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U CHARTS By Steven H. Baker
AGENDA Control Charts U Charts Application Exercise Summary
Control Charts ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Source:  http://deming.eng.clemson.edu/pub/tutorials/qctools/ccmain1.htm#Top   (11/26/07)
Control Charts Source:  http://www.adeptscience.co.uk/kb/article/642A   (11/26/07) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],2-10 Any More than 10 np Constant Binomial Attribute p Varying u Varying c Constant Poisson Individual and moving  R 1 Variable Control Chart Sample Size Distribution Data Type
U Charts Data Type:  Attribute Data consists of categories or discrete values.  For example, measure whether a sample does or does not contain defects, or how many defects it contains. Distribution:  Poisson Poisson data is a count of infrequent events.  For control charts, events are defects occurring in a given area. Probability of events occurring is proportionally the same and must be rare. Sample Size:  Varying The sample size varies from sample to sample. Adapted from:  http://www.adeptscience.co.uk/kb/article/642A   (11/26/07) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
U Charts Source:  http://www.adeptscience.co.uk/kb/article/642A   (11/26/07) Continuous Welds: Samples will vary in length of and number of welds in  different units.  Rolls of Paper: Samples may need to be manually torn, so size will vary.  Word Processing Errors: Variance in length of documents sampled. Others? Adapted from:  Quality Management, Third Edition.  Howard S. Gitlow ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
U Charts ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Source:  http://www.adeptscience.co.uk/kb/article/642A   (11/26/07) Given the number of events, or defects, and the sample size you can calculate the needed formulas to construct a u chart.
U Charts Source:  http://www.adeptscience.co.uk/kb/article/642A   (11/26/07) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
U Charts Source:  http://www.adeptscience.co.uk/kb/article/642A   (11/26/07) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Application Source:  http://www.adeptscience.co.uk/kb/article/642A   (11/26/07) Consider the case of a manufacturer of a certain grade of plastic.  The plastic is produced in rolls, with samples taken five times daily.  Because of the nature of the process, the square footage of each sample varies from sample to sample.  Defects are counted for each sample separately. Can a u chart be used for this? ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Adapted from:  Quality Management, Third Edition.  Howard S. Gitlow
Application โ€“ Step 1 Source:  http://www.adeptscience.co.uk/kb/article/642A   (11/26/07) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Adapted from:  Quality Management, Third Edition.  Howard S. Gitlow 4 4 12 5 2 1 2 4 c 5 10 1 4 2 3 7 5 c 250 14 80 6 180 16 220 8 230 15 200 7 200 13 120 5 90 12 90 4 170 11 100 3 80 10 250 2 140 9 200 1 n i n i
Application โ€“ Step 2 Source:  http://www.adeptscience.co.uk/kb/article/642A   (11/26/07) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],0.0222 180 4 16 0.0174 230 4 15 0.0480 250 12 14 0.0250 200 5 13 0.0222 90 2 12 0.0059 170 1 11 0.0250 80 2 10 0.0286 140 4 9 0.0227 220 5 8 0.0500 200 10 7 0.0125 80 1 6 0.0333 120 4 5 0.0222 90 2 4 0.0300 100 3 3 0.0280 250 7 2 0.0250 200 5 1 u n c i
Application โ€“ Step 3 Source:  http://www.adeptscience.co.uk/kb/article/642A   (11/26/07) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Application โ€“ Step 4 Source:  http://www.adeptscience.co.uk/kb/article/642A   (11/26/07) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],All LCLโ€™s lower than 0 so all values set to 0. 0.0222 0.0174 0.0480 0.0250 0.0222 0.0059 0.0250 0.0286 0.0227 0.0500 0.0125 0.0333 0.0222 0.0300 0.0280 0.0250 u 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 LCL 0.0643  180 4 16 0.0600  230 4 15 0.0587  250 12 14 0.0624  200 5 13 0.0796  90 2 12 0.0653  170 1 11 0.0827  80 2 10 0.0692  140 4 9 0.0607  220 5 8 0.0624  200 10 7 0.0827  80 1 6 0.0726  120 4 5 0.0796  90 2 4 0.0769  100 3 3 0.0587  250 7 2 0.0624  200 5 1 UCL n c i
Application โ€“ Step 5 Source:  http://www.adeptscience.co.uk/kb/article/642A   (11/26/07) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Application โ€“ Step 6 Source:  http://www.adeptscience.co.uk/kb/article/642A   (11/26/07) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Exercise Source:  http://www.adeptscience.co.uk/kb/article/642A   (11/26/07) Construct a  u  chart for the following data. ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Source:  Statistical Methods for Quality Improvement.  Thomas P. Ryan 18 17 16 15 14 13 i 12 11 10 9 8 7 i 6 5 4 3 2 1 i 115 12 155 15 145 14 155 13 180 17 135 11 160 15 175 18 115 10 180 16 150 14 150 15 195 19 130 12 140 13 135 14 145 15 125 12 n c n c n c
Exercise Source:  http://www.adeptscience.co.uk/kb/article/642A   (11/26/07) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Answer: 0.1812  0.0088  0.1043 115 12 18 0.1692  0.0207  0.0839 155 13 17 0.1681  0.0219  0.0938 160 15 16 0.1639  0.0261  0.0889 180 16 15 0.1612  0.0288  0.0974 195 19 14 0.1745  0.0154  0.1037 135 14 13 0.1692  0.0207  0.0968 155 15 12 0.1639  0.0261  0.0944 180 17 11 0.1649  0.0251  0.1029 175 18 10 0.1705  0.0195  0.0933 150 14 9 0.1761  0.0139  0.0923 130 12 8 0.1717  0.0182  0.1034 145 15 7 0.1717  0.0182  0.0966 145 14 6 0.1745  0.0154  0.0815 135 11 5 0.1812  0.0088  0.0870 115 10 4 0.1705  0.0195  0.1000 150 15 3 0.1731  0.0168  0.0929 140 13 2 0.1777  0.0123  0.0960 125 12 1 UCL LCL u n c i
Exercise Source:  http://www.adeptscience.co.uk/kb/article/642A   (11/26/07) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Answer:
Summary Source:  http://www.adeptscience.co.uk/kb/article/642A   (11/26/07) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Summary Source:  http://www.adeptscience.co.uk/kb/article/642A   (11/26/07) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],U charts can be constructed and analyzed using six steps:
Readings List Source:  http://www.adeptscience.co.uk/kb/article/642A   (11/26/07) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Statistical Methods For Quality Improvement - Thomas P. Ryan Quality Management, Third Edition - Howard S. Gitlow

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