Friday afternoon edits. Getting ready for 3 core chapters for 20AUG2010

component_failure_modes_definition/component_failure_modes_definition.tex

@@ -295,7 +295,7 @@ A set of failure modes where only one fault mode
 can be active at a time is termed a `unitary~state' failure mode set.
 %This is termed the $U$ set thoughout this study.
 This corresponds to the `mutually exclusive' definition in 
-probability theory\cite{probandstat}.
+probability theory\cite{probstat}.
 \end{definition}
 
 Let the set of all possible components to be $\mathcal{C}$
@@ -370,7 +370,7 @@ we have banned larger combinations as well.
 For some integrity levels of static analysis there is a need to consider not only single
 failure modes in isolation, but cases where more then one failure mode may occur
 simultaneously.
-It is an implied requirement of EN298 for instance to consider double simultaneous faults.
+It is an implied requirement of EN298\cite{en298} for instance to consider double simultaneous faults.
 To generalise, we may need to consider $N$ simultaneous 
 failure modes when analysing a functional group. This involves finding
 all combinations of failures modes of size $N$ and less.

introduction/introduction.tex

@@ -2,7 +2,7 @@
 
 \section{Introduction}
 
-$$ \int_{0\-}^{\infty}  f(t).e^{-s.t}.dt  \; | \; s \in \mathcal{C}$$
+%% $$ \int_{0\-}^{\infty}  f(t).e^{-s.t}.dt  \; | \; s \in \mathcal{C}$$
 
 This thesis describes the application of, mathematical (formal) techniques to
 the design of safety critical systems. 
@@ -30,19 +30,19 @@ They are generally left running unattended for long periods.
 They are subject to stringent safety regulations and 
 must conform to specific `EN' standards. 
 
-One cannot merely comply with the standards.
+For a non-safety critical product one can merely comply with the standards, and `self~certify' by applying a CE mark sticker.
-
+Safety critical products are categorised and listed. These require
-The product must be `certified' by an independent 
+certification by an independent and `competent body' recognised under European law.
-and 
+The certification process typically involves stress testing with repeated operation cycles
-`competent body' recognised under European law.
+over a specified a range of temperatures, electrical stress testing with high voltage interference, 
-The certification involved stress testing with repeated operation cycles,
+power supply voltage ranges with surges and dips, electro static discharge testing, and
-over a specified a range of temperatures, electrical stress testing with high voltage interference, and
-power supply voltage surges and dips, electro static discharge testing, and
 EMC (Electro Magnetic Compatibility). A significant part
-of this process however, was `static testing'. This involved looking at the design of the products,
+of this process however, is `static testing'. This involves looking at the design of the products,
-from the perspective of components failing, and the effect on safety this would have.
+from the perspective of environmental stresses, natural input fault conditions\footnote{For instance in a burner controller, the gas supply pressure reducing}, 
-Some of the static testing involved checking that the germane `EN' standards had
+components failing, and the effects on safety this could have.
-been complied with. Failure Mode Effects Analysis (FMEA) was also applied. This involved
+Some static testing involves checking that the germane `EN' standards have
+been complied with\footnore{for instance protection levels of enclosure, or down rating of electrical components}.
+Failure Mode Effects Analysis (FMEA) was also applied. This involved
 looking in detail at selected critical sections of the product and proposing
 component failure scenarios. 
 For each failure scenario proposed either a satisfactory
@@ -311,15 +311,15 @@ fault conditions are missed.
 
 % http://en.wikipedia.org/wiki/Autopilot
 \paragraph{Importance of self checking}
-To take an example of an Autopilot, simple early autopilots, 
+To take an example of an Aircraft Autopilot, simple early devices\footnote{from the 1920's simple aircraft autopilots were in service}, 
-prevented the aircraft staying from a compass bearing and kept it flying striaght and level. 
+prevented the aircraft straying from a compass bearing and kept it flying straight and level. 
 Were they to fail the pilot would notice quite quickly
 and resume manual control of the bearing.
 
 Modern autopilots control all aspects of flight including the engines, take off and landing phases.
-The automated system does not have the 
+The automated system do not have the 
-common sense of a human pilot either and if fed the wrong sensory information
+common sense of a human pilot; and if fed the incorrect sensory information
-could make horrendous mistakes. This means that simply reading sensors and applying control
+can make horrendous mistakes. This means that simply reading sensors and applying control
 corrections cannot be enough.
 Checking for error conditions must also be incorporated. 
 It could also develop an internal fault, and must be able to recognise and cope with this.
@@ -345,7 +345,7 @@ It could also develop an internal fault, and must be able to recognise and cope
 
 
 \paragraph{Component added to detect errors}
-The op-amp in the circuit in figure \ref{fig:imillivolt}, supplies a gain of $\approx 180$ \footnote{
+The op-amp in the circuit in figure \ref{fig:millivolt}, supplies a gain of $\approx 180$ \footnote{
 applying formula for non-inverting op-amp gain\cite{aoe} $\frac{150 \times 10^3}{820}+ 1 = 183$ }.
 The safety case here is that
 any amplified signal between 0.5 and 4 volts on the ADC will be considered in range. 
@@ -355,7 +355,15 @@ are produced by the Seebeck effect\cite{aoe}}
 Should the sensor become disconnected the input will drift up due to the safety resistor $R18$.
 This will cause the opamp to supply its maximum voltage, telling the system the sensor reading is invalid. 
 Should the sensor become shorted, the input will fall below 3mV and the op amp will
-supply a voltage below 0.5.
+supply a voltage below 0.5. Note that the sensor breaking and becoming open, or 
+becoming disconnected is the `Raison d'être' of this safety addition.
+This circuit would typically be used to amplify a thermocouple, which typically 
+fails by going open circuit.
+It {\em does}
+detect several other failure modes of this circuit and a full analysis is given in appendix \ref{mvamp}.
+% Note C14 shorting is potentially v dangerous could lead to a high output by the opamp being seen as a 
+% low temperature.
+
 %
 \paragraph{Self Checking}
 This introduces a level of self checking into the system.
@@ -481,6 +489,12 @@ But because of the top down nature of the FTA technique, the safety designer mus
 the environemtnal constraints of all component parts in order to use this correctly.
 This element of FTA is discussed in \ref{surveysc}
 
+\section{Therac 25}
+
+%% Here need more detail of what therac 25 was and roughly how it failed
+%% with refs to nancy
+%% and then highlight the fact that the safety analysis did not integrate software and hardware domains.
+
 \section{Problems with Natural Language}
 
 Written natural language desciptions can not only be ambiguous or easy to misinterpret, it
@@ -534,7 +548,7 @@ temperature being the most typical. Very often what happens to the system outsid
 \begin{itemize}
 \item To create a Bottom up FMEA technique that permits a connected hierarchy to be 
 built representing the fault behaviour of a system.
-\item To create a procedure where no component failure mode can be un-handled.
+\item To create a procedure where no component failure mode can be accidentally ignored.
 \item To create a user friendly formal common visual notation to represent fault modes
 in Software, Electronic and Mechanical sub-systems.
 \item To formally define this visual language in concrete and abstract domains.
@@ -544,7 +558,7 @@ highest abstract system 'top level'.
 \item To formally define the hierarchies and procedure for bulding them.
 \item To produce a software tool to aid in the drawing of diagrams and
 ensuring that all fault modes are addressed.
-\item to provide for deterministic and probablistic failure mode analysis processes
+\item to provide a data model that can be used as a source for  deterministic and probablistic failure mode analysis reports.
 \item To allow the possiblility of MTTF calculation for statistical
 reliability/safety calculations.
 \end{itemize}

logic_diagram/logic_diagram.tex

@@ -614,10 +614,14 @@ by the FMMD software tool.
 
 \subsection { Inhibit Failure }
 
+%
+% very interesting here Inhibit is ENCLOSURE and simultaneous faults are PURE INTERSECTION
+%
+
 
 Very often a failure mode can only occur
 given a separate environmental condition.
-In Fault Tree Analysis (FTA) this is represented by an inhibit gate.\cite{NASA},\cite{NUK}
+In Fault Tree Analysis (FTA) this is represented by an inhibit gate.\cite{FTA}[pp41-42],\cite{NUK}
  
   \begin{figure}[h]
  \centering
@@ -634,7 +638,7 @@ In Fault Tree Analysis (FTA) this is represented by an inhibit gate.\cite{NASA},
 % \end{figure}
 
 The diagram \ref{fig:inhibit} has a test case in the contour $C$.
-Contour $C$ is enclosed by contour $A$. This says
+Contour $C$ is \textbf{enclosed} by contour $A$. This says
 that for failure~mode $C$ to occur failure mode $A$
 must have occurred.
 A well known example of this is the space shuttle `O' ring failure that
@@ -845,6 +849,8 @@ To cover this rigorously, we are bound to consider more than one fault being act
 Because we are allowed to repeat contours in a PLD diagram, 
 we can arrange them in a matrix like configuration as in figure \ref{fig:doublesim}.
 Note that we have here all the single and double failure test cases in one diagram.
+Also not that the contours intersect but do not enclose. This
+configuration is being termed \textbf{pure instersection} of contours, in this study.
 
 \begin{figure}[h]
  \centering

mybib.bib

@@ -89,6 +89,13 @@
 }
 
 
+@BOOK{probstat,
+  AUTHOR =       " M~R~Spiegel",
+  TITLE =        "Probability and Statistics Second edition : SHCAUM'S :  ISBN 0-07-135004-7",
+  PUBLISHER =    "Oxford University Press",
+  YEAR =         "1988"
+}
+
 @BOOK{idmfssz,
   AUTHOR =       " D~C~Ince",
   TITLE =        " An Introduction to Discrete Mathematics, Formal System Specification and Z : Oxford :  ISBN 0-19-853836-7",

symptom_ex_process/algorithm.tex

@@ -282,24 +282,34 @@ $$ FCS(R) = SP $$
 
    %\REQUIRE {All failure modes for the components in $fm_i = FM(fg_i)$}
  \STATE   {Let $sp_l$ be a set of `test cases results' where $l$ is an index set $L$} 
-   \STATE   {Let $SP$ be a set whose members are sets $sp_l$} 
+   \STATE   {Let $SP$ be a set whose members are the indexed `symptoms' $sp_l$} 
    \COMMENT{ $SP$ is the set of `fault symptoms' for the sub-system}
+    \STATE{$SP   := 0$} \COMMENT{ initialise the `symptom family set'}
 %   
    %\COMMENT{This corresponds to a fault symptom of the functional group $FG$}
     %\COMMENT{where double failure modes are required the cardinality constrained powerset of two must be applied to each failure mode}
+\REPEAT 
 
-   \FORALL { $ r_j \in R$ } 
+    \STATE{$sp_l := 0$} \COMMENT{ initialise the `symptom'}
-          \STATE    { $sp_l \in \mathcal{P} R \wedge sp_l \in SP$ } 
+    \STATE{$sp_l \in \mathcal{P} R$} \COMMENT{Select common symptoms from the results set}
-          %\STATE   { $sp_l \in \bigcap R \wedge sp_l \in SP$ } 
+    \STATE{$ R := R \backslash sp_l $} \COMMENT{remove the results used from the results set}
-     \COMMENT{ Collect common symptoms.
+    \STATE{$ SP := SP \cup sp_l$} \COMMENT{collect the symptom into the symtom family set SP}
- Analyse the sub-system's fault behaviour under the failure modes in $tc_j$ and determine the symptoms $sp_l$ that it
+    \STATE{$ l := l + 1 $} \COMMENT{move the index up for the next symptom to collect}
-causes in the functional group $FG$}
-       %\ENSURE { $ \forall l2 \in L ( \forall l1 \in L | \exists a \in sp_{l1} \neq \exists b \in sp_{l2} \wedge l1 \neq l2 ) $}
 
-      \ENSURE {$ \forall a \in sp_l  \;such\;that\;    \forall sp_i \in \bigcap_{i=1..L} SP  ( sp_i = sp_l  \implies a \in sp_i)$} 
+\UNTIL{ $ R = \emptyset $ } \COMMENT{continue until all results belong to a symptom}
-      \COMMENT { Ensure that the elements in each $sp_l$ are not present in any other $sp_l$ set }
 
-   \ENDFOR
+%%   \FORALL { $ r_j \in R$ } 
+%%          \STATE    { $sp_l \in \mathcal{P} R \wedge sp_l \in SP$ } 
+%%          %\STATE   { $sp_l \in \bigcap R \wedge sp_l \in SP$ } 
+%%     \COMMENT{ Collect common symptoms.
+%% Analyse the sub-system's fault behaviour under the failure modes in $tc_j$ and determine the symptoms $sp_l$ that it
+%%causes in the functional group $FG$}
+%%       %\ENSURE { $ \forall l2 \in L ( \forall l1 \in L | \exists a \in sp_{l1} \neq \exists b \in sp_{l2} \wedge l1 \neq l2 ) $}
+%%
+%%      \ENSURE {$ \forall a \in sp_l  \;such\;that\;    \forall sp_i \in \bigcap_{i=1..L} SP  ( sp_i = sp_l  \implies a \in sp_i)$} 
+%%      \COMMENT { Ensure that the elements in each $sp_l$ are not present in any other $sp_l$ set }
+%%       	  
+%%   \ENDFOR
     \STATE  { The Set $SP$ can now be considered to be the set of fault modes for the sub-system that $FG$ represents}
 
   \RETURN $SP$