added to introduction. Ill (bronchitis ~ off work ~ temperature)

but still need to finish the last example circuit for C Garret

old_thesis/opamp_circuits_C_GARRETT/opamps.tex

@@ -28,6 +28,7 @@
 
 \begin{document}
 \begin{abstract}
+\pagenumbering{roman}
 Circuits from email conversation.
 
 Not a document to be proof read.
@@ -37,24 +38,53 @@ Proof of analysis concept.
 Function $fm$ applied to a component returns its failure modes.
 
 
-The circuits specified are not typical saftey critical circuitry which usually
+The circuits specified are not typical safety critical circuitry which usually
 has both redundancy and self~checking and/or diagnostic features build in. 
 These are examples of the FMMD methodology being applied to some standard electronic circuits.
 \end{abstract}
 \maketitle
 \tableofcontents    
 \listoffigures  
+\listoftables
  
-
-\clearpage
+\clearpage \pagenumbering{arabic}
 \section{Basic Concepts Of FMMD}
 
+The idea behind FMMD is to modularise, from the bottom-up, traditional FMEA techniques.
+Traditional FMEA takes part failure modes and then determines what effect each of these
+failure modes could have on the system under investigation.
+It is worth defining clearly the term part here.
+Geoffry Hall writing in space Craft Systems Engineering~\cite{scse}[p.619], defines it thus: 
+``{Part(definition)}---The Lowest level of assembly, beyond which further disassembly irrevocably destroys the item''.
+In the field of electronics a resistor, capacitor and op-amp would fit this definition of a `part'.
+Failure modes for part types can be found in the literature~\cite{fmd91}\cite{mil1991}.
 
 
+Traditional FMEA, by looking at `part' level failure modes
+involves what we could term a large `reasoning~distance'; that is to say
+in a complex system, taking a particular failure mode, of a particular part
+and then trying to predict the outcome in the context of an entire system, is 
+a leap~of~faith. There will be numerous possibilities of effects and side effects on
+other components in the system; more than is practically possible to rigorously examine. 
+To simply trace a simple route from a particular part failure mode to a top level system error/symptom
+oversimplifies the task of failure mode analysis, and makes the process arbitrary and error prone.
+
+Fortunately most real-world designs take a modular approach. In Electronics
+for instance, commonly used configurations of parts are used to create
+amplifiers, filters, potential dividers etc.
+It is therefore natural to collect parts to form functional groups.
+These commonly used configurations of parts, or {\fgs}, will
+also have failure mode behaviour. We can take a {\fg} and determine its symptoms of failure.
+When we have done this we can treat this as a component in its own right.
+If we terms `parts' as base~components and components we have determined
+from functional groups as derived components, we can modularise the FMEA task.
+If we start building {\fgs} from derived components we can start to build a modular
+hierarchical failure mode model.
+
 \paragraph {Definitions}
 
 \begin{itemize}
-\item {\bc} - a component with a known set of unitary state failure modes. Base here mean a starting or `bought~in' component. 
+\item {\bc} - is taken to mean a `part' as defined above~\cite{scse}[p.619]. We should be able to define a set of failure modes for every {\bc}.
 \item {\fg} - a collection of components chosen to perform a particular task
 \item {\em symptom} - a failure mode of a functional group caused by one or more of its component failure modes.
 \item {\dc} - a new component derived from an analysed {\fg}
@@ -66,7 +96,6 @@ level up to the top, or system level, with analysis stages between each
 transition to a higher level in the hierarchy. 
 
 
-
 The first stage is to choose
 {\bcs} that interact and naturally form {\fgs}. The initial {\fgs} are   collections of base components.
 %These parts all have associated fault modes. A module is a set fault~modes.