%
\DeclareMathSymbol{\N}{\mathbin}{AMSb}{"4E}
\DeclareMathSymbol{\Z}{\mathbin}{AMSb}{"5A}
\DeclareMathSymbol{\R}{\mathbin}{AMSb}{"52}
\DeclareMathSymbol{\Q}{\mathbin}{AMSb}{"51}
\DeclareMathSymbol{\I}{\mathbin}{AMSb}{"49}
\DeclareMathSymbol{\C}{\mathbin}{AMSb}{"43}
%\DeclareMathSymbol{\hh}{\mathbin}{AMSb}{"48}


\newcommand{\ft}{\ensuremath{4\!\!\rightarrow\!\!20mA} }
\newcommand{\tenfifty}{\ensuremath{10\!\!\rightarrow\!\!50mA} }
\usepackage{graphicx}
\usepackage{fancyhdr}
\usepackage{tikz}
\usepackage{amsfonts,amsmath,amsthm}
\usetikzlibrary{shapes.gates.logic.US,trees,positioning,arrows}
\def\layersep{1.8cm}
%\input{../style}\def\layersep{1.8cm}
\usepackage{ifthen}
\usepackage{lastpage}
\usetikzlibrary{shapes,snakes}
\newcommand{\tickYES}{\checkmark}
%%   \newcommand{\fc}{fault~scenario}
\newcommand{\fc}{failure~cause}
%%   \newcommand{\fcs}{fault~scenarios}
\newcommand{\fcs}{failure~causes}
% Page layout definitions to suit A4 paper
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\setlength{\topmargin}{0mm}
\setlength{\textwidth}{160mm}      \setlength{\textheight}{220mm}
\setlength{\oddsidemargin}{0mm}    \setlength{\evensidemargin}{0mm}
%
\newcommand{\permil}{\ensuremath{0/{\!}_{00}}}

\newcommand{\emp}{} %% was italics
\newcommand{\sd}{\ensuremath{\Sigma \Delta ADC}} 
%\newcommand{\sd}{\ensuremath{Sigma\;Delta\;ADC}} 
\newcommand{\derivec}{{D}}
%\newcommand{\hh}{\ensuremath{{\stackrel{o}{H}}}}
\newcommand{\hh}{\ensuremath{{\hbar}}}
\newcommand{\abslev}{\ensuremath{\alpha}}
\newcommand{\oc}{\ensuremath{^{o}{C}}}
\newcommand{\adctw}{{${\mathcal{ADC}}_{12}$}}
\newcommand{\adcten}{{${\mathcal{ADC}}_{10}$}}
\newcommand{\ohms}[1]{\ensuremath{#1\Omega}}
\newcommand{\fm}{\emp failure~mode}
\newcommand{\fms}{\emp failure~modes}
\newcommand{\FG}{\ensuremath{{FG}}}
\newcommand{\DC}{\ensuremath{{DC}}}
\newcommand{\fg}{\emp functional~grouping}
\newcommand{\fgs}{\emp functional~groupings}
\newcommand{\Fgs}{\emp Functional~groupings}
\newcommand{\dc}{\emp derived~component}
\newcommand{\dcs}{\emp derived~components}
\newcommand{\bc}{\emp base~component}
\newcommand{\bcs}{\emp base~components}
\newcommand{\irl}{in~real~life}
\newcommand{\enc}{\ensuremath{\stackrel{enc}{\longrightarrow}}}
\newcommand{\pin}{\ensuremath{\stackrel{pi}{\longleftrightarrow}}}
\newcommand{\half}{\ensuremath{\frac{1}{2}}}
\newcommand{\cf}[1]{\textbf{#1()}}
\newcommand{\etc}{Energy~Technology~Control~Ltd}
%
% OK after about 3 years its not rigorous FMEA (RFMEA) anymore, oh no, its Exhaustive FMEA
% but since the fuckers might change it yet again, I am making this a macro.
\newcommand{\XFMEA}{XFMEA}
%

%\newcommand{\pic}{\em pure~intersection~chain}
\newcommand{\pic}{\emp pair-wise~intersection~chain}
\newcommand{\wrt}{\emp with~respect~to}
\newcommand{\swf}{software~function}
% DO NOT USE THIS ONE USE \abslev \newcommand{\abslevel}{\ensuremath{\Psi}}


%% GLOSSARY FORMAT
%
% \newcommand{\fmmdname}{\glossary{name={FMMDNAME},description={ }}

%\fmodegloss

\newcommand{\fmmdglossSYS}{\glossary{name={system}, description={
A product designed to work as a coherent entity}}}

\newcommand{\fmmdglossSS}{\glossary{name={sub-system}, description={
A part of a system, sub-systems may contain sub-systems and so-on}}}

\newcommand{\fmmdglossDC}{\glossary{name={{\dc}}, description={
A theoretical component, derived from a collection of components (which may be derived components themselves)}}}

\newcommand{\fmmdglossFG}{\glossary{name={{\fg}}, description={
A collection of sub-systems and/or components that interact to perform a specific function}}}

\newcommand{\fmmdglossSYMPTOM}{\glossary{name={symptom}, description={
A failure mode of a {\fg}, caused by a combination of its component failure modes}}}

\newcommand{\fmmdglossBC}{\glossary{name={{\bc}}, description={
Any bought in component, or lowest level module/or part}}}

%\newcommand{\fmmdglossFIT}{\glossary{name={FIT},description={Failure in Time (FIT). The statistical likelihood of failure mode occurring within a $10^9$ hour period.}}
\newcommand{\fmmdglossFIT}{\glossary{name={FIT}, description={
Failure in Time (FIT). The number of times a particular 
failure is expected to occur within a $10^{9}$ hour time period}}}

\newcommand{\fmmdglossHFMEA}{\glossary{name={HFMEA},description={
Hardware FMEA. FMEA applied to hardware i.e. mechanical or electrical equipment}}}

\newcommand{\fmmdglossSFMEA}{\glossary{name={SFMEA},description={
Software FMEA (SFMEA). FMEA techniques applied to software}}}

\newcommand{\fmmdglossXFMEA}{\glossary{name={XFMEA},description={
Exhaustive FMEA (XFMEA). Applying FMEA exhaustively means checking each failure mode 
for effects on all components in a given system}}}

\newcommand{\fmmdglossDFMEA}{\glossary{name={DFMEA},description={
Design FMEA. FMEA applied in design stages of a product. 
Can be used as a discussion/brain~storming method to 
reveal safety weakness and improve built in safety}}}

\newcommand{\fmmdglossPFMEA}{\glossary{name={PFMEA},description={
Production FMEA (PFMEA). 
FMEA applied for cost benefit analysis typically used in mass production}}}

\newcommand{\fmmdglossSFTA}{\glossary{name={SFTA},description={
Software Fault Tree Analysis (SFTA): 
top down failure investigation applied to software}}}

\newcommand{\fmmdglossSA}{\glossary{name={Symptom Abstraction},description={
By applying failure mode analysis to a module, the symptoms of failure for the it are determined
given the failure modes of its components, its topology and expected behaviour.}}}

\newcommand{\fmmdglossMUTEX}{\glossary{name={mutually~exclusive},description={
Mutual exclusivity applied to component failure modes
means that for each component it is ensured that
only one of its failure modes may be active at any given time}}}

\newcommand{\fmmdglossSTATEEX}{\glossary{name={State~explosion},description={
State Explosion is the effect where very large numbers of combinations of conditions, or combinations of
conditions and entities have to be processed. The number to be processed can quickly become too large 
for practical consideration, and when this happens `state~explosion' can be said to have occurred.
}}}

\newcommand{\fmmdglossFTA}{\glossary{name={FTA},description={
Fault Tree Analysis (FTA). 
A top down failure analysis technique which starts with undesirable 
top level events, and using symbols from digital logic builds
a tree, working downwards to putative causes}}}

\newcommand{\fmmdglossFMEDA}{\glossary{name={FMEDA},description={
Failure Mode Effects and Diagnostic Analysis (FMEDA).
An extended FMEA technique which provides for diagnostic 
mitigation and has a final statistical safety level as a result}}}

\newcommand{\fmmdglossFMECA}{\glossary{name={FMECA},description={
Failure Mode Effects and Criticality Analysis (FMECA). 
An extended FMEA technique, based on Bayesian statistics,
which is used to order the severity or criticality of top level events/symptoms}}}

\newcommand{\fmmdglossFS}{\glossary{name={forward~search},description={
Failure analysis where the start points are base component failure modes and the result is system level failure/symptom.
Sometimes termed `bottom~up'}}}

\newcommand{\fmmdglossBS}{\glossary{name={backward~search},description={
Failure analysis where the start points are system level failure/symptom and the results are lower level putative causes.
Sometimes termed `top~down'}}}

\newcommand{\fmmdglossINHIBIT}{\glossary{name={inhibit},description={
A guard on a process such that if a condition is not met, the process may not continue}}}

\newcommand{\fmmdglossSIGPATH}{\glossary{name={signal~path},description={
The components (software or hardware) and connections from which a particular signal or value is derived}}}

\newcommand{\fmmdglossRD}{\glossary{name={reasoning~distance},description={
A reasoning distance is the number of stages of logic and reasoning, 
counted by the number of components examined, used to map a failure cause to its potential outcomes}}}

\newcommand{\fmmdglossOBS}{\glossary{name={observability}, description={
If a failure mode cannot be detected it is termed unobservable or undetectable}}}

\newcommand{\fmmdglossSMARTINSTRUMENT}{\glossary{name={smart~instrument}, description={
A smart instrument is  one that uses software 
in conjunction with its sensing electronics, rather than
analogue electronics only~\cite{smart_instruments_1514209}}}}

\newcommand{\fmmdglossCONTRACTPROG}{\glossary{name={contract~programming}, description={
A software discipline whereby each function is assigned strict pre and post conditions
which define a `contract' formalising the function's behaviour}}}

%
%\newcommand{\fmmdglossRD}{\glossary{name={reasoning~distance}{yahda yahda ya}}}
%
\newcommand{\fmmdgloss}{\glossary{name={FMMD},description={
Failure Mode Modular De-Composition (FMMD). A bottom-up methodology for incrementally building 
failure mode models, using a procedure taking functional groups of components and creating 
derived components representing them, and in turn using the 
derived components to create higher level functional groups, and so on, 
%that are used to build a 
building a hierarchical failure mode model}}} % of a system}}}


\newcommand{\fmodegloss}{\glossary{name={failure mode},description={ % The way in which a failure occurs. 
A component or sub-system may fail in a number of ways, and each of these is a 
failure mode of that particular component type}}}

\newcommand{\fmeagloss}{\glossary{name={FMEA}, description={
Failure Mode and Effects analysis (FMEA) is a process where each 
{\bc} failure mode in a given system
is analysed to determine system level failures/symptoms}}}

\newcommand{\frategloss}{\glossary{name={failure rate}, description={
The number of failures expected over a given time interval}}}


\newcommand{\pecgloss}{\glossary{name={PEC},description={
A Programmable Electronic controller, 
will typically consist of sensors and actuators interfaced electronically, 
with some firmware/software component in overall control}}}

\usepackage{amsthm}

\newtheorem{example}{Example:}
\newtheorem{definition}{Definition:}
\newtheorem*{summary}{Summary:}


%
\newcommand{\Fam}{{\mathbb F}}
\newcommand{\Pow}{{\mathbb P}}
\newcommand{\Dis}{{\vee}}
\newcommand{\Con}{{\wedge}}
\newcommand{\FMEA}{{\bowtie}}
%
\newcommand{\Nat}{{\mathbb N}}
\newcommand{\Real}{{\mathbb R}}
\newcommand{\Complex} {{\mathbb C}}
\newcommand{\Rational} {{\mathbb Q}}
%
