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crammed this into 5 pages

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papers/fmmd_software_hardware/software_fmmd.tex
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@ -65,10 +65,10 @@
\newcommand{\ohms}[1]{\ensuremath{#1\Omega}} \newcommand{\ohms}[1]{\ensuremath{#1\Omega}}
\newcommand{\fm}{failure~mode} \newcommand{\fm}{failure~mode}
\newcommand{\fms}{failure~modes} \newcommand{\fms}{failure~modes}
\newcommand{\fg}{functional~group} \newcommand{\fg}{functional~grouping}
\newcommand{\FG}{\mathcal{G}} \newcommand{\FG}{\mathcal{G}}
\newcommand{\DC}{\mathcal{DC}} \newcommand{\DC}{\mathcal{DC}}
\newcommand{\fgs}{functional~groups} \newcommand{\fgs}{functional~groupings}
\newcommand{\dc}{derived~component} \newcommand{\dc}{derived~component}
\newcommand{\dcs}{derived~components} \newcommand{\dcs}{derived~components}
\newcommand{\bc}{base~component} \newcommand{\bc}{base~component}
@ -99,9 +99,9 @@ failure mode of the component or sub-system}}}
\setlength{\topmargin}{0in} \setlength{\topmargin}{0in}
\setlength{\headheight}{0in} \setlength{\headheight}{0in}
\setlength{\headsep}{0in} \setlength{\headsep}{0in}
\setlength{\textheight}{22cm} %\setlength{\textheight}{22cm}
\setlength{\textwidth}{18cm} \setlength{\textwidth}{18cm}
\setlength{\textheight}{24cm} \setlength{\textheight}{24.5cm}
%\setlength{\textwidth}{20cm} %\setlength{\textwidth}{20cm}
\setlength{\oddsidemargin}{0in} \setlength{\oddsidemargin}{0in}
\setlength{\evensidemargin}{0in} \setlength{\evensidemargin}{0in}
@ -115,7 +115,13 @@ failure mode of the component or sub-system}}}
\setlength{\topmargin}{0pt} \setlength{\topmargin}{0pt}
\setlength{\topsep}{0pt} \setlength{\topsep}{0pt}
\setlength{\partopsep}{0pt} \setlength{\partopsep}{0pt}
%\linespread{0.5} \setlength{\itemsep}{1pt}
% \renewcommand\subsection{\@startsection
% {subsection}{2}{0mm}%
% {-\baslineskip}
% {0.5\baselineskip}
% {\normalfont\normalsize\itshape}}
\linespread{0.6}
\begin{document} \begin{document}
%\pagestyle{fancy} %\pagestyle{fancy}
@ -129,7 +135,7 @@ failure mode of the component or sub-system}}}
%\lhead{Developing a rigorous bottom-up modular static failure modelling methodology} %\lhead{Developing a rigorous bottom-up modular static failure modelling methodology}
% numbers at outer edges % numbers at outer edges
\pagenumbering{arabic} % Arabic page numbers hereafter \pagenumbering{arabic} % Arabic page numbers hereafter
\author{R.Clark$^\star$ \\ % , A.~Fish$^\dagger$ , C.~Garrett$^\dagger$, J.~Howse$^\dagger$ \\ \author{R.Clark$^\star$,A.~Fish$^\dagger$ , C.~Garrett$^\dagger$, J.~Howse$^\dagger$ \\
$^\star${\em Energy Technology Control, UK. r.clark@energytechnologycontrol.com} \and $^\dagger${\em University of Brighton, UK} $^\star${\em Energy Technology Control, UK. r.clark@energytechnologycontrol.com} \and $^\dagger${\em University of Brighton, UK}
} }
@ -181,7 +187,7 @@ can be applied to software, and is compatible
and integrate-able with FMMD performed on mechanical and electronic systems. and integrate-able with FMMD performed on mechanical and electronic systems.
} }
\today %\today
\nocite{en298} \nocite{en298}
\nocite{en61508} \nocite{en61508}
@ -199,7 +205,8 @@ to define failure modes and failure symptoms for
software functions. software functions.
% %
With these definitions we can apply the FMMD modular form of FMEA With these definitions we can apply the FMMD modular form of FMEA
to existing software\footnote{Existing software excluding recursive~\cite{misra}[16.2] code, and unstructured non-functional languages}. to existing software\footnote{Existing software excluding recursive~\cite{misra}[16.2] code,
and unstructured non-functional languages}.
} }
\section{FMEA Background} \section{FMEA Background}
@ -209,10 +216,11 @@ to existing software\footnote{Existing software excluding recursive~\cite{misra}
Failure Mode effects Analysis is the process of taking Failure Mode effects Analysis is the process of taking
component failure modes, and by reasoning, tracing their effects through a system component failure modes, and by reasoning, tracing their effects through a system
and determining what system level failure modes could be caused. and determining what system level failure modes could be caused.
%
FMEA dates from the 1940s where simple electro-mechanical systems were the norm. FMEA dates from the 1940s where simple electro-mechanical systems were the norm.
Modern control systems nearly always have a significant software/firmware element, Modern control systems nearly always have a significant software/firmware element,
and not being able to model software with current FMEA methodologies and not being able to model software with current FMEA methodologies
is a cause for criticism~\cite{easw}~\cite{safeware}~\cite{bfmea}. is a cause for criticism~\cite{safeware}.
%Several variants of FMEA exist, %Several variants of FMEA exist,
% traditional FMEA being associated with the manufacturing industry, with the aims of prioritising % traditional FMEA being associated with the manufacturing industry, with the aims of prioritising
@ -240,10 +248,10 @@ hardware and software models, but to perform
FMEA on the software in isolation~\cite{procsfmea}. FMEA on the software in isolation~\cite{procsfmea}.
Some work has been performed using databases Some work has been performed using databases
to track the relationships between variables to track the relationships between variables
and system failure modes~\cite{procsfmeadb}, and work has been performed to and system failure modes~\cite{procsfmeadb}, work has been performed to
introduce automation into the FMEA process~\cite{appswfmea} and code analysis introduce automation into the FMEA process~\cite{appswfmea} and code analysis
automation~\cite{modelsfmea}. Although the SFMEA and hardware FMEAs are performed separately automation~\cite{modelsfmea}. Although the SFMEA and hardware FMEAs are performed separately
some schools of thought aim for FTA~\cite{nasafta}~\cite{nucfta} (top down - deductive) and FMEA (bottom-up inductive) some schools of thought aim for FTA~\cite{nasafta,nucfta} (top down - deductive) and FMEA (bottom-up inductive)
to be performed on the same system to provide insight into the to be performed on the same system to provide insight into the
software hardware/interface~\cite{embedsfmea}. software hardware/interface~\cite{embedsfmea}.
% %
@ -255,15 +263,16 @@ through the top (and therefore ultimately controlling) layer of software.
\subsection{Current FMEA techniques are not suitable for software} \subsection{Current FMEA techniques are not suitable for software}
The main FMEA methodologies are all based on the concept of taking The main FMEA methodologies are all based on the concept of taking
base component {\fms}, and translating them into system level events/failures~\cite{sfmea}~\cite{sfmeaa}. base component {\fms}, and translating them into system level events/failures~\cite{sfmea,sfmeaa}.
In a complicated system, mapping a component failure mode to a system level failure In a complicated system, mapping a component failure mode to a system level failure
will mean a long reasoning distance; that is to say the actions of the failed component will have to be traced through will mean a long reasoning distance; that is to say the actions of the failed component will have to be traced through
several sub-systems and the effects of other components on the way. several sub-systems and the effects of other components on the way.
% %
With software at the higher levels of these sub-systems With software at the higher levels of these sub-systems
we have yet another layer of complication. we have yet another layer of complication.
%
In order to integrate software, in a meaningful way we need to re-think the In order to integrate software, %in a meaningful way
we need to re-think the
FMEA concept of simply mapping a base component failure to a system level event. FMEA concept of simply mapping a base component failure to a system level event.
% %
One strategy would be to modularise FMEA. To break down the failure effect One strategy would be to modularise FMEA. To break down the failure effect
@ -301,7 +310,6 @@ using all the failure modes of all its components.
When we have its failure mode behaviour, or the symptoms of failure from the perspective of the {\fg}, When we have its failure mode behaviour, or the symptoms of failure from the perspective of the {\fg},
we now treat the {\fg} as a {\dc}, where the failure modes of the {\dc} are the symptoms of failure of the {\fg}. we now treat the {\fg} as a {\dc}, where the failure modes of the {\dc} are the symptoms of failure of the {\fg}.
% %
%
We can now use {\dcs} to build higher level {\fgs} until we have a complete hierarchical model We can now use {\dcs} to build higher level {\fgs} until we have a complete hierarchical model
of the failure mode behaviour of a system. An example of this process, applied to an inverting op-amp configuration of the failure mode behaviour of a system. An example of this process, applied to an inverting op-amp configuration
is given in~\cite{syssafe2011}. is given in~\cite{syssafe2011}.
@ -386,7 +394,7 @@ derived component (which has the system---or top---level failure modes).
\begin{figure} \begin{figure}
\centering \centering
\includegraphics[width=200pt]{./fmmdh.png} \includegraphics[width=150pt]{./fmmdh.png}
% fmmdh.png: 365x405 pixel, 72dpi, 12.88x14.29 cm, bb=0 0 365 405 % fmmdh.png: 365x405 pixel, 72dpi, 12.88x14.29 cm, bb=0 0 365 405
\caption{FMMD Hierarchy} \caption{FMMD Hierarchy}
\label{fig:fmmdh} \label{fig:fmmdh}
@ -428,7 +436,7 @@ We can thus apply the $\derivec$ function to software functions, by viewing them
mode behaviour. To simplify things as well, software already fits into a hierarchy. mode behaviour. To simplify things as well, software already fits into a hierarchy.
For Electronics and Mechanical systems, although we may be guided by the original designers For Electronics and Mechanical systems, although we may be guided by the original designers
concepts of modularity and sub-systems in design, applying FMMD means deciding on the members for {\fgs} concepts of modularity and sub-systems in design, applying FMMD means deciding on the members for {\fgs}
and the subsequent hierarchy. With software already written, that hierarchy is fixed. and the subsequent hierarchy. With software already written, that hierarchy is fixed/given.
% map the FMMD concepts of {\fms}, {\fgs} and {\dcs} % map the FMMD concepts of {\fms}, {\fgs} and {\dcs}
%to software functions. %to software functions.
@ -452,45 +460,43 @@ What is potentially difficult with a software function, is deciding what
are its `failure~modes', and later what are its `failure~symptoms'. are its `failure~modes', and later what are its `failure~symptoms'.
% %
With electronic components, we can use literature to point us to suitable sets of With electronic components, we can use literature to point us to suitable sets of
{\fms}~\cite{fmd91}~\cite{mil1991}~\cite{en298}.%~\cite{en61508}~\cite{en298}. {\fms}~\cite{fmd91,mil1991,en298}.%,en61508}.%~\cite{en298}.
% %
With software, only some library functions are well known and rigorously documented With software, only some library functions are well known and rigorously documented
enough to have the equivalent of known failure modes. enough to have the equivalent of known failure modes.
Most software is `bespoke'. We need a different strategy to Most software is `bespoke'. We need a different strategy to
describe the failure mode behaviour of software functions. describe the failure mode behaviour of software functions.
We can use definitions from contract programming to assist here. We can use definitions from contract programming to assist here.
%
\subsection{Contract programming description} \subsection{Contract programming description}
%
Contract programming is a discipline~\cite{dbcbe} for building software functions in a controlled Contract programming is a discipline~\cite{dbcbe} for building software functions in a controlled
and traceable way. Each function is subject to pre-conditions (constraints on its inputs), and traceable way. Each function is subject to pre-conditions (constraints on its inputs),
post-conditions (constraints on its outputs) and function wide invariants (rules). post-conditions (constraints on its outputs) and function wide invariants (rules).
%
\paragraph{Mapping contract `pre-condition' violations to failure modes} \paragraph{Mapping contract `pre-condition' violations to failure modes}
%
A precondition, or requirement for a contract software function A precondition, or requirement for a contract software function
defines the correct ranges of input conditions for the function defines the correct ranges of input conditions for the function
to operate successfully. to operate successfully.
% %
For a software function, a violation of a pre-condition is For a software function, a violation of a pre-condition is
in effect a failure mode of `one of its components'. in effect a failure mode of `one of its components'.
%
\paragraph{Mapping contract `post-condition' violations to symptoms} \paragraph{Mapping contract `post-condition' violations to symptoms}
%
A post condition is a definition of correct behaviour by a function. A post condition is a definition of correct behaviour by a function.
A violated post condition is a symptom of failure of a function. A violated post condition is a symptom of failure of a function.
Post conditions could be either actions performed (i.e. the state of hardware changed) or an output value of a function. Post conditions could be either actions performed (i.e. the state of hardware changed) or an output value of a function.
%
\paragraph{Mapping contract `invariant' violations to symptoms and failure modes} \paragraph{Mapping contract `invariant' violations to symptoms and failure modes}
%
Invariants in contract programming may apply to inputs to the function (where they can be considered {\fms} in FMMD terminology), Invariants in contract programming may apply to inputs to the function (where they can be considered {\fms} in FMMD terminology),
and to outputs (where they can be considered {failure symptoms} in FMMD terminology). and to outputs (where they can be considered {failure symptoms} in FMMD terminology).
\subsection{Software FMMD} \subsection{Software FMMD}
%
For the purpose of example, we chose a simple common safety critical industrial circuit For the purpose of example, we chose a simple common safety critical industrial circuit
that is nearly always used in conjunction with a programmatic element. that is nearly always used in conjunction with a programmatic element.
A common method for delivering a quantitative value in analogue electronics is A common method for delivering a quantitative value in analogue electronics is
@ -509,15 +515,17 @@ and is therefore easy to detect as an error rather than an incorrect value.
Should the driving electronics go wrong at the source end, it will usually Should the driving electronics go wrong at the source end, it will usually
supply far too little or far too much current, making an error condition easy to detect. supply far too little or far too much current, making an error condition easy to detect.
% %
At the receiving end, we only require one simple component to convert the At the receiving end, need a resistor to convert the
current signal into a voltage that we can read with an ADC: the humble resistor! current signal into a voltage that we can read with an ADC.%
%we only require one simple component to convert the
%current signal into a voltage that we can read with an ADC: the humble resistor!
%BLOCK DIAGRAM HERE WITH FT CIRCUIT LOOP %BLOCK DIAGRAM HERE WITH FT CIRCUIT LOOP
\begin{figure}[h] \begin{figure}[h]
\centering \centering
\includegraphics[width=230pt]{./ftcontext.png} \includegraphics[width=200pt]{./ftcontext.png}
% ftcontext.png: 767x385 pixel, 72dpi, 27.06x13.58 cm, bb=0 0 767 385 % ftcontext.png: 767x385 pixel, 72dpi, 27.06x13.58 cm, bb=0 0 767 385
\caption{Context Diagram for {\ft} loop} \caption{Context Diagram for {\ft} loop}
\label{fig:ftcontext} \label{fig:ftcontext}
@ -545,15 +553,16 @@ As a voltage, we use ohms law~\cite{aoe} to determine the voltage ranges: $V=IR$
and $0.020A * \ohms{220} = 4.4V$. and $0.020A * \ohms{220} = 4.4V$.
% %
Our acceptable voltage range is therefore Our acceptable voltage range is therefore
%
$$(V \ge 0.88) \wedge (V \le 4.4) \; .$$ $(V \ge 0.88) \wedge (V \le 4.4) \; .$
This voltage range forms our input requirement. This voltage range forms our input requirement.
% %
We can now examine a software function that performs a conversion from the voltage read to We can now examine a software function that performs a conversion from the voltage read to
a per~mil representation of the {\ft} input current. a per~mil representation of the {\ft} input current.
% %
For the purpose of example the `C' programming language~\cite{kandr} is used\footnote{ C coding examples use the Misra~\cite{misra} and SIL 3 recomended language constraints~\cite{en61508}.}. For the purpose of example the `C' programming language~\cite{DBLP:books/ph/KernighanR88} is
used\footnote{ C coding examples use the Misra~\cite{misra} and SIL 3 recommended language constraints~\cite{en61508}.}.
We initially assume a function \textbf{read\_ADC} which returns a floating point %double precision We initially assume a function \textbf{read\_ADC} which returns a floating point %double precision
value which represents the voltage read (see code sample in figure~\ref{fig:code_read_4_20_input}). value which represents the voltage read (see code sample in figure~\ref{fig:code_read_4_20_input}).
@ -661,16 +670,18 @@ double read_ADC( int channel ) {
%} %}
We now have a very simple software structure, a call tree, shown in figure~\ref{fig:ct1}. We now have a very simple software structure, a call tree, where {\em read\_4\_20\_input}
calls {\em read\_ADC}, which in turn interacts with the hardware/electronics.
\begin{figure}[h] %shown in figure~\ref{fig:ct1}.
\centering %
\includegraphics[width=100pt]{./ct1.png} % \begin{figure}[h]
% ct1.png: 151x224 pixel, 72dpi, 5.33x7.90 cm, bb=0 0 151 224 % \centering
\caption{Call tree for software example} % \includegraphics[width=56pt]{./ct1.png}
\label{fig:ct1} % % ct1.png: 151x224 pixel, 72dpi, 5.33x7.90 cm, bb=0 0 151 224
\end{figure} % \caption{Call tree for software example}
% \label{fig:ct1}
% \end{figure}
%
This software is above the hardware in the conceptual call tree---from a programmatic perspective---%in software terms---the This software is above the hardware in the conceptual call tree---from a programmatic perspective---%in software terms---the
software is reading values from the `lower~level' electronics. software is reading values from the `lower~level' electronics.
% %
@ -697,11 +708,11 @@ Our functional group, $G_1$ is thus the set of base components: $G_1 = \{R, ADC\
We now determine the {\fms} of all the components in $G_1$. We now determine the {\fms} of all the components in $G_1$.
For the resistor we can use a failure mode set from the literature~\cite{en298}. For the resistor we can use a failure mode set from the literature~\cite{en298}.
Where the function $fm$ returns a set of failure modes for a given component we can state: Where the function $fm$ returns a set of failure modes for a given component we can state:
%
$$ fm(R) = \{OPEN,SHORT\}. $$ $ fm(R) = \{OPEN,SHORT\}. $
\vbox{ \vbox{
For the ADC we can determine the following failure modes: For the ADC we can determine the following failure modes:
%
\begin{itemize} \begin{itemize}
\item STUCKAT --- The ADC outputs a constant value, \item STUCKAT --- The ADC outputs a constant value,
\item MUXFAIL --- The ADC cannot select its input channel correctly, \item MUXFAIL --- The ADC cannot select its input channel correctly,
@ -710,8 +721,8 @@ For the ADC we can determine the following failure modes:
\end{itemize} \end{itemize}
} }
We can use the function $fm$ to define the {\fms} of an ADC thus: We can use the function $fm$ to define the {\fms} of an ADC thus:
$$ fm(ADC) = \{ STUCKAT, MUXFAIL,LOW, HIGH \}. $$ $ fm(ADC) = \{ STUCKAT, MUXFAIL,LOW, HIGH \}. $
%
With these failure modes, we can analyse our first functional group, see table~\ref{tbl:cmatv}. With these failure modes, we can analyse our first functional group, see table~\ref{tbl:cmatv}.
{ {
@ -758,10 +769,10 @@ We now collect the symptoms for the hardware functional group, $\{ HIGH , LOW, V
We now create a {\dc} to represent this called $CMATV$. We now create a {\dc} to represent this called $CMATV$.
% %
We can express this using the `$\derivec$' function thus: We can express this using the `$\derivec$' function thus:
$$ CMATV = \; \derivec (G_1) .$$ $ CMATV = \; \derivec (G_1) .$
% %
As its failure modes are the symptoms of failure from the functional group we can now state: As its failure modes are the symptoms of failure from the functional group we can now state:
$$fm ( CMATV ) = \{ HIGH , LOW, V\_ERR \} .$$ $fm ( CMATV ) = \{ HIGH , LOW, V\_ERR \} .$
\paragraph{Functional Group - Software - Read\_ADC - RADC} \paragraph{Functional Group - Software - Read\_ADC - RADC}
@ -788,8 +799,7 @@ of this function, which we can call $V\_REF$.
Taken as a component for use in FMEA/FMMD our function has Taken as a component for use in FMEA/FMMD our function has
two failure modes. We can therefore treat it as a generic component, $Read\_ADC$, two failure modes. We can therefore treat it as a generic component, $Read\_ADC$,
by stating: by stating:
$ fm(Read\_ADC) = \{ CHAN\_NO, VREF \} $
$$ fm(Read\_ADC) = \{ CHAN\_NO, VREF \} $$
As we have a failure mode model for our function, we can now use it in conjunction with As we have a failure mode model for our function, we can now use it in conjunction with
with the ADC hardware {\dc} CMATV, to form a {\fg} $G_2$, where $G_2 =\{ CMSTV, Read\_ADC \}$. with the ADC hardware {\dc} CMATV, to form a {\fg} $G_2$, where $G_2 =\{ CMSTV, Read\_ADC \}$.
@ -843,10 +853,10 @@ for the function.
This postcondition, {\em /* ensure: value is voltage input to within 0.1\% */ }, This postcondition, {\em /* ensure: value is voltage input to within 0.1\% */ },
corresponds to $VV\_ERR$, and is already in the {\fm} set for this {\fg}. corresponds to $VV\_ERR$, and is already in the {\fm} set for this {\fg}.
% %
We can now create a {\dc} called $RADC$ thus: $$RADC = \; \derivec(G_2)$$ which has the following We can now create a {\dc} called $RADC$ thus: $RADC = \; \derivec(G_2)$ which has the following
{\fms}: {\fms}:
%
$$ fm(RADC) = \{ VV\_ERR, HIGH, LOW \} .$$ $ fm(RADC) = \{ VV\_ERR, HIGH, LOW \} .$
@ -861,9 +871,9 @@ to determine its {\fms}.
Its pre-condition is, {\em /* require: input from ADC to be between 0.88 and 4.4 volts */}. Its pre-condition is, {\em /* require: input from ADC to be between 0.88 and 4.4 volts */}.
We can map this violation of the pre-condition, to the {\fm} VRNGE; %As this function has one pre-condition We can map this violation of the pre-condition, to the {\fm} VRNGE; %As this function has one pre-condition
we can state, we can state,
%
$$ fm(read\_4\_20\_input) = \{ VRNGE \} .$$ $ fm(read\_4\_20\_input) = \{ VRNGE \} .$
%
We can now form a functional group with the {\dc} $RADC$ and the We can now form a functional group with the {\dc} $RADC$ and the
software component $read\_4\_20\_input$, i.e. $G_3 = \{read\_4\_20\_input, RADC\} $. software component $read\_4\_20\_input$, i.e. $G_3 = \{read\_4\_20\_input, RADC\} $.
@ -894,12 +904,7 @@ software component $read\_4\_20\_input$, i.e. $G_3 = \{read\_4\_20\_input, RADC\
4: $RADC_{LOW}$ & ADC may read & $OUT\_OF\_$ \\ 4: $RADC_{LOW}$ & ADC may read & $OUT\_OF\_$ \\
& wrong channel & $RANGE$ \\ \hline & wrong channel & $RANGE$ \\ \hline
\hline \hline
\hline
\end{tabular} \end{tabular}
\end{table} \end{table}
} }
@ -913,26 +918,22 @@ can fail. An $OUT\_OF\_RANGE$ will be flagged by the error flag variable.
The $VAL\_ERR$ will mean that the value read is simply wrong. The $VAL\_ERR$ will mean that the value read is simply wrong.
% %
We can finally make a {\dc} to represent a failure mode model for our function $read\_4\_20\_input$ thus: We can finally make a {\dc} to represent a failure mode model for our function $read\_4\_20\_input$ thus:
%
$$ R420I = \; \derivec(G_3) .$$ $ R420I = \; \derivec(G_3) .$
%
This new {\dc} has the following {\fms}: This new {\dc} has the following {\fms}:
$$fm(R420I) = \{OUT\_OF\_RANGE, VAL\_ERR\} .$$ $fm(R420I) = \{OUT\_OF\_RANGE, VAL\_ERR\} .$
% %
% Using the derived components, CMATV and VTPM we create % Using the derived components, CMATV and VTPM we create
% a new functional group. This % a new functional group. This
% integrates FMEA's from software and eletronics % integrates FMEA's from software and eletronics
% into the same failure mode model. % into the same failure mode model.
We can now represent the software/hardware FMMD analysis We can now represent the software/hardware FMMD analysis
as a hierarchical diagram, see figure~\ref{fig:hd}. as a hierarchical diagram, see figure~\ref{fig:hd}.
\begin{figure}[h] \begin{figure}[h]
\centering \centering
\includegraphics[width=200pt]{./hd.png} \includegraphics[width=60pt]{./hd.png}
% hd.png: 363x520 pixel, 72dpi, 12.81x18.34 cm, bb=0 0 363 520 % hd.png: 363x520 pixel, 72dpi, 12.81x18.34 cm, bb=0 0 363 520
\caption{FMMD hierarchy with hardware and software elements} \caption{FMMD hierarchy with hardware and software elements}
\label{fig:hd} \label{fig:hd}
@ -952,39 +953,39 @@ using the groups as intermediate stages:
% \end{eqnarray*} % \end{eqnarray*}
%or, %or,
with a nested definition, with a nested definition,
$$ \derivec \Big( \derivec \big( \derivec(R,ADC), read\_4\_20\_input \big), read\_4\_20\_input \Big). $$ $ \derivec \Big( \derivec \big( \derivec(R,ADC), read\_4\_20\_input \big), read\_4\_20\_input \Big). $
%
This nested structure means that we have multiple traceable This nested structure means that we have multiple traceable
stages of failure mode reasoning in our analysis. Traditional FMEA would have only one stage stages of failure mode reasoning in our analysis. Traditional FMEA would have only one stage
of reasoning for each component failure mode. of reasoning for each component failure mode.
\section{Heuristic Comments on {\ft} Input Circuit} % \section{Heuristic Comments on {\ft} Input Circuit}
%
Part of the design philosophy of a {\ft} loop, is that % Part of the design philosophy of a {\ft} loop, is that
if anything goes wrong, we should be able to detect it. % if anything goes wrong, we should be able to detect it.
In fact unless all electrical elements in the loop % In fact unless all electrical elements in the loop
are in working order we will detect a failure in % are in working order we will detect a failure in
the majority of cases. % the majority of cases.
\paragraph{Sending side of a {\ft} loop} % \paragraph{Sending side of a {\ft} loop}
A current loop has to be actively maintained. If the sending side looses power, % A current loop has to be actively maintained. If the sending side looses power,
the current will drop to zero, and thus be detectable as an error because it is below 4mA. % the current will drop to zero, and thus be detectable as an error because it is below 4mA.
Should the sending circuitry fail, it is far more likely to drive too high or too low, rather than supply % Should the sending circuitry fail, it is far more likely to drive too high or too low, rather than supply
an erroneous but in bounds ($4mA \ge \wedge \le 20mA$) value. % an erroneous but in bounds ($4mA \ge \wedge \le 20mA$) value.
\paragraph{Receiving side of a {\ft} loop} % \paragraph{Receiving side of a {\ft} loop}
The most common fault is disconnection, and this is easily detected ($0mA\; \le \; 4mA$--out of bounds). % The most common fault is disconnection, and this is easily detected ($0mA\; \le \; 4mA$--out of bounds).
Other failure modes, such as the resistor going open or shorted % Other failure modes, such as the resistor going open or shorted
also immediately push the voltage signal out of bounds. % also immediately push the voltage signal out of bounds.
The software side of the interface, is easy to test, either as software modules % The software side of the interface, is easy to test, either as software modules
or as an integrated system (hand-held precision current sources are cheaply available). % or as an integrated system (hand-held precision current sources are cheaply available).
\paragraph{What could go wrong---Production} % \paragraph{What could go wrong---Production}
PCB construction contractors are well known for random polarity placement of diodes. % PCB construction contractors are well known for random polarity placement of diodes.
Less likely is that the resistor fitted will be an incorrect value, which could % Less likely is that the resistor fitted will be an incorrect value, which could
lead to the range being incorrect. Were this the case, we would have to be very unlucky % lead to the range being incorrect. Were this the case, we would have to be very unlucky
and get a value very close to our chosen \ohms{220} for this to be a problem, and % and get a value very close to our chosen \ohms{220} for this to be a problem, and
in safety critical equipment, a production test rig would pick this up. % in safety critical equipment, a production test rig would pick this up.
Worse perhaps, a resistor with poor temperature coefficient could be % Worse perhaps, a resistor with poor temperature coefficient could be
erroneously chosen (this would be a cheaper component), and could contribute small errors. % erroneously chosen (this would be a cheaper component), and could contribute small errors.
@ -994,11 +995,13 @@ erroneously chosen (this would be a cheaper component), and could contribute sma
The {\dc} representing the {\ft} reader The {\dc} representing the {\ft} reader
in software shows that by taking a modular approach for FMEA, we can integrate in software shows that by taking a modular approach for FMEA, we can integrate
software and electro-mechanical FMEA models. software and electro-mechanical FMEA models.
%
With this analysis With this analysis
we have a complete `reasoning~path' linking the failures modes from the we have a complete `reasoning~path' linking the failures modes from the
electronics to those in the software. electronics to those in the software.
Each functional group to {\dc} transition represents a Each functional group to {\dc} transition represents a
reasoning stage. reasoning stage.
%
With traditional FMEA methods the reasoning~distance is large, because With traditional FMEA methods the reasoning~distance is large, because
it stretches from the component failure mode to the top---or---system level failure. it stretches from the component failure mode to the top---or---system level failure.
For this reason applying traditional FMEA to software stretches For this reason applying traditional FMEA to software stretches
@ -1034,7 +1037,7 @@ Using FMMD we can determine an accurate failure model for the interface as well.
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