System Models

2 tools in the Reliability area.

System Reliability

Reliability of a system from its reliability block diagram: components listed one per line with an exponential (failure rate or MTBF), Weibull (shape, scale) or fixed probability model and an optional repair time, and the structure typed as a text expression over their names with and (series), or (active parallel), k-of-n voting groups such as 2of3(D, E, F) and standby(G, H) cold-standby chains with perfect switching; a name used in more than one path (a bridge) is handled exactly by pivotal decomposition. The page reports each component's reliability at the mission time, the system reliability with the structure written back in words, the equivalent series product, the reliability curve and the mission times at which it reaches 90 % and 50 %, the system MTTF by numerical integration and the hazard rate at t, the steady-state availability from the MTBF and MTTR of each component, the Birnbaum and criticality importance of every component, Poisson spares provisioning for a chosen confidence and period, and an equal or ARINC apportionment of a target reliability. The default case is the series-parallel example of MIL-HDBK-338B §6.4.4.2.1.3, whose printed probability of success 0.13572 the page reproduces.

4 worked examples reproduced, listed on the tool page.

Fault Tree Analysis

Qualitative and quantitative fault tree analysis of a tree typed as text: gates as OR(...), AND(...), k-of-n voting gates such as 2of3(...), NOT and XOR, basic events given as a probability, as a failure rate with a mission time, a mean repair time or a test interval, house events set true or false, and common-cause groups by the β-factor model. The page echoes the tree as an indented list and a drawing with the standard gate symbols, finds the minimal cut sets by top-down (MOCUS) expansion with Boolean reduction and orders them by probability with the cumulative share, gives the top-event probability by the rare-event approximation, the min-cut upper bound and the exact value (Shannon decomposition over the cut sets, with the inclusion–exclusion brackets), ranks the basic events by Fussell–Vesely, Birnbaum, criticality, risk achievement worth and risk reduction worth, reports the common-cause contribution and lists the minimal path sets of the dual tree. The default case is the pressure tank of the NUREG-0492 Fault Tree Handbook (Chapter VIII, Table VIII-1), whose five minimal cut sets and cut-set importances of 14 % and 86 % the page reproduces.

1 worked example reproduced, listed on the tool page.

Other Reliability sections

Life Data · Growth and Testing · Physics of Failure · Maintainability and Availability · Safety Analysis