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Statistical Quality Control N.Obeidi

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Descriptive Statistics Descriptive Statistics include: Descriptive Statistics include: – The Mean- measure of central tendency – The Range- difference between largest/smallest observations in a set of data – Standard Deviation measures the amount of data dispersion around mean – Distribution of Data shape Normal or bell shaped or Normal or bell shaped or Skewed Skewed

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Statistics – ‘Mode’ Mode = most frequently occurring value Find the mode of 4,6,7,9,4 The most popular, or mode is 4

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Normal Distribution Frequency 4.7’4.8’4.9’Mean5.1’5.2’5.3’

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Normal Distribution Mean

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Distribution of Data Normal distributions Skewed distribution

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Setting Control Limits Percentage of values under normal curve

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Constructing an X-bar Chart: A quality control inspector at the Cocoa Fizz soft drink company has taken three samples with four observations each of the volume of bottles filled. If the standard deviation of the bottling operation is.2 ounces, use the below data to develop control charts with limits of 3 standard deviations for the 16 oz. bottling operation. Time 1Time 2Time 3 Observation 115.816.116.0 Observation 216.0 15.9 Observation 315.8 15.9 Observation 415.9 15.8 Sample means (X-bar) 15.87515.97515.9 Sample ranges (R) 0.20.30.2

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Solution and Control Chart (x-bar) Center line (x-double bar):

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Levey-Jennings Chart

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12 Levey-Jennings Chart

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Chapter 814 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery. Copyright (c) 2005 John Wiley & Sons, Inc.

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Cusum Chart

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C-Chart Example: The number of weekly customer complaints are monitored in a large hotel using a c-chart. Develop three sigma control limits using the data table below. WeekNumber of Complaints 13 22 33 41 53 63 72 81 93 101 Total22 Solution:

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Interpreting patterns in control charts Downward trend in R-chart…

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Control Chart Even control charts in which all points lie between the control limits might suggest that a process is out of control. In particular, the existence of a pattern in eight or more consecutive points indicates a process out of control, because an obvious pattern violates the assumption of random variability.

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Control Chart The first eight observations are below the center line, whereas the second seven observations all lie above the center line. Because of prolonged periods where values are either small or large, this process is out of control.

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P-Chart: Steel rod defects

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Moving Range I-chart

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Levey-Jennings Chart - Record and Evaluate the Control Values Mean Day +1SD +2SD +3SD -1SD -2SD -3SD

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Westgard Rules “Multirule Quality Control” “Multirule Quality Control” Uses a combination of decision criteria or control rules Uses a combination of decision criteria or control rules Allows determination of whether an analytical run is “in-control” or “out-of- control” Allows determination of whether an analytical run is “in-control” or “out-of- control”

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Westgard Rules ( Generally used where 2 levels of control material are analyzed per run) 1 2S rule 1 2S rule 1 3S rule 1 3S rule 2 2S rule 2 2S rule R 4S rule R 4S rule 4 1S rule 4 1S rule 10 X rule 10 X rule

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Westgard – 1 2S Rule “warning rule” “warning rule” One of two control results falls outside ±2SD One of two control results falls outside ±2SD Alerts tech to possible problems Alerts tech to possible problems Not cause for rejecting a run Not cause for rejecting a run Must then evaluate the 1 3S rule Must then evaluate the 1 3S rule

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1 2S Rule = A warning to trigger careful inspection of the control data Mean Day +1SD +2SD +3SD -1SD -2SD -3SD 1 2S rule violation

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Westgard – 1 3S Rule If either of the two control results falls outside of ±3SD, rule is violated If either of the two control results falls outside of ±3SD, rule is violated Run must be rejected Run must be rejected If 1 3S not violated, check 2 2S If 1 3S not violated, check 2 2S

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1 3S Rule = Reject the run when a single control measurement exceeds the +3SD or -3SD control limit Mean Day +1SD +2S D +3SD -1SD -2SD -3SD 1 3S rule violatio n

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Westgard – 2 2S Rule 2 consecutive control values for the same level fall outside of ±2SD in the same direction, or 2 consecutive control values for the same level fall outside of ±2SD in the same direction, or Both controls in the same run exceed ±2SD Both controls in the same run exceed ±2SD Patient results cannot be reported Patient results cannot be reported Requires corrective action Requires corrective action

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2 2S Rule = Reject the run when 2 consecutive control measurements exceed the same +2SD or -2SD control limit Mean Day +1SD +2S D +3SD -1SD -2SD -3SD 2 2S rule violatio n

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Westgard – R 4S Rule One control exceeds the mean by – 2SD, and the other control exceeds the mean by +2SD One control exceeds the mean by – 2SD, and the other control exceeds the mean by +2SD The range between the two results will therefore exceed 4 SD The range between the two results will therefore exceed 4 SD Random error has occurred, test run must be rejected Random error has occurred, test run must be rejected

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R 4S Rule = Reject the run when 1 control measurement exceed the +2SD and the other exceeds the -2SD control limit Mean Day +1SD +2S D +3SD -1SD -2SD -3SD R 4S rule violatio n

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Westgard – 4 1S Rule Requires control data from previous runs Requires control data from previous runs Four consecutive QC results for one level of control are outside ±1SD, or Four consecutive QC results for one level of control are outside ±1SD, or Both levels of control have consecutive results that are outside ±1SD Both levels of control have consecutive results that are outside ±1SD

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Westgard – 10 X Rule Requires control data from previous runs Requires control data from previous runs Ten consecutive QC results for one level of control are on one side of the mean, or Ten consecutive QC results for one level of control are on one side of the mean, or Both levels of control have five consecutive results that are on the same side of the mean Both levels of control have five consecutive results that are on the same side of the mean

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10 x Rule = Reject the run when 10 consecutive control measurements fall on one side of the mean Mean Day +1SD +2S D +3SD -1SD -2SD -3SD 10 x rule violation

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Westgard Multirule QC

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