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  5. Bootstrap method for evaluating the reliability indicators of the airborne equipment of the surface-to-air guided missiles with the use of the priority information for solving the problems of extension of the appointed indicators

Bootstrap method for evaluating the reliability indicators of the airborne equipment of the surface-to-air guided missiles with the use of the priority information for solving the problems of extension of the appointed indicators

B. Lanetsky, V. Dedenok, I. Koval, V. Luk′yanchuk
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Description: The article substantiates the urgency of researching a method that uses data on the results of operational tests of on-board equipment of surface-to-air guided missiles (SAM) and a priori information on the storageability, which is given in the design documentation for the SAM. A priori information that characterizes the probability of faultless storage of products are this exact probability set at the beginning of the shelf life period (according to technical specifications regarding reliability of SAM during guaranteed service life interval) and that set at the end of the shelf life period (assigned service life term of SAM specified in design documentation). The performance test data is a censored small sample of product storage times to failure, which is obtained on a short observation interval. A bootstrap method is proposed for assessing the reliability of products on which a new distribution function is constructed based on known points and a priori information. For evaluating reliability, this method uses the data on the operation of products as well as the data on their shelf life that extends beyond the observation interval. The new distribution function is used to generate bootstrap samples of pseudo-random values of the durations of product storage to failure. Point and interval estimates of the average residual service life of the products are obtained, which are calculated for two variants: according to operational tests only; according to operational tests and a priori information. The results of modeling the probabilities of storing products to failure and estimating the average residual life of the products according to different options are given. To simulate the dependencies of the storage to failure probabilities versus time of storage for the time intervals that extend beyond the observation interval, every single bootstrap sample gets approximated and extrapolated by a polynomial. It is shown that using the bootstrap method using a priori information allows obtaining a point estimate of the average residual resource, which is closest to the benchmark estimate. The developed method makes it possible to obtain estimates of the average residual shelf life of products of acceptable accuracy and reliability for solving the tasks of prolonging the assigned shelf life intervals for SAM.


Keywords: a priori information, bootstrap-method, censored small sample, operational tests, extension of assigned indicators, average residual shelf life

Reference:
 Lanetskyi, B.M., Dedenok, V.P., Koval, I.V. and Lukianchuk, V.V. (2018), “Butstrep-metod otsiniuvannia pokaznykiv nadiinosti bortovoho obladnannia zenitnykh kerovanykh raket z vykorystanniam apriornoi informatsii dlia vyrishennia zavdan prodovzhennia pryznachenykh pokaznykiv” [Bootstrap method for evaluating the reliability indicators of the airborne equipment of the surface-to-air guided missiles with the use of the priority information for solving the problems of extension of the appointed indicators], Science and Technology of the Air Force of Ukraine, No. 3(32), pp. 25-31. https://doi.org/10.30748/nitps.2018.32.04.