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## Statistical Process Control

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**Statistical Process Control**Variables Data Click Here to Begin**Objectives:**• Introduce Statistical Process Control • Understand the process of creating an X bar R Chart • Understand the methods used in monitoring SPC charts**SPC**Introduction**Variability**• Normal Variability: • -Normal variability is the inherent variability within a process (It is the best the process can do in terms of variability) • -If you want to reduce normal, or inherent, variability you will usually have to redesign the process • Non-Normal Variability: • -Non-normal variability is a result of special causes • -The objective of the SPC chart is to determine when special causes are present**Developing X Charts:**• Per Juran’s Quality Handbook, the basic procedure for developing X Charts is as follows: • 1.) Select the measurable characteristic to be studied • 2.) Collect enough observations (20 or more) for a trial study (The observations should be far enough apart to allow the process to potentially be able to shift) • 3.) Calculate control limits and the centerline for the trial study using the formulas given later**Developing X Charts:**• 4.) Set up the trial control chart using the centerline and limits, and plot the observations obtained in step 2 (If all points are within the control limits and there are no unnatural patterns, extend the limits for future control) • 5.) Revise the control limits and centerline as needed (by removing out-of-control points by observing trends, etc.) to assist in improving the process • 6.) Periodically assess the effectiveness of the chart, revising it as needed or discontinuing it**SPC**Xbar R Chart**Equations:**• UCL = Ave + (3*Sigma) • LCL = Ave – (3*Sigma) • Vs. • UCL = Ave + (A2*Rbar) • LCL = Ave – (A2*Rbar) • (A2*Rbar) = (3*Sigma)**Xbar & R Chart**Average Range Average of Averages Constant**Example: Variable Data**To find the average take the sum and divide it by the number being added together. Determine Average(s) for data**Example: Variable Data**To find the range list the numbers under consideration from lowest to highest value, then subtract the lowest value from the highest value Next determine the range(s) of data**Example: Variable Data**• Now calculate the UCL: • To calculate the UCL first find the sum of all sample averages: • = Sum = 8.36 • Then take the sum and divide it by the number of numbers added together: • 8.36/16 = 0.52 • Average of Averages (X double bar) = 0.52**Example: Variable Data**• Now calculate the UCL: • To calculate the UCL next find the sum of all sample ranges: • = Sum = 9.44 • Then take the sum and divide it by the number of numbers added together: • 9.44/16 = 0.59 • Average range (R bar) = 0.59**Example: Variable Data**• Now calculate the UCL: • Recall the formula for the UCL is: • UCL = Average of Averages + (A2*Average Range) • -or- • UCL = X double bar + (A2*R bar) • Thus far we have calculated the average of the averages and the average range, so the formula becomes: • UCL = 0.52 + (A2*0.59)**Example: Variable Data**• Now we will find A2. A2 is a constant found on the following table:**Example: Variable Data**• To finish the calculation of UCL we simply plug the values into the formula: • UCL = X double bar + (A2*R bar) • UCL = 0.52 + (0.577 * 0.59) UCL = 0.86**Example: Variable Data**• Calculate the LCL: • Now calculate the LCL using the formula: • LCL = X double bar - (A2*R bar) • LCL = 0.52 - (0.577 * 0.59) LCL = 0.18**Example Recap:**• The UCL and LCL have been calculated and were found to equal: • UCL = 0.86 • LCL = 0.18 • What does this mean? One would expect 99.73% of sample averages (n = 5) to lie within the range of the UCL and LCL due to normal variation. . . In other words, one could expect 99.73% of all sample averages to lie between 0.86 and 0.18**R Chart:**• The next steps are to calculate the upper and lower control limits for the Range Chart • --The objective of the Range chart is to detect changes in variability • Recall: • UCL = (D4*R bar) • LCL = (D3*R bar)**Now complete the R Chart:**• We have already found R bar to be = 0.59 • -so- • UCL = 2.114*0.59 • LCL = 0*0.59 • UCL = 1.25 • LCL = 0**SPC**Monitoring Control Charts**Control Chart Interpretation Rules:**• Look for Special Causes, which are suspect when: • 1.) One or more points are above the UCL or below the LCL • 2.) Seven or more consecutive points are above or below the centerline • 3.) One in twenty plotted points is in the 1/3 outer edge of the chart • 4.) Movements of five or more consecutive points are either up or down**Completed X bar R Charts:**Special Cause**Special Cause Variation**• If special causes are identified, the process is considered to be ‘unstable’ • Removing special causes when they are harmful (which is most of the time) is an important part of process improvement • Tracking down special causes often relies heavily on people’s (operators, supervisors, etc.) memories of what made that occurrence different**Special Cause Variation**• When you spot a special cause: • Control any damage or problems with immediate (short term) fix • Once a ‘quick fix’ is in place, search for the cause • Once you determine the special cause, develop a longer-term remedy**Statistical Process Control**Variables Data—The End