Reliability of Safety-Critical Systems —— Theory and Applications

----- 安全关键系统的可靠性：理论与应用

ISBN: 9781118112724 出版年：2014 页码：468 Marvin Rausand Wiley

Section 8.4 provides approximation formulas for the frequency of dangerous group failures (DGFs) and the PFDavg for general koon voted groups of independent and identical channels in (8.39) and (8.48), respectively. A DGF occurs when at least n − k + 1 channels have simultaneous D faults. The two formulas, (8.39) and (8.48), are adequate whenn−k+1 ≤ 2, but may be somewhat inaccurate when n − k + 1 ≥ 3. The inaccuracy is usually insigni cant since the probability that three or more independent channels are in a D fault state (simultaneously) in the same proof test interval will be very, very low for most practical SISs.1 The inaccuracies of the two formulas are therefore mostly of theoretical interest. Anyway, an improved derivation of the two formulas is presented in this note. For those of you who nd the presentation in Section 8.4 of the book to be inadequate, I have written a replacement version of pages 224–230 that may be downloaded from http://www.ntnu.edu/ross/books/sis – see Errata. The current note provides a more thorough derivation and several examples.