editing fmmdset and using FG and C instead of modules and derived sets etc

fmmdset/fmmdset.tex

@@ -130,10 +130,24 @@ at a higher abstraction level.
 \subsubsection{An algebraic notation for identifying FMMD enitities}
 Each component $C$ is a set of failure modes for the component.
 We can define a function $FM$ that returns the 
-set of failure modes $S$ for the component.
+set of failure modes $F$ for the component $C$.
+
+Let the set of all possible components  be $\mathcal{C}$
+and let the set of all possible failure modes be $\mathcal{F}$.
+
+We can define a function $FM$
+
+\begin{equation}
+FM : \mathcal{C} \mapsto \mathcal{P}\mathcal{F}
+\end{equation}
+
+defined by, where C is a component and F is a set of failure modes.
+
+$$  FM ( C ) = F $$
+
 
 %$$ \mathcal{FM}(C) \rightarrow S $$
-$$ {FM}(C) \rightarrow S $$
+%$$ {FM}(C) \rightarrow S $$
 
 We can indicate the abstraction level of a component by using a superscript.
 Thus for the component $C$, where it is a `base component' we can asign it
@@ -223,7 +237,7 @@ We can represent this analysis process in a diagram see figure \ref{fig:onestage
 
 \begin{figure}[h]
  \centering
- \includegraphics[width=400pt,bb=0 0 555 520,keepaspectratio=true]{fmmdset/fmmdh.png}
+ \includegraphics[width=400pt,bb=0 0 555 520,keepaspectratio=true]{fmmdset/fmmdh.jpg}
  % fmmdh.png: 555x520 pixel, 72dpi, 19.58x18.34 cm, bb=0 0 555 520
  \caption{FMMD Example Hierarchy}
  \label{fig:fmmdh}
@@ -235,15 +249,20 @@ We can represent this analysis process in a diagram see figure \ref{fig:onestage
 Figure \ref{fig:fmmdh} shows a hierarchy of failure mode de-composition.
 
 It can be seen that the derived fault~mode sets are higher level abstractions of the fault behaviour of the modules.
-We can take this one stage further by combining the $D^{1}_{N}$ sets to form modules. These 
-$M^2_{N}$ fault mode collections can be used to create $D^3_{N}$ derived fault~modes sets and so on.
+We can take this one stage further by combining the derived component $C^{1}_{N}$ sets to form functional~groups. These 
+$FG^2_{N}$ functional~groups can be used to create $C^3_{N}$ derived components and so on.
 At the top of the hierarchy, there will be one final (where $t$ is the 
-top level) set $D^{t}_{N}$ of abstract fault modes. The causes for these
-system level fault~modes will be traceable down to part fault modes. 
+top level) component $C^{t}_{N}$ and {\em its fault modes, are the failure modes of the SYSTEM}. The causes for these
+system level fault~modes will be traceable down to part fault modes, traversing the tree
+through the lower level functional groups and components. 
+each SYSTEM level fault may have a number of paths through the 
+tree to different low level of base component failure modes.
+In FTA terminology, these paths through the tree are called `minimal cut sets'.
 
 
 A hierarchy of levels of faults becoming more abstract at each level should
 converge to a small sub-set of system level errors.
+
 This thinning out of the number of system level errors is borne out in practise;
 real time control systems often have a small number of major reportable faults (typically $ < 50$), 
 even though they may have accompanying diagnostic data.
@@ -287,6 +306,13 @@ Also this means that we may need dummy modules so as not to violate jumping up t
 %% CASE STUDY BEGIN
 
 \subsection{Case Study FMMD Hierarchy:\\ Simple RS-232 voltage reader}
+\begin{figure}[h]
+ \centering
+ \includegraphics[width=340pt,bb=0 0 532 192,keepaspectratio=true]{./mvsblock.jpg}
+ % mvsblock.png: 532x192 pixel, 72dpi, 18.77x6.77 cm, bb=0 0 532 192
+ \caption{Milli-Volt Sensor Block Diagram}
+ \label{fig:mvsblock}
+\end{figure}
 
 
 %%% This is the tikz picture ??/
@@ -300,13 +326,13 @@ Also this means that we may need dummy modules so as not to violate jumping up t
 %\end{figure}
 %
 Consider a simple electronic system, that provides say two milli-volt amplifiers
-which passes the values onward via serial link - RS232. This is simple in concept, plug in a 
+which passes the values onward via serial link - RS232 (see figure \ref{fig:mvsblock}). This is simple in concept, plug in a 
 computer, run a terminal program, and the instrument will report the milli volt readings in ASCII
 with any error messages.
 
 % in CRC checksum protected packets.
 
-It is interesting to look at one of `functional groups'. The milli-volt amplifiers are a good example.
+It is interesting to look at one of `functional~groups'. The milli-volt amplifiers are a good example.
 These can be analysed by taking a functional~group, the components surrounding the op-amp, 
 a few resistors to determine offset and gain,
 a safety resistor, and perhaps some smoothing capacitors.
@@ -327,12 +353,22 @@ via the RS232 serial line.
 
 \begin{figure}[h]
  \centering
- \includegraphics[width=400pt,bb=0 0 749 507,keepaspectratio=true]{fmmdset/millivolt_sensor.png}
- % millivolt_sensor.png: 749x507 pixel, 72dpi, 26.42x17.89 cm, bb=0 0 749 507
- \caption{Hierarchial Module Diagram : Millivolt Sensor Example}
- \label{fig:mvs}
+ \includegraphics[width=400pt,bb=0 0 783 638,keepaspectratio=true]{./millivolt_sensor.jpg}
+ % millivolt_sensor.jpg: 783x638 pixel, 72dpi, 27.62x22.51 cm, bb=0 0 783 638
+ \caption{FMMD Hierarchy: Milli-volt sensor Example}
+ \label{fig:vs}
 \end{figure}
 
+
+% 
+% \begin{figure}[h]
+%  \centering
+%  \includegraphics[width=400pt,bb=0 0 749 507,keepaspectratio=true]{fmmdset/millivolt_sensor.png}
+%  % millivolt_sensor.png: 749x507 pixel, 72dpi, 26.42x17.89 cm, bb=0 0 749 507
+%  \caption{Hierarchial Module Diagram : Millivolt Sensor Example}
+%  \label{fig:mvs}
+% \end{figure}
+
 This has a number of obvious functional~groups, the PCB power supply, the milli-volt amplifiers,
 the analog to digital conversion circuitry, the micro processor and the UART (serial link - RS232 transceiver).
 It would make sense when analysing this system to take each one of these functional~groups in turn and examine them closely.
@@ -401,13 +437,25 @@ a  `CHANNEL\_1' input fault.
 %\end{list}
 \end{description}
 
-
-
-
-
 Thus we have looked at a single part fault and analysed its effect from the
 bottom up on the system as a whole, going up through the abstraction layers.
 
+\subsection{Natural Fault finding}
+
+Suppose that we were handed one of these `dual milli-volt' sensors and told that it had a ``Channel 1''
+fault and asked to trouble shoot and hopefully fix it.
+The natural process would be to work from the top down.
+First of all we would look at perhaps a circuit schematic.
+We might, not beliving the operator that the equipment is actually faulty, feed in a known and valid milli-volt signal into the input.
+On verifying it was actually faulty,
+we could then find the ADC port pins used to make the reading, and measure a voltage on them.
+We would find that the voltage was indeed out of range and our attention would turn to
+the circuitry between the input milli-volt signal and the ADC/Microcontroller.
+On examining this we would probably measure the in circuit resistances
+and discover the faulty resistor.
+With the natural fault finding process, we have narrowed down until we come to
+the faulty component. FMMD analysis works from the bottom~up, and this is
+because it must cover all component failure modes.
 %%
 %% END CASE STUDY
 %%
@@ -465,8 +513,8 @@ This is commponly referred to as a multi-channel safety critical system.
 Where there are 2 channels and one arbiter, the term 1oo2 is used (one out of two).
 The Ericsson AXE telephone exchange hardware is a 1oo2 system, and the arbiter (the AMD)
 can detect and switch control within on processor instruction. Should a hardware error
-be detected,\footnote{or in a test plant environment more likely someone coming along and `borrowing' a cpu board from
-your working exchange} the processor will side to the redundant side without breaking any telephone calls
+be detected,\footnote{Or in a test plant environment, more likely someone coming along and `borrowing' a cpu board from
+your working exchange} the processor will switch to the redundant side without breaking any telephone calls
 or any being set up. An alarm will be raised to inform that this has happened, but the impact to
 the 1oo2 system, is a one micro-processor instruction delay to the entire process.