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<doi>0185-cd</doi>
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<article-title>Comparison of Analytical Formulas of PFH and PMHF Calculation for M-out-of-N Redundancy Architecture</article-title>
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<author>Elena Rogova<sup>a</sup>, Christian Nowak<sup>b</sup>, Matthias Ramold<sup>c</sup> and Udo Steininger<sup>d</sup></author>

<aff>T&#220;V S&#220;D Rail GmbH, Germany.</aff>
<email><a href="mailto:elena.rogova@tuev-sued.de"><sup>a</sup>elena.rogova@tuev-sued.de</a></email>
<email><a href="mailto:christian.nowak@tuev-sued.de"><sup>b</sup>christian.nowak@tuev-sued.de</a></email>
<email><a href="mailto:matthias.ramold@tuev-sued.de"><sup>c</sup>matthias.ramold@tuev-sued.de</a></email>
<email><a href="mailto:udo.steininger@tuev-sued.de"><sup>d</sup>udo.steininger@tuev-sued.de</a></email>



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<title>ABSTRACT</title>
<p>The international functional safety standard for road vehicles ISO 26262 proposes to use probabilistic metric for random hardware failures (PMHF) as a quantitative way to estimate probability of random hardware failures violating the safety goal. The example of calculation of PMHF is presented in ISO 26262. However, the standard does not contain an analytical formula of PMHF calculation for M-out-of-N redundancy architecture. This formula can find an important application in drive-by-wire systems where the question of redundancy and calculation of probabilistic metrics of redundant architectures is especially relevant. In this paper the formula of PMHF calculation for M-out-of-N redundancy architecture has been developed and compared with the formula of average frequency of dangerous failures per hour (PFH) which is defined in the international functional safety standard IEC 61508 for safety systems in high- and continuous demand mode. Comparative analysis presented in this paper, demonstrates that PFH and PMHF formulas give similar results for different case studies. These case studies are investigated by considering different types of failures defined in IEC 61508 and in ISO 26262.</p>
<p><italic>Keywords: </italic>PMHF, PFH, Redundancy, ISO 26262, IEC 61508, Drive-by-wire.</p>
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