trying to get this fir for Andrew to see

component_failure_modes_definition/Makefile

@@ -0,0 +1,17 @@
+
+#
+# Make the propositional logic diagram a paper
+#
+
+
+paper:	paper.tex component_failure_modes_definition_paper.tex
+	#latex paper.tex
+	#dvipdf paper     pdflatex cannot use eps ffs
+	pdflatex paper.tex
+	okular paper.pdf
+
+
+# Remove the need for referncing graphics in subdirectories
+#
+component_failure_modes_definition_paper.tex: component_failure_modes_definition.tex
+	cat component_failure_modes_definition.tex | sed 's/component_failure_modes_definition\///' > component_failure_modes_definition_paper.tex

component_failure_modes_definition/component_failure_modes_definition.tex

@@ -1,67 +1,98 @@
 
 \abstract{ This chapter defines what is meant by the terms
-components, component fault modess and atomic component fault modes.
+components, component fault modess and `unitary~state' component fault modes.
 Mathematical constraints and definitions are made using set theory.
 }
 
  
 \section{Introduction}
-When building a system the components used, will have known failure modes.
+When building a system from components, 
+we should be able to find all known failure modes for each component.
 For most common electrical and mechanical components, the failure modes
 for a given type of part can be obtained from standard literature\cite{mil1991}
-\cite{mech}.
+\cite{mech}. %The failure modes for a given component $K$ form a set $F$.
 
-We can define a function $FM()$ to represent thiss, where K is the component
+An important factor in defining a failure mode is that they
-and F is the set of failure modes and A represents the set of atomic failure mode sets.
+should be as clearly defined as possible.
+%
+It should not be possible for instance for
+a component to have two or more failure modes active at once.
+Should this be the case, the failure modes have not been clearly analysed.
+The combination could be represented by a new failure mode, or
+the component should be re-analysed. A set of failure modes where only one fault mode
+can be active at a time is termed a `unitary~state' failure mode set.
 
-$$ FM : K \mapsto F | F \exits A $$
+We can define a function $FM()$ to 
+take a given component $K$ and return its set of failure modes $F$.
+
+$$  FM : K \mapsto F $$
+
+We can further define a set $U$ which is a set of sets of failure modes, where
+the component failure modes in each of its members are unitary~state.
+Thus if the failure modes of $F$ are unitary~state, we can say $F \in U$.
 
 
-\subsection{Component failure modes : Atomic definition}
+\subsection{Component failure modes : Unitary State example}
 
-Electrical resistors can fail by going OPEN or SHORTED for instance.
+A component with simple ``unitary~state'' failure modes is the electrical resistor.
+
+Electrical resistors can fail by going OPEN or SHORTED.
 However they cannot fail with both conditions active. The conditions
 OPEN and SHORT are mutually exlusive.
-Because of this these failure modes can be considered `atomic'.
+Because of this the failure mode set $F=FM(R)$ is `unitary~state'.
-A more complex component, say a micro controller could have several
+%A more complex component, say a micro controller could have several
-faults active. It could for instance have a broken I/O output
+%faults active. It could for instance have a broken I/O output
-and an unstable ADC input. Here the faults cannot be considered atomic.
+%and an unstable ADC input. Here the faults cannot be considered `unitary~state'.
 
-A set of failure modes, where only one or no failure modes
+% A set of failure modes, where only one or no failure modes
-are active is termed an atomic failure mode set. This
+% are active is termed an `unitary~state' failure mode set. This
-will be donoted as set $A$.
+% will be donoted as set $A$.
+% 
+To define `unitary~state' using set theory we can define a function
+`active'.
+The function $active(f)$ deontes that the failure mode $f$ (where $f$ is an element of $F$) is currently active.
 
-The function $active(f)$ deontes that the failure mode f is currently active.
+Thus for the set $F$ to exist in $U$ the following condition must be true.
-
-Thus for the set $F$ to exist in $A$ the following condition must be true.
 
 \begin{equation}
-\label{atomic_def}
+\label{unitarystate_def}
- active(f) | f \in F \wedge f1 \in F | f1 \neq f  \wedge \neg active(f1) 
+ F \in U | f \in F \wedge active(f) \wedge f1 \in \wedge  \neq f  \wedge \neg active(f1) 
 \end{equation}
 
 As an example the resistor $R$ 
-has two failure modes $_{open}$ and $R_{shorted}$. 
+has two failure modes $R_{open}$ and $R_{shorted}$. 
 
-$$ F = FM(R) = \{ R_{open}, R_{shorted} \} $$
+$$ FM(R) =  F = \{ R_{open}, R_{shorted} \} $$
  
-Applying equation \ref{atomic_definition} to a resistor
+Applying equation \ref{`unitarystate'_definition} to a resistor
 for both fault modes
 
- $$ active(R_{short}) | R_{short} \in F \wedge R_{open} \in F | R_{open} \neq R_{short}  \wedge \neg active(R_{open})  $$
+ $$ active(R_{short}) | R_{short} \in F \wedge R_{open} \in F \wedge R_{open} \neq R_{short}  \wedge \neg active(R_{open})  $$
- $$ active(R_{open}) | R_{open} \in F \wedge R_{short} \in F | R_{short} \neq R_{open}  \wedge \neg active(R_{short})  $$
+ $$ active(R_{open}) | R_{open} \in F \wedge R_{short} \in F \wedge R_{short} \neq R_{open}  \wedge \neg active(R_{short})  $$
 
 For the case of the resistor with only two failure modes the results above, being true,
-show that the failure modes for a resistor of $ F = \{ R_{open}, R_{shorted} \} $ are atomic
+show that the failure modes for a resistor of $ F = \{ R_{open}, R_{shorted} \} $ are `unitary~state'
 component failure modes.
 
-A general case can be stated by taking equation \ref{atomnic_def} and making it a function thus.
+Thus 
+     $$ FM(R) =  \{ R_{open}, R_{shorted} \} \in U $$
+
+
+A general case can be stated by taking equation \ref{unitary_state_def} and making it a function thus.
 
 
 \begin{equation}
-\label{atomic_def}
+\label{`unitarystate'_def}
- Atomic(F) =  \forall f \in F | active(f) \wedge  f1 \in F \wedge f1 \neq f  \wedge \neg active(f1) 
+ UnitaryState(F) =  \forall f \in F | active(f) \wedge  f1 \in F \wedge f1 \neq f  \wedge \neg active(f1) 
 \end{equation}
 
+%Which can be written
+
+%$$  UnitaryState(FM(K)) $$
+
+
+
+% should this be a paragraph in Symptom Abstraction ????
+
 
 

component_failure_modes_definition/paper.tex

@@ -0,0 +1,27 @@
+
+\documentclass[a4paper,10pt]{article}
+\usepackage{graphicx}
+\usepackage{fancyhdr}
+\usepackage{tikz}
+\usepackage{amsfonts,amsmath,amsthm}
+\input{style}
+
+%\newtheorem{definition}{Definition:}
+
+\begin{document}
+\pagestyle{fancy}
+
+\outerhead{{\small\bf Unitary State Failure Mode Sets}}         
+%\innerfoot{{\small\bf R.P. Clark } }   
+                                              % numbers at outer edges
+\pagenumbering{arabic}                        % Arabic page numbers hereafter
+\author{R.P.Clark}
+\title{Unitary State Failure Mode Sets}
+\maketitle 
+\input{component_failure_modes_definition_paper}
+
+\bibliographystyle{plain}
+\bibliography{vmgbibliography,mybib}
+
+\today
+\end{document}