Faults and Fault Detection
Last Edit July 22, 2001
The problem is to construct a complete and minimal test set such that
any single fault condition is detected, provided that masking has not
covered the effects.
During research into applications of Svoboda's Boolean Analyzer, a method
of deriving a Minimal Test Sequence was discovered. It was, at that time,
applied to combinatorial circuits and indicated that it could probably
be applied to sequential circuits [Svoboda, White, 1974]. Since that time,
the method for deriving test sequences for sequential circuits has been
The first step in developing a Minimal Test Sequence is the derivation
of the circuit equations. These have been found to be implementation-independent.
They may be derived on a gate by gate basis from a particular implementation,
but the resulting sequence will always be the same as that derived for
a minimized implementation of the circuit. Internal nets (intermediate
variables) are not required to be in the final equations. If intermediate
variables are to be carried through, they are treated as unknowns
Primary output variables are treated as unknowns. Primary input variables
are the knowns.
A primary input is an input that is connected to an external source.
A primary output is an output going to an external sink or connection.
After all equations for all gates are listed for a circuit, form the Existence
Function by solving the equation:
( F = G ) <==> ( y = 1 )
where y is the output. Equations of the form F = G can be rewritten as:
( F G ' + F ' G = 0 ) <==> ( y = 0 )
where F G ' + F ' G = 0
expresses the validity requirements for the complement functions.
The Existence Function contains all behavior properties of the circuit.
Fault testing problems are solved by adding equations to the system equations
or by processing the Existence Function after it is derived.