulin V. S., “Analiz metodov statisticheskoi otsenki ekspluatatsionnoi nadezhnosti vychislitelnykh kompleksov”, Naukoemkie tekhnologii v kosmicheskikh issledovaniyakh Zemli, 12:1 (2020), 64–69

[3] Chepurko V. A., “Yadernaya otsenka parametra potoka otkazov. Diagnostika i prognozirovanie sostoyaniya slozhnykh sistem”, Sb. nauchnykh trudov kaf. ASU NIYaU MIFI, 15, 2004, 19–31

[4] Antonov A. V., Nikulin M. S., Statisticheskie modeli v teorii nadezhnosti, Abris, M., 2012, 390 pp.

[5] Parzen E., “On estimation of a probability density function and mode”, Ann. Math. Statistics, 33 (1962), 1065–1076 | DOI | MR | Zbl

[6] Silverman B., Density estimation for Statistics and Data Analysis, Chapman Hall/CRC, London–N.Y., 1986 | MR | Zbl

[7] Nikulin V. S., “Metodika podgotovki dannykh dlya intellektualnogo analiza nadezhnosti vychislitelnykh kompleksov”, Vestnik SIBGUTI, 2020, no. 3(51), 26–37