Analysis of the precision problem in numerical calculation of the reliability indices of technical systems by the topological method at application of the floating-point arithmetic

Abstract

This paper deals with the problem of precision error arising in numerical calculation of the reliability indices of technical systems by the topological method at application of the floating-point arithmetic. The topological method for calculation of the reliability indices in accordance with the reliability models based on the Markov chains is discussed. An example of correct calculation of the reliability indices on the basis of analytical derivation of calculating formulas and substitution of the initial reliability parameters into them is given. The floating-point types and arithmetic supported in hardware by the modern computers and examples of the precision loss in floating-point arithmetic operations are also observed. Finally, an example of incorrect calculation of the reliability indices, based on the numerical solving of the system of linear algebraic equations, using the floating-point arithmetic is also given.