<p> Attribute Control Chart Examples Fall 2011</p><p>Thirteen samples of size n=100 each were collected. The number of defective items for each sample are shown below.</p><p>Sample Number of # Defectives 1 5 2 4 3 3 4 3 5 2 6 4 7 4 8 4 9 2 10 5 11 2 12 6 13 3</p><p>Use Minitab to build a P chart and evaluate the process control.</p><p>JMB Fall 2011 Page 1 Results: </p><p>The y-axis of the P chart is the proportion defective for each sample.</p><p>P Chart of Example</p><p>0.09 UCL=0.0922</p><p>0.08</p><p>0.07</p><p>0.06 n o i t</p><p> r 0.05 o p</p><p> o 0.04 _ r</p><p>P P=0.0362 0.03</p><p>0.02</p><p>0.01</p><p>0.00 LCL=0</p><p>1 2 3 4 5 6 7 8 9 10 11 12 13 Sample</p><p>The process does not exhibit any out-of-control characteristics.</p><p>JMB Fall 2011 Page 2 Given the following data on defects and sample size, use Minitab to build a C chart and evaluate the process control. </p><p>Example</p><p>DataC SizeC</p><p>2 50</p><p>1 50</p><p>3 50</p><p>4 50</p><p>2 50</p><p>4 50</p><p>6 50</p><p>4 50</p><p>2 50</p><p>5 50</p><p>2 50</p><p>5 50</p><p>3 50</p><p>Note that there were 13 samples of size n=50 taken.</p><p>JMB Fall 2011 Page 3 Note that Minitab does not ask for the sample size. As is the case for P charts, you are given the option of performing tests for special causes.</p><p>Results:</p><p>Sum of ExampleData_C = 43</p><p>Mean of ExampleData_C = 43/13 = 3.30769 = cbar </p><p>Square root of cbar = 1.81871</p><p>UCL = cbar+ 3 sqrt cbar = 8.76381</p><p>Note that the sample size information is not used for calculating C bar or the control limits. C bar is calculated as the sum of the defects divided by the samples taken. In this example C bar = 31/13.</p><p>JMB Fall 2011 Page 4 C Chart of ExampleData_C 9 UCL=8.764 8</p><p>7</p><p>6 t n u</p><p> o 5 C</p><p> e l</p><p> p 4 _ m</p><p> a C=3.308</p><p>S 3</p><p>2</p><p>1</p><p>0 LCL=0</p><p>1 2 3 4 5 6 7 8 9 10 11 12 13 Sample</p><p>C Chart of ExampleData_C with Four Tests 9 UCL=8.764 8</p><p>7</p><p>6 t n u</p><p> o 5 C</p><p> e l</p><p> p 4 _ m</p><p> a C=3.308</p><p>S 3</p><p>2</p><p>1</p><p>0 LCL=0</p><p>1 2 3 4 5 6 7 8 9 10 11 12 13 Sample</p><p>Note the label on the y-axis of the Minitab C chart. The Sample Count is the number of defects in each of the thirteen samples.</p><p>JMB Fall 2011 Page 5 Given the following data on defects and sample size, use Minitab to build a U chart and evaluate the process control. The U chart measures defects per unit and is used when the number of units inspected varies from one sample to another.</p><p>DataU SizeU</p><p>5 50</p><p>4 60</p><p>3 40</p><p>5 40</p><p>5 50</p><p>5 60</p><p>5 30</p><p>4 30</p><p>3 30</p><p>1 30</p><p>1 30</p><p>6 50</p><p>3 50</p><p>2 50</p><p>5 60</p><p>2 60</p><p>JMB Fall 2011 Page 6 The centerline of the U chart is the overall U bar (total defects / total items sampled).</p><p>JMB Fall 2011 Page 7 U Chart of ExampleData_U Four Tests Applied 0.25</p><p>0.20 UCL=0.1928 t i n U</p><p> r</p><p> e 0.15 P</p><p> t n u o C</p><p>0.10</p><p> e _ l</p><p> p U=0.0819 m a S 0.05</p><p>0.00 LCL=0</p><p>1 3 5 7 9 11 13 15 Sample</p><p>U Chart of ExampleData_U 0.25</p><p>0.20</p><p> t UCL=0.1928 i n U</p><p> r</p><p> e 0.15 P</p><p> t n u o C 0.10 _ e l</p><p> p U=0.0819 m a</p><p>S 0.05</p><p>0.00 LCL=0</p><p>1 3 5 7 9 11 13 15 Sample Tests performed with unequal sample sizes</p><p>Note the label on the y-axis of the U charts (defects per unit). Also note that the two charts appear to be alike, even though one tested for all special causes and the other tested for none. </p><p>JMB Fall 2011 Page 8</p>