From e6dadcdef0fbf52a064193641c9395ae0743f6db Mon Sep 17 00:00:00 2001 From: Robin Clark Date: Mon, 28 Jun 2010 18:44:58 +0100 Subject: [PATCH] After swim in pells --- .../component_failure_modes_definition.tex~ | 108 ------------------ ...mponent_failure_modes_definition_paper.tex | 79 ------------- logic_diagram/logic_diagram.tex | 51 ++++++++- symptom_ex_process/symptom_ex_process.tex | 1 + 4 files changed, 46 insertions(+), 193 deletions(-) delete mode 100644 component_failure_modes_definition/component_failure_modes_definition.tex~ delete mode 100644 component_failure_modes_definition/component_failure_modes_definition_paper.tex diff --git a/component_failure_modes_definition/component_failure_modes_definition.tex~ b/component_failure_modes_definition/component_failure_modes_definition.tex~ deleted file mode 100644 index 18c3cd1..0000000 --- a/component_failure_modes_definition/component_failure_modes_definition.tex~ +++ /dev/null @@ -1,108 +0,0 @@ - -\abstract{ This chapter defines what is meant by the terms -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 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}. %The failure modes for a given component $K$ form a set $F$. - -An important factor in defining a set of failure modes is that they -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. - -Having a set of failure modes whhere $N$ modes could be active simultaneously -would mean having to consider $2^N$ failure mode scenarios. -% -Should a component be analysed and simultaneous failure mode cases exit, -the combinations could be represented by a new failure modes, or -the component should be considered from a fresh perspective, -perhaps considering it as several smaller components -within one package. - -\begin{definition} -A set of failure modes where only one fault mode -can be active at a time is termed a `unitary~state' failure mode set. -\end{definition} - -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 : Unitary State example} - -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 the failure mode set $F=FM(R)$ is `unitary~state'. -%A more complex component, say a micro controller could have several -%faults active. It could for instance have a broken I/O output -%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 -% are active is termed an `unitary~state' failure mode set. This -% 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. - -Thus for the set $F$ to exist in $U$ the following condition must be true. - -\begin{equation} -\label{unitarystate_def} - F \in U | f \in F \wedge active(f) \wedge f1 \in F \wedge f1 \neq f \wedge \neg active(f1) -\end{equation} - -As an example the resistor $R$ -has two failure modes $R_{open}$ and $R_{shorted}$. - -$$ FM(R) = F = \{ R_{open}, R_{shorted} \} $$ - -Applying equation \ref{`unitarystate'_definition} to a resistor -for both fault modes - - $$ active(R_{short}) | R_{short} \in F \wedge R_{open} \in F \wedge R_{open} \neq R_{short} \wedge \neg active(R_{open}) $$ - $$ active(R_{open}) | R_{open} \in F \wedge R_{short} \in F \wedge R_{short} \neq R_{open} \wedge \neg active(R_{short}) $$ - -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 `unitary~state' -component failure modes. - -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{`unitarystate'_def} - 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 ???? - - - diff --git a/component_failure_modes_definition/component_failure_modes_definition_paper.tex b/component_failure_modes_definition/component_failure_modes_definition_paper.tex deleted file mode 100644 index 660885f..0000000 --- a/component_failure_modes_definition/component_failure_modes_definition_paper.tex +++ /dev/null @@ -1,79 +0,0 @@ - -\abstract{ This chapter defines what is meant by the terms -components, component fault modes and `unitary~state' component fault modes. -Mathematical constraints and definitions are made using set theory. -} - - -\section{Introduction} -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}. %The failure modes for a given component $K$ form a set $F$. - -An important factor in defining a set of failure modes is that they -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. - -Having a set of failure modes where $N$ modes could be active simultaneously -would mean having to consider $2^N$ failure mode scenarios. -% -Should a component be analysed and simultaneous failure mode cases exit, -the combinations could be represented by a new failure modes, or -the component should be considered from a fresh perspective, -perhaps considering it as several smaller components -within one package. - -\begin{definition} -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}. -\end{definition} - -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 : Unitary State example} - -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 exclusive. -Because of this the failure mode set $F=FM(R)$ is `unitary~state'. - - -Thus - -$$ R_{SHORTED} \cap R_{OPEN} = \emptyset $$ - - -We can make this a general case by taking a set $C$ representing a collection -of component failure modes, -We can now state that - - -$$ c1 \cap c2 \neq \emptyset | c1 \neq c2 \wedge c1,c2 \in C \wedge C \not\in U $$ - -That is to say that if it is impossible that any pair of failure modes can be active at the same time -the failure mode set is not unitary~state and does not exist in the family of sets $U$ - - Note where that are more than two failure~modes, by banning pairs from happening at the same time - we have banned larger combinations as well - -%$$ c1 \cap c2 \eq \emptyset | c1 \neq c2 \wedge c1,c2 \in C \wedge C \in U $$ - -%Thus if the failure~modes are pairwaise mutually exclusive they qualify for inclusion into the -%unitary~state set family. diff --git a/logic_diagram/logic_diagram.tex b/logic_diagram/logic_diagram.tex index 9adf610..e134c40 100644 --- a/logic_diagram/logic_diagram.tex +++ b/logic_diagram/logic_diagram.tex @@ -3,13 +3,17 @@ { \begin{abstract} %This chapter describes using diagrams to represent propositional logic. -Propositial Logic Diagrams have been designed to provide an intuitive method for visualising and manipulating +Propositial Logic Diagrams (PLD) have been designed to provide an intuitive method for visualising and manipulating a specific sub-set of logic equations, to express fault modes in Mechanical and Electronic Systems. +PLDs are a variant of constraint diagrams. Contours used to express +sets represent failure modes and the Symptomatically merged groups +are akin to the `spiders' of constraint diagrams\ref{constraint}. %To aid hierarchical stages of fault analysis, it has been specifically developed for the purpose of %joining conjunctive conditions with disjuctive conditions %to group the effects of failure modes. -Diagrams of this type can also be used to model the logical conditions -that control the flow of a computer program. This type of diagram can therefore +PLD Diagrams can also be used to model the structure of software +and the flow of data through a computer program. +This type of diagram can therefore integrate logical models from mechanical, electronic and software domains. Nearly all modern safety critical systems involve these three disiplines. % @@ -29,7 +33,37 @@ The Diagrams described here form the mathematical basis for a new visual and for for the analysis of safety critical software and hardware systems. \end{abstract} } -{} +{ +\section{Intrduction} +Propositial Logic Diagrams (PLD) have been designed to provide an intuitive method for visualising and manipulating +a specific sub-set of logic equations, to express fault modes in Mechanical and Electronic Systems. +PLDs are a variant of constraint diagrams. Contours used to express +sets represent failure modes and the Symptomatically merged groups +are akin to the `spiders' of constraint diagrams\ref{constraint}. +%To aid hierarchical stages of fault analysis, it has been specifically developed for the purpose of +%joining conjunctive conditions with disjuctive conditions +%to group the effects of failure modes. +PLD Diagrams can also be used to model the structure of software +and the flow of data through a computer program. +This type of diagram can therefore +integrate logical models from mechanical, electronic and software domains. +Nearly all modern safety critical systems involve these three disiplines. +% +It is intended to be used for analysis of automated safety critical systems. +Many types of safety critical systems now legally +require fault mode effects analysis\cite{FMEA}, +but few formal systems exist and wide-spread take-up is +not yet the norm.\cite{takeup}. +% +Because of its visual nature, it is easy to manipulate and model +complicated conditions that can lead to dangerous failures in +automated systems. + +% No need to talk about abstraction yet, just define PLD PROPERLY + +The Diagrams described here form the mathematical basis for a new visual and formal system +for the analysis of safety critical software and hardware systems. +} %\title{Propositional Logic Diagrams} %\begin{keyword} @@ -44,14 +78,19 @@ for the analysis of safety critical software and hardware systems. % it deserves a whole chapter. +\ifthenelse {\boolean{paper}} +{ \section{Introduction} +} +{ -Propositional Logic Diagrams (PLDs) have been devised +} +Propositional Logic Diagrams (PLDs) have been created to collect and simplfy fault~modes in safety critical systems undergoing static analysis\cite{FMEA}\cite{SIL}. % This type of analysis treats failure modes within a system as logical -states. +states. PLD provides a visual method for modelling failure~mode analysis within these systems, and aids the collection of common failure symptoms. diff --git a/symptom_ex_process/symptom_ex_process.tex b/symptom_ex_process/symptom_ex_process.tex index 3386126..58b79e0 100644 --- a/symptom_ex_process/symptom_ex_process.tex +++ b/symptom_ex_process/symptom_ex_process.tex @@ -88,6 +88,7 @@ This chapter focuses on the process of building the blocks, the symptom extracti %\clearpage +\section{Fault Finding and Failure Mode Analysis} \subsection{Top Down or natural trouble shooting} It is interesting here to look at the `natural' trouble shooting process.