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| % Default to the notebook output style | |
| % Inherit from the specified cell style. | |
| \documentclass[11pt]{article} | |
| \usepackage[T1]{fontenc} | |
| % Nicer default font (+ math font) than Computer Modern for most use cases | |
| \usepackage{mathpazo} | |
| % Basic figure setup, for now with no caption control since it's done | |
| % automatically by Pandoc (which extracts  syntax from Markdown). | |
| \usepackage{graphicx} | |
| % We will generate all images so they have a width \maxwidth. This means | |
| % that they will get their normal width if they fit onto the page, but | |
| % are scaled down if they would overflow the margins. | |
| \makeatletter | |
| \def\maxwidth{\ifdim\Gin@nat@width>\linewidth\linewidth | |
| \else\Gin@nat@width\fi} | |
| \makeatother | |
| \let\Oldincludegraphics\includegraphics | |
| % Set max figure width to be 80% of text width, for now hardcoded. | |
| \renewcommand{\includegraphics}[1]{\Oldincludegraphics[width=.8\maxwidth]{#1}} | |
| % Ensure that by default, figures have no caption (until we provide a | |
| % proper Figure object with a Caption API and a way to capture that | |
| % in the conversion process - todo). | |
| \usepackage{caption} | |
| \DeclareCaptionLabelFormat{nolabel}{} | |
| \captionsetup{labelformat=nolabel} | |
| \usepackage{adjustbox} % Used to constrain images to a maximum size | |
| \usepackage{xcolor} % Allow colors to be defined | |
| \usepackage{enumerate} % Needed for markdown enumerations to work | |
| \usepackage{geometry} % Used to adjust the document margins | |
| \usepackage{amsmath} % Equations | |
| \usepackage{amssymb} % Equations | |
| \usepackage{textcomp} % defines textquotesingle | |
| % Hack from http://tex.stackexchange.com/a/47451/13684: | |
| \AtBeginDocument{% | |
| \def\PYZsq{\textquotesingle}% Upright quotes in Pygmentized code | |
| } | |
| \usepackage{upquote} % Upright quotes for verbatim code | |
| \usepackage{eurosym} % defines \euro | |
| \usepackage[mathletters]{ucs} % Extended unicode (utf-8) support | |
| \usepackage[utf8x]{inputenc} % Allow utf-8 characters in the tex document | |
| \usepackage{fancyvrb} % verbatim replacement that allows latex | |
| \usepackage{grffile} % extends the file name processing of package graphics | |
| % to support a larger range | |
| % The hyperref package gives us a pdf with properly built | |
| % internal navigation ('pdf bookmarks' for the table of contents, | |
| % internal cross-reference links, web links for URLs, etc.) | |
| \usepackage{hyperref} | |
| \usepackage{longtable} % longtable support required by pandoc >1.10 | |
| \usepackage{booktabs} % table support for pandoc > 1.12.2 | |
| \usepackage[inline]{enumitem} % IRkernel/repr support (it uses the enumerate* environment) | |
| \usepackage[normalem]{ulem} % ulem is needed to support strikethroughs (\sout) | |
| % normalem makes italics be italics, not underlines | |
| % Colors for the hyperref package | |
| \definecolor{urlcolor}{rgb}{0,.145,.698} | |
| \definecolor{linkcolor}{rgb}{.71,0.21,0.01} | |
| \definecolor{citecolor}{rgb}{.12,.54,.11} | |
| % ANSI colors | |
| \definecolor{ansi-black}{HTML}{3E424D} | |
| \definecolor{ansi-black-intense}{HTML}{282C36} | |
| \definecolor{ansi-red}{HTML}{E75C58} | |
| \definecolor{ansi-red-intense}{HTML}{B22B31} | |
| \definecolor{ansi-green}{HTML}{00A250} | |
| \definecolor{ansi-green-intense}{HTML}{007427} | |
| \definecolor{ansi-yellow}{HTML}{DDB62B} | |
| \definecolor{ansi-yellow-intense}{HTML}{B27D12} | |
| \definecolor{ansi-blue}{HTML}{208FFB} | |
| \definecolor{ansi-blue-intense}{HTML}{0065CA} | |
| \definecolor{ansi-magenta}{HTML}{D160C4} | |
| \definecolor{ansi-magenta-intense}{HTML}{A03196} | |
| \definecolor{ansi-cyan}{HTML}{60C6C8} | |
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| \definecolor{ansi-white}{HTML}{C5C1B4} | |
| \definecolor{ansi-white-intense}{HTML}{A1A6B2} | |
| % commands and environments needed by pandoc snippets | |
| % extracted from the output of `pandoc -s` | |
| \providecommand{\tightlist}{% | |
| \setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}} | |
| \DefineVerbatimEnvironment{Highlighting}{Verbatim}{commandchars=\\\{\}} | |
| % Add ',fontsize=\small' for more characters per line | |
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| \title{ME3263\_Lab-01} | |
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| \maketitle | |
| \begin{Verbatim}[commandchars=\\\{\}] | |
| {\color{incolor}In [{\color{incolor}10}]:} \PY{k+kn}{import} \PY{n+nn}{numpy} \PY{k}{as} \PY{n+nn}{np} | |
| \PY{k+kn}{from} \PY{n+nn}{scipy}\PY{n+nn}{.}\PY{n+nn}{stats} \PY{k}{import} \PY{n}{norm}\PY{p}{,} \PY{n}{t} | |
| \PY{k+kn}{import} \PY{n+nn}{matplotlib}\PY{n+nn}{.}\PY{n+nn}{pyplot} \PY{k}{as} \PY{n+nn}{plt} | |
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| \end{Verbatim} | |
| \section{ME 3263}\label{me-3263} | |
| \subsection{Lab \#1 - Measurements of machining precision and | |
| accuracy}\label{lab-1---measurements-of-machining-precision-and-accuracy} | |
| \subsubsection{How can you measure | |
| something?}\label{how-can-you-measure-something} | |
| All measurements have traceable standards. There are seven base units in | |
| SI - meter (length), second (time), Mole (amount of substance), Ampere | |
| (electric current), Kelvin (temperature), Candela (Luminous intensity), | |
| and kilogram (mass) | |
| \href{https://www.nist.gov/pml/weights-and-measures/metric-si/si-units}{1}. | |
| Any measurement you make should have some method to check against a | |
| reference. In this lab, we will use calipers that measure dimensions | |
| i.e. meter*10\(^{-3}\) (length). Calipers can always be verified to work | |
| with gage blocks. | |
| \subsubsection{Sources of measurement | |
| variations}\label{sources-of-measurement-variations} | |
| No measurement is exact. No surface is compeletely flat. Every | |
| measurement you make has two types of uncertainties, \emph{systematic} | |
| and \emph{random}. \emph{Systematic} uncertainties come from faults in | |
| your assumptions or equipment. Here are some examples for caliper | |
| measurements: | |
| \begin{itemize} | |
| \item | |
| Your calipers were dropped on the floor and bent, now all of your | |
| measurements will be too long or too short. | |
| \item | |
| The bar stock was not machined with square edges so each measurement | |
| along the sides increases or decreases | |
| \item | |
| You align the calipers with the bar stock, instead of measuring | |
| point-to-point. Now your measurements are only the maximum length from | |
| edge-to-edge | |
| \end{itemize} | |
| \emph{Random} uncertainties are associated with unpredictable (or | |
| unforeseen at the time) experimental conditions. These can also be due | |
| to simplifications of your model. Here are some examples for caliper | |
| measurements: | |
| \begin{itemize} | |
| \item | |
| You assume the surface is flat, but it is in fact rough | |
| \item | |
| The temperature in the room changes the dimensions through thermal | |
| expansion | |
| \item | |
| Your calipers are not aligned parallel to the edges of the bar stock | |
| \end{itemize} | |
| In theory, all uncertainies could be accounted for by factoring in all | |
| physics in a problem e.g. Temperature-dependence, Coriolis effect, | |
| electrical disturbances in your readings. In practice, the diminishing | |
| return on investment prevents this practice. For something like | |
| measuring bar stock, it is more than sufficient to report the average | |
| and standard deviation with good calipers. | |
| \subsubsection{Procedure - Measuring tolerances and comparing groups and | |
| samples}\label{procedure---measuring-tolerances-and-comparing-groups-and-samples} | |
| You are given four groups, A-D, of 5 samples, 1-5. You will use 4-inch | |
| calipers to measure the lengths of the four groups of samples. Make sure | |
| each lab member takes measurements. Measure the length of each sample | |
| four times, fill in Table 1. | |
| \textbf{Table 1. Lengths of machined bar stock. Sets A-D, samples 1-5, | |
| length measurements 1-4. Calculate the average and standard deviation | |
| and note the lab member.} | |
| \begin{longtable}[]{@{}lllllllll@{}} | |
| \toprule | |
| Set & Sample & Length 1 & Length 2 & Length 3 & Length 4 & Average & | |
| Stand. Dev. & User\tabularnewline | |
| \midrule | |
| \endhead | |
| A & 1 & \_\_\_ & \_\_\_ & \_\_\_ & \_\_\_ & \_\_\_\_\_\_ & \_\_\_\_\_\_ | |
| & \_\_\_\_\_\_\tabularnewline | |
| A & 2 & \_\_\_ & \_\_\_ & \_\_\_ & \_\_\_ & \_\_\_\_\_\_ & \_\_\_\_\_\_ | |
| & \_\_\_\_\_\_\tabularnewline | |
| A & 3 & \_\_\_ & \_\_\_ & \_\_\_ & \_\_\_ & \_\_\_\_\_\_ & \_\_\_\_\_\_ | |
| & \_\_\_\_\_\_\tabularnewline | |
| A & 4 & \_\_\_ & \_\_\_ & \_\_\_ & \_\_\_ & \_\_\_\_\_\_ & \_\_\_\_\_\_ | |
| & \_\_\_\_\_\_\tabularnewline | |
| A & 5 & \_\_\_ & \_\_\_ & \_\_\_ & \_\_\_ & \_\_\_\_\_\_ & \_\_\_\_\_\_ | |
| & \_\_\_\_\_\_\tabularnewline | |
| B & 1 & \_\_\_ & \_\_\_ & \_\_\_ & \_\_\_ & \_\_\_\_\_\_ & \_\_\_\_\_\_ | |
| & \_\_\_\_\_\_\tabularnewline | |
| B & 2 & \_\_\_ & \_\_\_ & \_\_\_ & \_\_\_ & \_\_\_\_\_\_ & \_\_\_\_\_\_ | |
| & \_\_\_\_\_\_\tabularnewline | |
| B & 3 & \_\_\_ & \_\_\_ & \_\_\_ & \_\_\_ & \_\_\_\_\_\_ & \_\_\_\_\_\_ | |
| & \_\_\_\_\_\_\tabularnewline | |
| B & 4 & \_\_\_ & \_\_\_ & \_\_\_ & \_\_\_ & \_\_\_\_\_\_ & \_\_\_\_\_\_ | |
| & \_\_\_\_\_\_\tabularnewline | |
| B & 5 & \_\_\_ & \_\_\_ & \_\_\_ & \_\_\_ & \_\_\_\_\_\_ & \_\_\_\_\_\_ | |
| & \_\_\_\_\_\_\tabularnewline | |
| C & 1 & \_\_\_ & \_\_\_ & \_\_\_ & \_\_\_ & \_\_\_\_\_\_ & \_\_\_\_\_\_ | |
| & \_\_\_\_\_\_\tabularnewline | |
| C & 2 & \_\_\_ & \_\_\_ & \_\_\_ & \_\_\_ & \_\_\_\_\_\_ & \_\_\_\_\_\_ | |
| & \_\_\_\_\_\_\tabularnewline | |
| C & 3 & \_\_\_ & \_\_\_ & \_\_\_ & \_\_\_ & \_\_\_\_\_\_ & \_\_\_\_\_\_ | |
| & \_\_\_\_\_\_\tabularnewline | |
| C & 4 & \_\_\_ & \_\_\_ & \_\_\_ & \_\_\_ & \_\_\_\_\_\_ & \_\_\_\_\_\_ | |
| & \_\_\_\_\_\_\tabularnewline | |
| C & 5 & \_\_\_ & \_\_\_ & \_\_\_ & \_\_\_ & \_\_\_\_\_\_ & \_\_\_\_\_\_ | |
| & \_\_\_\_\_\_\tabularnewline | |
| D & 1 & \_\_\_ & \_\_\_ & \_\_\_ & \_\_\_ & \_\_\_\_\_\_ & \_\_\_\_\_\_ | |
| & \_\_\_\_\_\_\tabularnewline | |
| D & 2 & \_\_\_ & \_\_\_ & \_\_\_ & \_\_\_ & \_\_\_\_\_\_ & \_\_\_\_\_\_ | |
| & \_\_\_\_\_\_\tabularnewline | |
| D & 3 & \_\_\_ & \_\_\_ & \_\_\_ & \_\_\_ & \_\_\_\_\_\_ & \_\_\_\_\_\_ | |
| & \_\_\_\_\_\_\tabularnewline | |
| D & 4 & \_\_\_ & \_\_\_ & \_\_\_ & \_\_\_ & \_\_\_\_\_\_ & \_\_\_\_\_\_ | |
| & \_\_\_\_\_\_\tabularnewline | |
| D & 5 & \_\_\_ & \_\_\_ & \_\_\_ & \_\_\_ & \_\_\_\_\_\_ & \_\_\_\_\_\_ | |
| & \_\_\_\_\_\_\tabularnewline | |
| \bottomrule | |
| \end{longtable} | |
| Sample groups A-D were machined with two different methods, a saw and a | |
| computer numerical control (CNC) mill. There is a roughness associated | |
| with the process and a randomness associated with the mounting and | |
| cutting of the four groups of samples. The roughness affects the | |
| variation of the multiple measurements on one sample i.e. Length 1, 2, | |
| 3, and 4. The mounting and cutting process introduces variations between | |
| A1, A2, etc. | |
| Next, you will determine the probability that two groups of | |
| samples-\/-e.g. group A and group B-\/-have the same average length. | |
| This process is called the Student t-test {[}2{]}. The variable, | |
| \(t=\frac{|M_A-M_B|}{\sqrt{ab}}\) | |
| \(a=\frac{N_A+N_B}{N_A N_B}\) | |
| \(b=\frac{(N_A-1)S_A^2+(N_B-1)S_B^2}{N_A+N_B-2}\) | |
| is a function of the two group means, \(M_A\) and \(M_B\), two group | |
| deviations, \(S_A\) and \(S_B\), and number of samples per group, | |
| \(N_A\) and \(N_B\). Calculate \(t\) for groups A and B by filling in | |
| Table 2. | |
| \textbf{Table 2: Determining t for groups A and B} | |
| \begin{longtable}[]{@{}lllll@{}} | |
| \toprule | |
| Sample & A Length & \((L-M_A)^2\) & B Length & | |
| \((L-M_A)^2\)\tabularnewline | |
| \midrule | |
| \endhead | |
| 1 &\tabularnewline | |
| 2 &\tabularnewline | |
| 3 &\tabularnewline | |
| 4 &\tabularnewline | |
| 5 &\tabularnewline | |
| \textbf{sum} &\tabularnewline | |
| \(M\) and \(S^2\) & \(sum/N_A\) & \(sum/(N_A-1)\) & \(sum/N_B\) & | |
| \(sum/(N_B-1)\)\tabularnewline | |
| \bottomrule | |
| \end{longtable} | |
| \subsection{Example calculations in | |
| Python}\label{example-calculations-in-python} | |
| Compare two groups of samples: | |
| \begin{longtable}[]{@{}llllll@{}} | |
| \toprule | |
| group & sample 1 & sample 2 & sample 3 & sample 4 & sample | |
| 5\tabularnewline | |
| \midrule | |
| \endhead | |
| A & 104.14 mm & 101.61 mm & 99.06 mm & 102.87 mm & 106.68 | |
| mm\tabularnewline | |
| B & 104.12 mm & 101.63 mm & 97.79 mm & 101.58 mm & 104.17 | |
| mm\tabularnewline | |
| \bottomrule | |
| \end{longtable} | |
| \begin{Verbatim}[commandchars=\\\{\}] | |
| {\color{incolor}In [{\color{incolor}11}]:} \PY{n}{A}\PY{o}{=}\PY{n}{np}\PY{o}{.}\PY{n}{array}\PY{p}{(}\PY{p}{[}\PY{l+m+mf}{104.14}\PY{p}{,} \PY{l+m+mf}{101.61} \PY{p}{,} \PY{l+m+mf}{99.06}\PY{p}{,} \PY{l+m+mf}{102.87}\PY{p}{,} \PY{l+m+mf}{106.68}\PY{p}{]}\PY{p}{)} | |
| \PY{n}{B}\PY{o}{=}\PY{n}{np}\PY{o}{.}\PY{n}{array}\PY{p}{(}\PY{p}{[}\PY{l+m+mf}{104.12}\PY{p}{,} \PY{l+m+mf}{101.63} \PY{p}{,} \PY{l+m+mf}{97.79}\PY{p}{,} \PY{l+m+mf}{101.58} \PY{p}{,} \PY{l+m+mf}{104.17}\PY{p}{]}\PY{p}{)} | |
| \PY{n}{meanA}\PY{o}{=}\PY{n}{np}\PY{o}{.}\PY{n}{sum}\PY{p}{(}\PY{n}{A}\PY{p}{)}\PY{o}{/}\PY{n+nb}{len}\PY{p}{(}\PY{n}{A}\PY{p}{)} | |
| \PY{n}{meanB}\PY{o}{=}\PY{n}{np}\PY{o}{.}\PY{n}{sum}\PY{p}{(}\PY{n}{B}\PY{p}{)}\PY{o}{/}\PY{n+nb}{len}\PY{p}{(}\PY{n}{B}\PY{p}{)} | |
| \PY{n}{s2A}\PY{o}{=}\PY{n}{np}\PY{o}{.}\PY{n}{sum}\PY{p}{(}\PY{p}{(}\PY{n}{A}\PY{o}{\PYZhy{}}\PY{n}{meanA}\PY{p}{)}\PY{o}{*}\PY{o}{*}\PY{l+m+mi}{2}\PY{p}{)}\PY{o}{/}\PY{p}{(}\PY{n+nb}{len}\PY{p}{(}\PY{n}{A}\PY{p}{)}\PY{o}{\PYZhy{}}\PY{l+m+mi}{1}\PY{p}{)} | |
| \PY{n}{s2B}\PY{o}{=}\PY{n}{np}\PY{o}{.}\PY{n}{sum}\PY{p}{(}\PY{p}{(}\PY{n}{B}\PY{o}{\PYZhy{}}\PY{n}{meanB}\PY{p}{)}\PY{o}{*}\PY{o}{*}\PY{l+m+mi}{2}\PY{p}{)}\PY{o}{/}\PY{p}{(}\PY{n+nb}{len}\PY{p}{(}\PY{n}{B}\PY{p}{)}\PY{o}{\PYZhy{}}\PY{l+m+mi}{1}\PY{p}{)} | |
| \PY{n}{a}\PY{o}{=}\PY{p}{(}\PY{n+nb}{len}\PY{p}{(}\PY{n}{A}\PY{p}{)}\PY{o}{+}\PY{n+nb}{len}\PY{p}{(}\PY{n}{B}\PY{p}{)}\PY{p}{)}\PY{o}{/}\PY{p}{(}\PY{n+nb}{len}\PY{p}{(}\PY{n}{A}\PY{p}{)}\PY{o}{*}\PY{n+nb}{len}\PY{p}{(}\PY{n}{B}\PY{p}{)}\PY{o}{*}\PY{l+m+mf}{1.0}\PY{p}{)} | |
| \PY{n}{b}\PY{o}{=}\PY{p}{(}\PY{p}{(}\PY{n+nb}{len}\PY{p}{(}\PY{n}{A}\PY{p}{)}\PY{o}{\PYZhy{}}\PY{l+m+mi}{1}\PY{p}{)}\PY{o}{*}\PY{n}{s2A}\PY{o}{+}\PY{p}{(}\PY{n+nb}{len}\PY{p}{(}\PY{n}{B}\PY{p}{)}\PY{o}{\PYZhy{}}\PY{l+m+mi}{1}\PY{p}{)}\PY{o}{*}\PY{n}{s2B}\PY{p}{)}\PY{o}{/}\PY{p}{(}\PY{n+nb}{len}\PY{p}{(}\PY{n}{A}\PY{p}{)}\PY{o}{+}\PY{n+nb}{len}\PY{p}{(}\PY{n}{B}\PY{p}{)}\PY{o}{\PYZhy{}}\PY{l+m+mi}{2}\PY{p}{)} | |
| \PY{c+c1}{\PYZsh{}tstat=(meanA\PYZhy{}meanB)/np.sqrt(s2A/len(A)+s2B/len(B))} | |
| \PY{n}{tstat}\PY{o}{=}\PY{p}{(}\PY{n}{meanA}\PY{o}{\PYZhy{}}\PY{n}{meanB}\PY{p}{)}\PY{o}{/}\PY{n}{np}\PY{o}{.}\PY{n}{sqrt}\PY{p}{(}\PY{n}{a}\PY{o}{*}\PY{n}{b}\PY{p}{)} | |
| \PY{n+nb}{print}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{example groups A and B have t=}\PY{l+s+si}{\PYZpc{}1.2f}\PY{l+s+s1}{\PYZsq{}}\PY{o}{\PYZpc{}}\PY{k}{tstat}) | |
| \end{Verbatim} | |
| \begin{Verbatim}[commandchars=\\\{\}] | |
| example groups A and B have t=0.59 | |
| \end{Verbatim} | |
| \begin{Verbatim}[commandchars=\\\{\}] | |
| {\color{incolor}In [{\color{incolor}12}]:} \PY{n}{df}\PY{o}{=}\PY{n+nb}{len}\PY{p}{(}\PY{n}{A}\PY{p}{)}\PY{o}{+}\PY{n+nb}{len}\PY{p}{(}\PY{n}{B}\PY{p}{)}\PY{o}{\PYZhy{}}\PY{l+m+mi}{2} | |
| \PY{c+c1}{\PYZsh{} Print out the table for df degrees of freedom (N1+N2\PYZhy{}2)} | |
| \PY{n+nb}{print}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{df=}\PY{l+s+si}{\PYZpc{}i}\PY{l+s+s1}{\PYZsq{}}\PY{o}{\PYZpc{}}\PY{k}{df} ) | |
| \PY{n+nb}{print}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{| p=0.05 | p=0.025 | p=0.01 | p=0.005 |}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)} | |
| \PY{n+nb}{print}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{| \PYZhy{}\PYZhy{}\PYZhy{} | \PYZhy{}\PYZhy{}\PYZhy{} | \PYZhy{}\PYZhy{}\PYZhy{} | \PYZhy{}\PYZhy{}\PYZhy{} |}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)} | |
| \PY{n+nb}{print}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{| }\PY{l+s+si}{\PYZpc{}1.2f}\PY{l+s+s2}{ | }\PY{l+s+si}{\PYZpc{}1.2f}\PY{l+s+s2}{ | }\PY{l+s+si}{\PYZpc{}1.2f}\PY{l+s+s2}{ | }\PY{l+s+si}{\PYZpc{}1.2f}\PY{l+s+s2}{ |}\PY{l+s+s2}{\PYZdq{}}\PY{o}{\PYZpc{}}\PY{p}{(}\PY{n}{t}\PY{o}{.}\PY{n}{interval}\PY{p}{(}\PY{l+m+mf}{0.95}\PY{p}{,} \PY{n}{df}\PY{p}{)}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{]}\PY{p}{,}\PYZbs{} | |
| \PY{n}{t}\PY{o}{.}\PY{n}{interval}\PY{p}{(}\PY{l+m+mf}{0.975}\PY{p}{,} \PY{n}{df}\PY{p}{)}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{]}\PY{p}{,}\PYZbs{} | |
| \PY{n}{t}\PY{o}{.}\PY{n}{interval}\PY{p}{(}\PY{l+m+mf}{0.99}\PY{p}{,} \PY{n}{df}\PY{p}{)}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{]}\PY{p}{,}\PYZbs{} | |
| \PY{n}{t}\PY{o}{.}\PY{n}{interval}\PY{p}{(}\PY{l+m+mf}{0.995}\PY{p}{,} \PY{n}{df}\PY{p}{)}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{]}\PY{p}{)}\PY{p}{)} | |
| \end{Verbatim} | |
| \begin{Verbatim}[commandchars=\\\{\}] | |
| df=8 | |
| | p=0.05 | p=0.025 | p=0.01 | p=0.005 | | |
| | --- | --- | --- | --- | | |
| | 2.31 | 2.75 | 3.36 | 3.83 | | |
| \end{Verbatim} | |
| \begin{Verbatim}[commandchars=\\\{\}] | |
| {\color{incolor}In [{\color{incolor}13}]:} \PY{n}{plt}\PY{o}{.}\PY{n}{hist}\PY{p}{(}\PY{n}{A}\PY{p}{,}\PY{n}{np}\PY{o}{.}\PY{n}{linspace}\PY{p}{(}\PY{l+m+mi}{97}\PY{p}{,}\PY{l+m+mi}{105}\PY{p}{,}\PY{l+m+mi}{5}\PY{p}{)}\PY{p}{,}\PY{n}{histtype}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{step}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,}\PY{n}{label}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{A}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)} | |
| \PY{n}{plt}\PY{o}{.}\PY{n}{hist}\PY{p}{(}\PY{n}{B}\PY{p}{,}\PY{n}{np}\PY{o}{.}\PY{n}{linspace}\PY{p}{(}\PY{l+m+mi}{97}\PY{p}{,}\PY{l+m+mi}{105}\PY{p}{,}\PY{l+m+mi}{5}\PY{p}{)}\PY{p}{,}\PY{n}{histtype}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{step}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,}\PY{n}{label}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{B}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)} | |
| \PY{n}{plt}\PY{o}{.}\PY{n}{xlabel}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{length (mm)}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)} | |
| \PY{n}{plt}\PY{o}{.}\PY{n}{ylabel}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{counts}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)} | |
| \PY{n}{plt}\PY{o}{.}\PY{n}{legend}\PY{p}{(}\PY{p}{)} | |
| \end{Verbatim} | |
| \begin{Verbatim}[commandchars=\\\{\}] | |
| {\color{outcolor}Out[{\color{outcolor}13}]:} <matplotlib.legend.Legend at 0x7f5d002c1be0> | |
| \end{Verbatim} | |
| \begin{center} | |
| \adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_8_1.png} | |
| \end{center} | |
| { \hspace*{\fill} \\} | |
| \subsubsection{Your Report}\label{your-report} | |
| \begin{enumerate} | |
| \def\labelenumi{\arabic{enumi}.} | |
| \tightlist | |
| \item | |
| Introduction | |
| \end{enumerate} | |
| \begin{enumerate} | |
| \def\labelenumi{\alph{enumi}.} | |
| \item | |
| Describe sources of uncertainty in machining and measuring parts | |
| \item | |
| How do we measure parts and roughness? | |
| \item | |
| How can we use statistics to evaluate machining tolerances? | |
| \item | |
| What is the cost of tighter tolerances? | |
| \end{enumerate} | |
| \begin{enumerate} | |
| \def\labelenumi{\arabic{enumi}.} | |
| \setcounter{enumi}{1} | |
| \tightlist | |
| \item | |
| Methods | |
| \end{enumerate} | |
| \begin{enumerate} | |
| \def\labelenumi{\alph{enumi}.} | |
| \item | |
| Describe parts used | |
| \item | |
| Describe tools used | |
| \item | |
| How did you take the measurements? | |
| \end{enumerate} | |
| \begin{enumerate} | |
| \def\labelenumi{\arabic{enumi}.} | |
| \setcounter{enumi}{2} | |
| \tightlist | |
| \item | |
| Results and Discussion | |
| \end{enumerate} | |
| \begin{enumerate} | |
| \def\labelenumi{\alph{enumi}.} | |
| \item | |
| What are the average part dimensions? | |
| \item | |
| What tolerance can you assign to the machining methods? | |
| \item | |
| How similar are the four sets of parts: A, B, C, and D? | |
| \item | |
| How can you use the t-distribution to describe and compare the parts? | |
| \end{enumerate} | |
| \begin{enumerate} | |
| \def\labelenumi{\arabic{enumi}.} | |
| \setcounter{enumi}{3} | |
| \tightlist | |
| \item | |
| Conclusion | |
| \end{enumerate} | |
| \begin{enumerate} | |
| \def\labelenumi{\alph{enumi}.} | |
| \item | |
| How do the two methods of machining compare? | |
| \item | |
| What are the benefits to each method? | |
| \item | |
| Is there any way to reduce the number of measurements when determining | |
| tolerances? | |
| \end{enumerate} | |
| \subsubsection{References}\label{references} | |
| \begin{enumerate} | |
| \def\labelenumi{\arabic{enumi}.} | |
| \item | |
| \url{https://www.nist.gov/pml/weights-and-measures/metric-si/si-units} | |
| \item | |
| \href{https://courses.washington.edu/phys431/uncertainty_notes.pdf}{Uncertainty | |
| Notes} | |
| \item | |
| \href{https://www.ruf.rice.edu/~bioslabs/tools/stats/ttest.html}{Student | |
| t-test} | |
| \end{enumerate} | |
| % Add a bibliography block to the postdoc | |
| \end{document} |