diff --git a/component_failure_modes_definition/component_failure_modes_definition.tex b/component_failure_modes_definition/component_failure_modes_definition.tex index 00e3be8..d22cb19 100644 --- a/component_failure_modes_definition/component_failure_modes_definition.tex +++ b/component_failure_modes_definition/component_failure_modes_definition.tex @@ -375,6 +375,8 @@ be less. What must actually be done is to subtract the number of component `internal combinations' from the cardinality constrain powerset number. +\subsubsection{Example: Two Component functional group \\ cardinality Constraint of 2} + Thus were we to have a simple functional group with two components R and T, of which $$FM(R) = \{R_o, R_s\}$$ and $$FM(T) = \{T_o, T_s, T_h\}$$. @@ -426,6 +428,10 @@ And by inspection $$ |\mathcal{P}_{2}(FG_cfg)| = 11 $$ + +\subsubsection{Establishing Formulae for unitary state failure mode \\ +cardinality calculation} + The cardinality constrained powerset equation \ref{eqn:ccps} corrected for unitary state failure modes can be written as a general formula (see equation \ref{eqn:correctedccps}), where C is a set of the components (indexed by j where J @@ -446,10 +452,10 @@ Expanding the combination in equation \ref{eqn:correctedccps} \label{eqn:correctedccps2} \end{equation} -The equation \ref{eqn:correctedccps2} is now useful for an automated tool that +Equation \ref{eqn:correctedccps2} is useful for an automated tool that would verify that a `N' simultaneous failures model had been completly covered. By knowing how many test case should be covered, and checking the cardinality -associated with the test cases complete coverage could be confirmed. +associated with the test cases complete coverage would be confirmed. %$$ \#\mathcal{P}_{cc} S = \sum^{k}_{1..cc} \big[ \frac{\#S!}{k!(\#S-k)!} - \sum_{j} (\#C_{j} \choose cc \big] $$