FMMD software paper proof read.

diagrams updted to D rather than bowtie notation

papers/fmmd_software_hardware/mybib.bib

@@ -0,0 +1 @@
+../../mybib.bib

papers/fmmd_software_hardware/software_fmmd.tex

@@ -56,6 +56,7 @@
 %\renewcommand{\rmdefault}{tnr}
 %\newboolean{paper}
 %\setboolean{paper}{true} % boolvar=true or false
+\newcommand{\derivec}{{D}}
 \newcommand{\ft}{\ensuremath{4\!\!\rightarrow\!\!20mA} }
 \newcommand{\permil}{\ensuremath{{ }^0/_{00}}}
 \newcommand{\oc}{\ensuremath{^{o}{C}}}
@@ -352,11 +353,11 @@ of the {\fg} from which it was derived.
 % in a specific configuration. This specific configuration corresponds to 
 % a {\fg}. Our use of it as a building block corresponds to a {\dc}.
 
-We can use the symbol `$\bowtie$' to represent the creation of a derived component 
+We can use the symbol `$\derivec$' to represent the creation of a derived component 
 from a {\fg}. This symbol is convenient for drawn hierarchy diagrams. % (see figure~\ref{fmmdh}). 
-We define the $\bowtie$ function, where $\FG$ is the set of all {\fgs} and $\DC$ is the set of all {\dcs},
+We define the $\derivec$ function, where $\FG$ is the set of all {\fgs} and $\DC$ is the set of all {\dcs},
 
-$$ \bowtie ( {\FG} ) \mapsto {\DC} .$$
+$$ \derivec ( {\FG} ) \mapsto {\DC} .$$
 
 We show an FMMD hierarchy in figure~\ref{fig:fmmdh}.
 Using this diagram, we can follow the creation of the hierarchy in 
@@ -368,7 +369,7 @@ That is to say their component failure modes are examined, and thus
 the ways in which the {\fgs} can fail. The ways in which a 
 {\fg} can fail, can be viewed as symptoms of failure for the {\fg}.
 %
-The `$\bowtie$' function is now applied to create {\dcs}.
+The `$\derivec$' function is now applied to create {\dcs}.
 These are shown in  figure~\ref{fig:fmmdh} above the {\fgs}.
 Now that we have {\dcs}, we can use them to form a higher level functional group.
 We apply the same FMEA process to this and can derive a top level
@@ -414,7 +415,7 @@ When we have analysed a software function---using failure conditions
 of its inputs as failure modes---we can 
 determine its symptoms of failure (i.e. how calling functions will see its failure mode behaviour).
 
-We can thus apply the $\bowtie$ process to software functions, by viewing them in terms of their failure
+We can thus apply the $\derivec$ function to software functions, by viewing them in terms of their failure
 mode behaviour. To simplify things as well, software already fits into a hierarchy.
 For Electronics and Mechanical systems, although we may be guided by the original designers
 concepts of modularity and sub-systems in design, applying FMMD means deciding on the members for {\fgs}
@@ -757,8 +758,8 @@ With these failure modes, we can analyse our first functional group, see table~\
 We now collect the symptoms for the hardware functional group, $\{ HIGH , LOW, V\_ERR \} $.
 We now create a {\dc} to represent this called $CMATV$.
 
-We can express this using the `$\bowtie$' function thus:
+We can express this using the `$\derivec$' function thus:
-$$ CMATV = \; \bowtie (G_1) .$$
+$$ CMATV = \; \derivec (G_1) .$$
 
 As its failure modes are the symptoms of failure from the functional group we can now state:
 $$fm ( CMATV ) =  \{ HIGH , LOW, V\_ERR \} .$$
@@ -844,7 +845,7 @@ for the function.
 This postcondition, {\em /* ensure: value is voltage input to within 0.1\% */ },
 corresponds to $VV\_ERR$, and is already in the {\fm} set for this {\fg}.
 
-We can now create a {\dc} called $RADC$ thus: $$RADC = \; \bowtie(G_2)$$ which has the following
+We can now create a {\dc} called $RADC$ thus: $$RADC = \; \derivec(G_2)$$ which has the following
 {\fms}:
 
 $$ fm(RADC) = \{ VV\_ERR, HIGH, LOW \} .$$
@@ -914,7 +915,7 @@ The $VAL\_ERR$ will mean that the value read is simply wrong.
 
 We can finally make a {\dc} to represent a failure mode model for our function $read\_4\_20\_input$ thus:
 
-$$ R420I = \; \bowtie(G_3) .$$
+$$ R420I = \; \derivec(G_3) .$$
 
 This new {\dc} has the following {\fms}:
 $$fm(R420I) = \{OUT\_OF\_RANGE, VAL\_ERR\} .$$
@@ -940,18 +941,18 @@ as a hierarchical diagram, see figure~\ref{fig:hd}.
 
 
 
-We can represent the hierarchy in figure~\ref{fig:hd} algebraically, using the `$\bowtie$' function
+We can represent the hierarchy in figure~\ref{fig:hd} algebraically, using the `$\derivec$' function
 using the groups as intermediate stages:
 \begin{eqnarray*}
 G_1 &=&  \{R,ADC\} \\
-CMATV &=&  \;\bowtie (G_1) \\
+CMATV &=&  \;\derivec (G_1) \\
 G_2 &=& \{CMATV, read\_ADC \} \\
-RADC &=&  \; \bowtie (G_2) \\
+RADC &=&  \; \derivec (G_2) \\
 G_3 &=& \{ RADC, read\_4\_20\_input \} \\
-R420I &=&  \; \bowtie (G_3) \\
+R420I &=&  \; \derivec (G_3) \\
 \end{eqnarray*}
 or, a nested definition,
-$$ \bowtie \Big( \bowtie \big( \bowtie(R,ADC), read\_4\_20\_input \big), read\_4\_20\_input \Big). $$ 
+$$ \derivec \Big( \derivec \big( \derivec(R,ADC), read\_4\_20\_input \big), read\_4\_20\_input \Big). $$