<?xml version="1.0" encoding="utf-8"?>
<ManualTopic ID="/baanerp/qm/onlinemanual/000110" xml:lang="en">
   <Header>
      <Title>To create distribution histograms</Title>
      <Keyword type="header" order="d1e1394223">
         <Level1>Distribution histograms</Level1>
      </Keyword>
   </Header>
   <AimSection>
      <Paragraph>Distribution Histograms are used to ascertain the variation in
		process related characteristic by displaying a standard distribution curve of
		measured values for an item <Link href="/baanerp/tc/glossary/glossary#Characterist_tc" role="glossary">characteristic</Link> or <Link href="/baanerp/tc/glossary/glossary#Aspects_tc" role="glossary">aspect</Link> for a defined time period.</Paragraph>
   </AimSection>
   <GeneralSection>
      <GeneralSection>
         <Paragraph>To plot this chart you must select the combination of item or
		  item/supplier, inspection order source, aspect/characteristic as well as the
		  relevant time period. This chart is based only on actual inspection
		  results.</Paragraph>
         <Paragraph>The centre line of the distribution curve is the ERP Enterprise calculated mean (µ).
		  The over/under tolerance limits of the process are the limits within which the
		  process is capable of producing parts of an acceptable quality. These tolerance
		  limits are generally expressed as the process mean plus or minus 3 standard
		  deviations (σ) that can capture 95 percent of the normal variance
		  spread.</Paragraph>
         <Paragraph>To plot this type of chart, complete the following steps:</Paragraph>
         <ProcedureList>
            <ListItem>Calculate measured values for a range of periods.</ListItem>
            <ListItem>Determine the spread R of the measured values: R = Xmax –
			 Xmin</ListItem>
            <ListItem>Determine the class width: W = R / SQRT (number of
			 measurements)</ListItem>
            <ListItem>Compose the classed: Class 1 Lower Tolerance (or Xmin in case
			 Xmin &lt; Lower Tolerance) then Class2 = Class1 + W and so on</ListItem>
            <ListItem>Populate the classes based on the measured values. Determine
			 the frequency within each class.</ListItem>
            <ListItem>Calculate the arithmetic means of the measured
			 values.</ListItem>
            <ListItem>Calculate the standard deviation</ListItem>
            <ListItem>Plot the histogram based on the classes
			 calculated.</ListItem>
         </ProcedureList>
         <ExampleSection>
            <SectionTitle>Example</SectionTitle>
            <Paragraph>Assume that 5 inspection orders are processed, each with 1
			 sample, resulting in one sample group for each order. All 5 inspection orders
			 have a sample size of 10 pieces and a test quantity of 1 piece. The following
			 results are displayed in the test data table:</Paragraph>
            <TABLE border="1" borderstyle="default" space-and-orientation="indented-estimated">
               <TBODY noTR="51">
                  <TR no="1" isLast="false">
                     <TD rowspan="1" colspan="1">Sample Group</TD>
                     <TD rowspan="1" colspan="1">Sample
					 Number</TD>
                     <TD rowspan="1" colspan="1">Measured
					 Value</TD>
                  </TR>
                  <TR no="2" isLast="false">
                     <TD rowspan="1" colspan="1">1</TD>
                     <TD rowspan="1" colspan="1">1</TD>
                     <TD rowspan="1" colspan="1">1</TD>
                  </TR>
                  <TR no="3" isLast="false">
                     <TD rowspan="1" colspan="1">1</TD>
                     <TD rowspan="1" colspan="1">2</TD>
                     <TD rowspan="1" colspan="1">1</TD>
                  </TR>
                  <TR no="4" isLast="false">
                     <TD rowspan="1" colspan="1">1</TD>
                     <TD rowspan="1" colspan="1">3</TD>
                     <TD rowspan="1" colspan="1">1.002</TD>
                  </TR>
                  <TR no="5" isLast="false">
                     <TD rowspan="1" colspan="1">1</TD>
                     <TD rowspan="1" colspan="1">4</TD>
                     <TD rowspan="1" colspan="1">0.997</TD>
                  </TR>
                  <TR no="6" isLast="false">
                     <TD rowspan="1" colspan="1">1</TD>
                     <TD rowspan="1" colspan="1">5</TD>
                     <TD rowspan="1" colspan="1">1</TD>
                  </TR>
                  <TR no="7" isLast="false">
                     <TD rowspan="1" colspan="1">1</TD>
                     <TD rowspan="1" colspan="1">6</TD>
                     <TD rowspan="1" colspan="1">1.001</TD>
                  </TR>
                  <TR no="8" isLast="false">
                     <TD rowspan="1" colspan="1">1</TD>
                     <TD rowspan="1" colspan="1">7</TD>
                     <TD rowspan="1" colspan="1">1</TD>
                  </TR>
                  <TR no="9" isLast="false">
                     <TD rowspan="1" colspan="1">1</TD>
                     <TD rowspan="1" colspan="1">8</TD>
                     <TD rowspan="1" colspan="1">1</TD>
                  </TR>
                  <TR no="10" isLast="false">
                     <TD rowspan="1" colspan="1">1</TD>
                     <TD rowspan="1" colspan="1">9</TD>
                     <TD rowspan="1" colspan="1">1</TD>
                  </TR>
                  <TR no="11" isLast="false">
                     <TD rowspan="1" colspan="1">1</TD>
                     <TD rowspan="1" colspan="1">10</TD>
                     <TD rowspan="1" colspan="1">0.999</TD>
                  </TR>
                  <TR no="12" isLast="false">
                     <TD rowspan="1" colspan="1">2</TD>
                     <TD rowspan="1" colspan="1">1</TD>
                     <TD rowspan="1" colspan="1">1</TD>
                  </TR>
                  <TR no="13" isLast="false">
                     <TD rowspan="1" colspan="1">2</TD>
                     <TD rowspan="1" colspan="1">2</TD>
                     <TD rowspan="1" colspan="1">0</TD>
                  </TR>
                  <TR no="14" isLast="false">
                     <TD rowspan="1" colspan="1">2</TD>
                     <TD rowspan="1" colspan="1">3</TD>
                     <TD rowspan="1" colspan="1">0</TD>
                  </TR>
                  <TR no="15" isLast="false">
                     <TD rowspan="1" colspan="1">2</TD>
                     <TD rowspan="1" colspan="1">4</TD>
                     <TD rowspan="1" colspan="1">0</TD>
                  </TR>
                  <TR no="16" isLast="false">
                     <TD rowspan="1" colspan="1">2</TD>
                     <TD rowspan="1" colspan="1">5</TD>
                     <TD rowspan="1" colspan="1">0</TD>
                  </TR>
                  <TR no="17" isLast="false">
                     <TD rowspan="1" colspan="1">2</TD>
                     <TD rowspan="1" colspan="1">6</TD>
                     <TD rowspan="1" colspan="1">0</TD>
                  </TR>
                  <TR no="18" isLast="false">
                     <TD rowspan="1" colspan="1">2</TD>
                     <TD rowspan="1" colspan="1">7</TD>
                     <TD rowspan="1" colspan="1">0</TD>
                  </TR>
                  <TR no="19" isLast="false">
                     <TD rowspan="1" colspan="1">2</TD>
                     <TD rowspan="1" colspan="1">8</TD>
                     <TD rowspan="1" colspan="1">0</TD>
                  </TR>
                  <TR no="20" isLast="false">
                     <TD rowspan="1" colspan="1">2</TD>
                     <TD rowspan="1" colspan="1">9</TD>
                     <TD rowspan="1" colspan="1">0</TD>
                  </TR>
                  <TR no="21" isLast="false">
                     <TD rowspan="1" colspan="1">2</TD>
                     <TD rowspan="1" colspan="1">10</TD>
                     <TD rowspan="1" colspan="1">0</TD>
                  </TR>
                  <TR no="22" isLast="false">
                     <TD rowspan="1" colspan="1">3</TD>
                     <TD rowspan="1" colspan="1">1</TD>
                     <TD rowspan="1" colspan="1">1.001</TD>
                  </TR>
                  <TR no="23" isLast="false">
                     <TD rowspan="1" colspan="1">3</TD>
                     <TD rowspan="1" colspan="1">2</TD>
                     <TD rowspan="1" colspan="1">1</TD>
                  </TR>
                  <TR no="24" isLast="false">
                     <TD rowspan="1" colspan="1">3</TD>
                     <TD rowspan="1" colspan="1">3</TD>
                     <TD rowspan="1" colspan="1">0.9</TD>
                  </TR>
                  <TR no="25" isLast="false">
                     <TD rowspan="1" colspan="1">3</TD>
                     <TD rowspan="1" colspan="1">4</TD>
                     <TD rowspan="1" colspan="1">0.988</TD>
                  </TR>
                  <TR no="26" isLast="false">
                     <TD rowspan="1" colspan="1">3</TD>
                     <TD rowspan="1" colspan="1">5</TD>
                     <TD rowspan="1" colspan="1">1.001</TD>
                  </TR>
                  <TR no="27" isLast="false">
                     <TD rowspan="1" colspan="1">3</TD>
                     <TD rowspan="1" colspan="1">6</TD>
                     <TD rowspan="1" colspan="1">1.004</TD>
                  </TR>
                  <TR no="28" isLast="false">
                     <TD rowspan="1" colspan="1">3</TD>
                     <TD rowspan="1" colspan="1">7</TD>
                     <TD rowspan="1" colspan="1">0.999</TD>
                  </TR>
                  <TR no="29" isLast="false">
                     <TD rowspan="1" colspan="1">3</TD>
                     <TD rowspan="1" colspan="1">8</TD>
                     <TD rowspan="1" colspan="1">0.989</TD>
                  </TR>
                  <TR no="30" isLast="false">
                     <TD rowspan="1" colspan="1">3</TD>
                     <TD rowspan="1" colspan="1">9</TD>
                     <TD rowspan="1" colspan="1">1.012</TD>
                  </TR>
                  <TR no="31" isLast="false">
                     <TD rowspan="1" colspan="1">3</TD>
                     <TD rowspan="1" colspan="1">10</TD>
                     <TD rowspan="1" colspan="1">1.03</TD>
                  </TR>
                  <TR no="32" isLast="false">
                     <TD rowspan="1" colspan="1">4</TD>
                     <TD rowspan="1" colspan="1">1</TD>
                     <TD rowspan="1" colspan="1">1.001</TD>
                  </TR>
                  <TR no="33" isLast="false">
                     <TD rowspan="1" colspan="1">4</TD>
                     <TD rowspan="1" colspan="1">2</TD>
                     <TD rowspan="1" colspan="1">1</TD>
                  </TR>
                  <TR no="34" isLast="false">
                     <TD rowspan="1" colspan="1">4</TD>
                     <TD rowspan="1" colspan="1">3</TD>
                     <TD rowspan="1" colspan="1">0.9</TD>
                  </TR>
                  <TR no="35" isLast="false">
                     <TD rowspan="1" colspan="1">4</TD>
                     <TD rowspan="1" colspan="1">4</TD>
                     <TD rowspan="1" colspan="1">0.988</TD>
                  </TR>
                  <TR no="36" isLast="false">
                     <TD rowspan="1" colspan="1">4</TD>
                     <TD rowspan="1" colspan="1">5</TD>
                     <TD rowspan="1" colspan="1">1.001</TD>
                  </TR>
                  <TR no="37" isLast="false">
                     <TD rowspan="1" colspan="1">4</TD>
                     <TD rowspan="1" colspan="1">6</TD>
                     <TD rowspan="1" colspan="1">1.004</TD>
                  </TR>
                  <TR no="38" isLast="false">
                     <TD rowspan="1" colspan="1">4</TD>
                     <TD rowspan="1" colspan="1">7</TD>
                     <TD rowspan="1" colspan="1">0.999</TD>
                  </TR>
                  <TR no="39" isLast="false">
                     <TD rowspan="1" colspan="1">4</TD>
                     <TD rowspan="1" colspan="1">8</TD>
                     <TD rowspan="1" colspan="1">0.989</TD>
                  </TR>
                  <TR no="40" isLast="false">
                     <TD rowspan="1" colspan="1">4</TD>
                     <TD rowspan="1" colspan="1">9</TD>
                     <TD rowspan="1" colspan="1">1.012</TD>
                  </TR>
                  <TR no="41" isLast="false">
                     <TD rowspan="1" colspan="1">4</TD>
                     <TD rowspan="1" colspan="1">10</TD>
                     <TD rowspan="1" colspan="1">1.03</TD>
                  </TR>
                  <TR no="42" isLast="false">
                     <TD rowspan="1" colspan="1">5</TD>
                     <TD rowspan="1" colspan="1">1</TD>
                     <TD rowspan="1" colspan="1">1.001</TD>
                  </TR>
                  <TR no="43" isLast="false">
                     <TD rowspan="1" colspan="1">5</TD>
                     <TD rowspan="1" colspan="1">2</TD>
                     <TD rowspan="1" colspan="1">1</TD>
                  </TR>
                  <TR no="44" isLast="false">
                     <TD rowspan="1" colspan="1">5</TD>
                     <TD rowspan="1" colspan="1">3</TD>
                     <TD rowspan="1" colspan="1">0.9</TD>
                  </TR>
                  <TR no="45" isLast="false">
                     <TD rowspan="1" colspan="1">5</TD>
                     <TD rowspan="1" colspan="1">4</TD>
                     <TD rowspan="1" colspan="1">0.988</TD>
                  </TR>
                  <TR no="46" isLast="false">
                     <TD rowspan="1" colspan="1">5</TD>
                     <TD rowspan="1" colspan="1">5</TD>
                     <TD rowspan="1" colspan="1">1.001</TD>
                  </TR>
                  <TR no="47" isLast="false">
                     <TD rowspan="1" colspan="1">5</TD>
                     <TD rowspan="1" colspan="1">6</TD>
                     <TD rowspan="1" colspan="1">1.004</TD>
                  </TR>
                  <TR no="48" isLast="false">
                     <TD rowspan="1" colspan="1">5</TD>
                     <TD rowspan="1" colspan="1">7</TD>
                     <TD rowspan="1" colspan="1">0.999</TD>
                  </TR>
                  <TR no="49" isLast="false">
                     <TD rowspan="1" colspan="1">5</TD>
                     <TD rowspan="1" colspan="1">8</TD>
                     <TD rowspan="1" colspan="1">0.989</TD>
                  </TR>
                  <TR no="50" isLast="false">
                     <TD rowspan="1" colspan="1">5</TD>
                     <TD rowspan="1" colspan="1">9</TD>
                     <TD rowspan="1" colspan="1">1.012</TD>
                  </TR>
                  <TR no="51" isLast="true">
                     <TD rowspan="1" colspan="1">5</TD>
                     <TD rowspan="1" colspan="1">10</TD>
                     <TD rowspan="1" colspan="1">1.03</TD>
                  </TR>
               </TBODY>
            </TABLE>
         </ExampleSection>
         <GeneralSection>
            <SectionTitle>Calculate the spread</SectionTitle>
            <Paragraph>Determine the spread of the measured values. The highest
			 measured value is 1.03 (Sample Group 1, Sample Number 10). The lowest measured
			 value is 0.9 (Sample Group 1, Sample Number 3).</Paragraph>
            <Figure space-and-orientation="indented-estimated">
               <HTML:IMG xmlns:HTML="http://www.w3.org/TR/REC-html40" width="182" height="48"
                         SRC="../images/histogram2.jpg"
                         alt="[...]"/>
            </Figure>
            <Formula space-and-orientation="indented-estimated">
               <Paragraph>Spread = 1.03 - 0.9 = 0.13</Paragraph>
            </Formula>
         </GeneralSection>
         <GeneralSection>
            <SectionTitle>Calculate the class width:</SectionTitle>
            <Figure space-and-orientation="indented-estimated">
               <HTML:IMG xmlns:HTML="http://www.w3.org/TR/REC-html40" width="97" height="74"
                         SRC="../images/histogram3.jpg"
                         alt="[...]"/>
            </Figure>
            <Paragraph>The class width is 0.13 / √50 =
			 0.02055480479109446565799280803881. This value is rounded off to
			 0.02.</Paragraph>
         </GeneralSection>
         <GeneralSection>
            <SectionTitle>Compose the classes</SectionTitle>
            <Paragraph>The classes are composed as follows <Emphasis>Class 1 Lower
			 Tolerance (or Xmin in case Xmin &lt; Lower Tolerance) then Class2 = Class1 + W</Emphasis> and so on. The following classes are generated:</Paragraph>
            <TABLE border="1" borderstyle="default" space-and-orientation="indented-estimated">
               <TBODY noTR="7">
                  <TR no="1" isLast="false">
                     <TD rowspan="1" colspan="1">Class 1</TD>
                     <TD rowspan="1" colspan="1">0.900000</TD>
                  </TR>
                  <TR no="2" isLast="false">
                     <TD rowspan="1" colspan="1">Class 2</TD>
                     <TD rowspan="1" colspan="1">0.920000</TD>
                  </TR>
                  <TR no="3" isLast="false">
                     <TD rowspan="1" colspan="1">Class 3</TD>
                     <TD rowspan="1" colspan="1">0.940000</TD>
                  </TR>
                  <TR no="4" isLast="false">
                     <TD rowspan="1" colspan="1">Class 4</TD>
                     <TD rowspan="1" colspan="1">0.960000</TD>
                  </TR>
                  <TR no="5" isLast="false">
                     <TD rowspan="1" colspan="1">Class
					 5</TD>
                     <TD rowspan="1" colspan="1">0.980000</TD>
                  </TR>
                  <TR no="6" isLast="false">
                     <TD rowspan="1" colspan="1">Class
					 6</TD>
                     <TD rowspan="1" colspan="1">1.000000</TD>
                  </TR>
                  <TR no="7" isLast="true">
                     <TD rowspan="1" colspan="1">Class
					 7</TD>
                     <TD rowspan="1" colspan="1">1.020000</TD>
                  </TR>
               </TBODY>
            </TABLE>
         </GeneralSection>
         <GeneralSection>
            <SectionTitle>Populate the classes</SectionTitle>
            <Paragraph>The values of the different measurements can be grouped into
			 a class, if the value is greater or equal to the class value, and less than the
			 class value + the class width. The result is:</Paragraph>
            <TABLE border="1" borderstyle="default" space-and-orientation="indented-estimated">
               <TBODY noTR="8">
                  <TR no="1" isLast="false">
                     <TD rowspan="1" colspan="1">Class</TD>
                     <TD rowspan="1" colspan="1">Number of
					 measurements</TD>
                  </TR>
                  <TR no="2" isLast="false">
                     <TD rowspan="1" colspan="1">1</TD>
                     <TD rowspan="1" colspan="1">1</TD>
                  </TR>
                  <TR no="3" isLast="false">
                     <TD rowspan="1" colspan="1">2</TD>
                     <TD rowspan="1" colspan="1">0</TD>
                  </TR>
                  <TR no="4" isLast="false">
                     <TD rowspan="1" colspan="1">3</TD>
                     <TD rowspan="1" colspan="1">0</TD>
                  </TR>
                  <TR no="5" isLast="false">
                     <TD rowspan="1" colspan="1">4</TD>
                     <TD rowspan="1" colspan="1">0</TD>
                  </TR>
                  <TR no="6" isLast="false">
                     <TD rowspan="1" colspan="1">5</TD>
                     <TD rowspan="1" colspan="1">12</TD>
                  </TR>
                  <TR no="7" isLast="false">
                     <TD rowspan="1" colspan="1">6</TD>
                     <TD rowspan="1" colspan="1">36</TD>
                  </TR>
                  <TR no="8" isLast="true">
                     <TD rowspan="1" colspan="1">7</TD>
                     <TD rowspan="1" colspan="1">1</TD>
                  </TR>
               </TBODY>
            </TABLE>
         </GeneralSection>
         <GeneralSection>
            <SectionTitle>Calculate the mean</SectionTitle>
            <Paragraph>For every measurement, the difference to the mean is
			 calculated and the square of the differences is added together. If the first
			 sample number has a measurement value of 1:</Paragraph>
            <Formula space-and-orientation="indented-estimated">
               <Paragraph>(1 - 0.995850)² = (0.00415)² = 0.0000172225</Paragraph>
            </Formula>
            <Paragraph>The square differences are calculated and summed together to
			 form a total square difference. For the above example the total is
			 1.311734.</Paragraph>
            <Formula space-and-orientation="indented-estimated">
               <Paragraph>Mean = Standard Deviation - √ 1.311734 /
		  50 = 0.160000</Paragraph>
            </Formula>
         </GeneralSection>
         <GeneralSection>
            <SectionTitle>Plot the chart</SectionTitle>
            <Paragraph>The following figure displays the chart plotted with the
			 above data:</Paragraph>
            <Figure space-and-orientation="indented-estimated">
               <HTML:IMG xmlns:HTML="http://www.w3.org/TR/REC-html40" width="599" height="366"
                         SRC="../images/histogram4.jpg"
                         alt="[...]"/>
            </Figure>
            <Paragraph>On the X-Axis the characteristics unit is displayed. It is
			 however possible that for a specific standard test procedure or for an
			 inspection order line, the measurement value is expressed in a different unit
			 that are later converted to the characteristic unit.</Paragraph>
         </GeneralSection>
      </GeneralSection>
   </GeneralSection>
</ManualTopic>