Domains of attraction of asymptotic reliability functions

摘要

Theorems about domains of attraction of limit distribution of extreme statistics of independent identically distributed random variables are well known and included in [R.E. Barlow, F. Proshan, Statistical Theory of Reliability of Life Testing, Probability Models, Holt. Reinehart and Winston, New York, 1975; H. Chernoff, H. Teicher, Trans. Amer. Math. Soc. 116 (1965) 474–491; B.W. Gnedenko, Ann. Math., 44 (1943) 432–453; B. Kopocinski, Zarys Teorii Odnowy i Niezawodnosci, PWN, Warszawa, 1973]. In [K. Kolowrocki, Appl. Math., 36 (1993) 56–69] a new four-element class of limit reliability functions for a regular, homogeneous series–parallel system in which the number of series components of the system has the order of logarithm of the number of parallel components is fixed. This paper presents the solution of the problem of domains of attraction for these asymptotic reliability functions. Moreover, some examples are given.