Changed all the diagrams to make zones consistent in the examples.

logic_diagram/Makefile

@@ -1,4 +1,4 @@
-PDF_READER = acroread
+PDF_READER = okular
 #
 # Make the propositional logic diagram a paper
 #

logic_diagram/logic_diagram.tex

@@ -127,7 +127,8 @@ All features may be labelled, and the labels must be unique within a diagram, ho
 
 %Regions defined by contours are used to represent given conjunctive logical conditions.
 
-Test~cases are marked by asterisks. These are used as a visual `anchor'
+Test~cases are marked by asterisks. The asterisk is used rather than a point, because is analogous to the constraint
+diagram universal qualifier~\cite{uconstraintd}. These are used as a visual `anchor'
 to mark a logical condition, the logical condition being defined by the contours
 that enclose the region on which the test~case has been placed.
 The contours that enclose represent conjunction.
@@ -136,7 +137,7 @@ test~cases.
 
 With these three visual syntax elements, we have the basic building blocks for all logic equations possible.
 \begin{description}
-\item Test cases - Points (asterisks) on the plane indicating a logical condition.
+\item Test cases - (asterisks) on the plane indicating a logical condition.
 \item Conjunction - Overlapping contours
 \item Exclusive Disjunction - Joining of named test~cases.
 %\item Negation - Countours negatively named
@@ -266,7 +267,7 @@ associating a test-point with a set of contours in the plane. This corresponds t
 
 Pairs of test cases may be joined by joining lines.
 The operator $\stackrel{join}{\leftrightarrow}$ is used to
-show that two points are joined by a line in the concrete diagram.
+show that two test~cases are joined by a line in the concrete diagram.
 
 {
 \definition{
@@ -280,7 +281,7 @@ associating a joining line with a pair of test cases. The Join t1,t2 is defined
 }
 
 %In English:
-Test points on the concrete diagram pair-wise connected by a `joining line'
+Test~cases on the concrete diagram pair-wise connected by a `joining line'
 
 The graph formed by test~cases connected by joining lines is called an $SMG$.
 %A collection of test cases connected by joining lines, is an  Symptom Merged Group, $SMG$
@@ -387,7 +388,7 @@ $$\mathcal{G}(fmg) = \bigoplus_{t \in fmg} (\; \mathcal{F}_{t} (t) \;) \; .$$
 
 The semantics of the diagram is the set of logic terms representing all its SMGs, 
 along with unused zones (i.e. zones that are not inhabited by SMGs).
-Thus the abstract representation of the diagram, becomes a list of logic terms
+Thus the interpretation of the diagram, is a list of logic terms
 % and unused available zones
 .
 
@@ -433,6 +434,9 @@ we can derive a new diagram from the $SMG$s. Each $SMG$ represents a failure
 mode of the functional group, therefore in the higher level diagram
 each $SMG$ is represented by a contour.
 
+
+\input{fmmdstereoexample}
+
 {
 \definition{
 \label{SMGderivation}
@@ -477,9 +481,9 @@ validation and consistency checks applied.
 PLD diagrams are read by first looking at the test case asterisks.
 The test case asterisk will be enclosed by one or more contours.
 These contours are collated and used to form the logical conjunction 
-equation for the test case. 
+term for the test case. 
-These test case points thus represent the conjunctive aspects
+These test~cases thus represent the conjunctive aspects
-of an equation defined in a PLD. Where these test cases are joined by lines;
+of an term defined in a PLD. Where these test cases are joined by lines;
 these represent disjunction of the conjunctive aspects defined by the test cases.
 Joining lines thus represent exclusive disjunction in a PLD.
 
@@ -511,14 +515,14 @@ Joining lines thus represent exclusive disjunction in a PLD.
 \end{figure}
 
 
-In the diagram \ref{fig:ld_and} the area of intersection between the contours $a$ and $b$
+In the diagram \ref{fig:ld_and} the area of intersection between the contours $a$ and $c$
 represents the conjunction of those conditions. The point $P$ represents the logic equation
-$$ P = (a \wedge b) $$
+$$ P = (a \wedge c) $$
 There are no  joining lines % and so this diagram represents one equation only, $ P = (a \wedge b) $.
 and this diagram represents an $SMG$ with one element. %, $ (a \wedge b) $
 
 \paragraph{How this would be interpreted in failure analysis} 
-In failure analysis, this could be considered to be a functional~group with two failure states $a$ and $b$.
+In failure analysis, this could be considered to be a functional~group with two failure states $a$ and $c$.
 The proposition $P$ considers the scenario where both failure~modes are active.
 
 For base component level analysis, this would be considering two base component failures
@@ -541,35 +545,15 @@ sub-system failures, for instance two fuel shutdown safety valves failing to clo
  \label{fig:ld_or}
 \end{figure}
 
-% \begin{figure}[h]
-%  \centering
-%  \includegraphics[width=250pt]{logic_diagram/ldor.jpg}
-%  % ldor.jpg: 476x264 pixel, 72dpi, 16.79x9.31 cm, bb=0 0 476 264
-%  \label{fig:ld_or}
-%  \caption{Logical XOR example PLD diagram}
-% \end{figure}
-
-% \begin{figure}[h+]
-% %\centering
-% %\input{ldor.tex}
-% \begin{center}
-%  \includegraphics[width=200pt,bb=0 0 450 404]{logic_diagram/ldor.jpg}
-%  % resistor_pld.eps: 0x0 pixel, 300dpi, 0.00x0.00 cm, bb=0 0 450 404
-% \end{center}
-% %\includegraphics[scale=0.60]{ldor.eps}
-% \caption{Logical OR}
-% \label{fig:ld_or}
-% \end{figure} % OR
-
 
 The diagram \ref{fig:ld_or} is converted to propositional logic by first looking at the test cases, and 
 the zones they are placed in. 
-$$ P = (a) $$ 
+$$ S = (a) $$ 
-$$ Q = (b) $$  
+$$ U = (b) $$  
 
 The two test cases are joined by a the line named $R$.
 We thus apply exclusive disjunction to the test cases:
-$$ R = P \oplus Q \; . $$ 
+$$ R = S \oplus U \; . $$ 
 substituting the test cases for their propositional logic equations gives
 \begin{equation}
  R = ((a) \oplus (b)) \; .
@@ -580,6 +564,7 @@ substituting the test cases for their propositional logic equations gives
 Equation \ref{eqn:l_or} would be interpreted to mean that
 either failure mode a or b occurring, would have the same failure symptom for the circuit/functional~group
 under analysis. If $a \wedge b$  occurred this could have a completely different failure mode symptom.
+The SMG $R$, says if either failure modes $a$ or $b$ occur singly, they have the same failure symptom.
 
 
 
@@ -595,9 +580,9 @@ under analysis. If $a \wedge b$  occurred this could have a completely different
 %two unnamed test cases.
 
 Diagram \ref{fig:ld_meq2} 
-shows three test~cases, Q, R and P.
+shows three test~cases, U, R and P.
 
-Z and W were labelled but this was not necessary for determination of the final expression
+S and T were labelled, but this was not necessary for determination of the final expression
 of $ R = b \oplus c $. 
 %The intended use of these diagrams, is that resultant logical conditions be used in a later stage of reasoning.
 %Test cases joined by disjunction, all become represented in one, resultant equation.
@@ -640,9 +625,11 @@ of $ R = b \oplus c $.
  \begin{tabular}{||c|c|l||} \hline \hline
    {\em $SMG$ }  & {\em Failure Mode equation } &  {\em comments  }      \\ \hline
      
-       P         &  $(b \wedge c)$    &  Symptom P is active when `$b \wedge a$' is     \\ \hline
+       P         &  $(a \wedge c)$    &  Symptom P is active when `$a \wedge c$' is     \\ \hline
-       Q         &  $(a)$           &    Symptom Q is active when fault mode `a` is     \\ \hline
+    
-       R         &  $(b \oplus c)$  &    Symptom R is active when either `b' or `c' is     \\ \hline
+       R         &  $(a \oplus c)$  &    Symptom R is active when either `a' or `c' is     \\ \hline
+       U        &  $(b)$           &    Symptom U is active when fault mode `b` is     \\ \hline
+       % symptom U is only guaranteed when it is the only active failure mode in the {\fg}
       % T         &  T  &    T     \\ \hline \hline
  \end{tabular}
 \vspace{0.3cm}
@@ -650,8 +637,8 @@ of $ R = b \oplus c $.
 
 \paragraph{How this would be interpreted in failure analysis} 
 In failure analysis, this could be considered to be a functional~group with three failure states $a$,$b$ and $c$.
-It has three SMG's Q,R and P. Thus there are three ways in which this functional~group is considered to fail.
+It has three SMG's $P$,$R$ and $U$. Thus there are three ways in which this functional~group is considered to fail.
-
+Note that symptom $U$ is only guaranteed when it is the only active failure mode in the {\fg}.
 %\clearpage
 
 
@@ -671,31 +658,15 @@ a software tool which assists in drawing these diagrams.
  \label{fig:repeated}
 \end{figure}
 
-% 
-% \begin{figure}[h]
-%  \centering
-%  \includegraphics[bb=0 0 485 206]{logic_diagram/repeated.jpg}
-%  % repeated.jpg: 539x229 pixel, 80dpi, 17.11x7.27 cm, bb=0 0 485 206
-%  \label{fig:repeat}
-% \end{figure}
-
-%  \begin{figure}[h]
-%  \centering
-%  \includegraphics[bb=0 0 486 206]{./repeated.jpg}
-%  % repeated.eps: 0x0 pixel, 300dpi, 0.00x0.00 cm, bb=0 0 486 206
-%  \label{fig:repeated}
-% \end{figure}
-
-
 
 The diagram \ref{fig:repeated} is converted to propositional logic by first looking at the test cases, and 
 the contours they are placed on thus: 
-$$ P = (b) \; ,$$ 
+$$ U = (b) \; ,$$ 
-$$ Q = (a) \wedge (c) \; .$$  
+$$ P = (a) \wedge (c) \; .$$  
 
 The two test cases are joined by a the line named $R1$.
 we thus apply disjunction to the test cases:
-$$ R1 = P \oplus Q \;,$$ 
+$$ R1 = U \oplus P \;,$$ 
 $$ R1 = b \oplus ( a \wedge c ) \; .$$
 
 $R2$ joins two other test cases
@@ -711,7 +682,7 @@ The third SMG %or  symptom
 shown is test case $R3$ (representing equation $a \wedge b$).
 This diagram is incomplete, there is no test case for the fault mode $a$.
 The `available region' $a \backslash b$ (i.e. the area defined by contour $a$ excluding contour $b$) has no test case, 
-and this would be considered a `syntax error'
+and this could be considered a `syntax error'
 by the FMMD software tool.
 
 
@@ -871,7 +842,23 @@ The test case AFE represents the condition where all four engines have failed \c
 
 \section{Conclusion}
 
-
+PLD's provide a means to visually model failure modes within {\fgs} and after analysis
+of the test cases, extract the {\fg}'s common failure symptoms.
+%
+Because PLD's model failure modes generally, they are not constrained to 
+any particular discipline.
+%
+Most methodologies are aimed at solving problems for a particular discipline, 
+UML for instance is only suitable for modelling software.
+FMEA, FMEDA and FMECA are good at modelling
+electronic and mechanical systems, but struggle with software.
+%
+FTA models all systems, but from the top down, and rarely giving complete coverage
+to all base component failure modes.
+%
+PLD's can be used to model Mechanical, Electrical and Software
+failure modes. More importantly the interfaces between these disciplines can be modelled
+seamlessly.
 % Elevator Pitch
 
 %\pagebreak[4]