1. A. BobbioBertinoro, March 10-14, 20031 Dependability Theory and Methods Part 4: Fault-tree analysis Andrea Bobbio Dipartimento di Informatica Università del Piemonte Orientale, “A. Avogadro” 15100 Alessandria (Italy) bobbio@unipmn.itbobbio@unipmn.it - http://www.mfn.unipmn.it/~bobbio Bertinoro, March 10-14, 2003

2. Elements of logic algebra

5. Logic algebra and Venn diagrams

6.  Events are binary events (working/non-working);  Events are statistically independent;  Relationships between events and causes are represented by logical AND and OR (Boolean) gates;  The root of the FT is the catastrophic undesired event called the Top Event (TE). Fundamental assumptions for FTA

7. A. BobbioBertinoro, March 10-14, 20037 Case study: a PLC architecture

8. A. BobbioBertinoro, March 10-14, 20038 Case study: a PLC architecture The considered failure rates for the elementary blocks are reported in the Table.

9. A. BobbioBertinoro, March 10-14, 20039 PLC architecture: FTA

10. A. BobbioBertinoro, March 10-14, 200310 Safety and dependability measures Safety assessment of the control system according to IEC 61508 (Functional safety of electrical/electronic/ programmable electronic safety-related systems)  SIL requirements (IEC 61508);  Unreliability versus time;  Safe Mission Time (SMT);  Mean Time To Failure;  Critical failure path (mcs).

11. A. BobbioBertinoro, March 10-14, 200311 FT Critical cuts The FT has 59 MCS, one of order 1 (the voter) and the remaining 58 of order 2.