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___________________________________________________ UDC 519.6 Technical mechanics, 2023, 1, 105  114 INTERVAL ESTIMATION OF RELIABILITY INDICES FROM THE RESULTS OF COMPLEX SYSTEM COMPONENT TESTS DOI: https://doi.org/10.15407/itm2023.01.105 Savonik O. M.
Savonik O. M.
The goal of this work is to find the lower estimate of the nofailure probability (NFP) of a complex
monotonic nonrecoverable system from the results of independent binomial tests of its components.
Using the generalandprobabilistic method, the NFP is considered as a probability function
polynomial, which is a linear homogeneous polynomial in each of the S variables where S is the
number of system component types. Based on the method of confidence sets, the NFP lower estimate is
found as the minimum of a function of an unknown multidimensional parameter at a probability of the
aggregate test results (failurefree operation) of the system components equal to one minus the
guaranteed confidence coefficient. The paper reports a system of equations, each of which for two
component types relates the component reliability derivatives of the NFP (and one more equation
relates the component reliability and the confidence coefficient). Conditions are found for the
initial guess in a numerical solution of the above system of nonlinear equations (the number of
the conditions is equal to the number of the component types minus one; each condition is a like
sign for two functions each of which depends on the probability of the test results of a particular
component type and the component reliability of this probability). In some specific cases, the
program dimension can be reduced due to the simple structure of the probability function polynomial.
The presented method gives a confidence reliability estimate with a guaranteed confidence
coefficient for complex system that cannot be reduced to a serialparallel or a parallelserial
structure and consist of components with an arbitrary type of failure time distribution. The method
allows one to get an estimate at a small number of tests and a small number of failures or in their
absence, which is of especial importance for highreliability systems.
complex system, binomial tests, reliability, confidence sets, monotonic system
1. Reliability of Engineering Systems: Handbook. Ushakov I. A. (Ed.). Moscow: Radio i Svyaz, 1985. 608 pp. (in Russian).
Copyright (©) 2023 Savonik O. M. Copyright © 20142023 Technical mechanics ____________________________________________________________________________________________________________________________ 
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