# An Introduction to Statistical Process Control

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An Introduction to Statistical Process Control
Control Charts An Introduction to Statistical Process Control

Process: Driving to Work Average Time: 12 minutes
Real Life Examples Process: Driving to Work Average Time: 12 minutes Standard Deviation: 2.5 minutes Common Causes Wind speed, miss one green light, driving speed, number of cars on road, time when leaving house, rainy weather Special Causes Stop for school bus crossing, traffic accident, pulled over for speeding, poor weather conditions, car mechanical problems, construction detour, stoplights not working properly, train crossing Let’s look at an example in real life, the process of driving to work. We collected data for one month, and calculated an average time of 12 minutes, with a standard deviation of 2.5 minutes The data could contain both common and special causes of variation, which could affect the average and standard deviation results. Examples are shown for each type of cause. The use of a control chart can help identify when a special cause may have been present. The driver should strive to eliminate the special causes from this process if they want to make their drive shorter (lower average) and more consistent (smaller std dev) Ask the participants to identify additional examples they have encountered on their drive to work

Range = Max of Data Subgroup – Min of Data Subgroup
Range Chart 6:55 PM 45 43 48 45 50 Range = 7 UCL CL 9:35 PM 44 48 43 42 45 Range = 6 We’ll look at the same data points. Using the same 5 readings at 6:55 PM, we see that the largest reading is 50, and the smallest reading is 43, so when we subtract 50-43, we get a range of 7. That number is plotted on the Range chart. LCL Range = Max of Data Subgroup – Min of Data Subgroup

Determine λ (between 0 and 1)
How to setup EWMA chart Determine λ (between 0 and 1) λ is the proportion of current value used for calculating newest value Recommend λ = 0.10, 0.20 or 0.40 (use smaller λ values to detect smaller shifts) Calculate new z values using λ = zi = λ*xi + (1 – λ) * zi-1 (where i = sample number) Lambda (λ) is the proportion of the current value used for calculating newest EWMA value Most resources recommend values between 0.10 and A good rule of thumb is to use smaller lambda to detect smaller shifts Review the formula for calculating the new EWMA value (z), using the current x value, and the previous z value For sample 2 on Oct 2nd, we calculate the new z value by taking 0.9*9.945 (previous z value) + 0.1*7.99 (current value) = The lambda value gets applied to the current x value, so the lower the lambda, the less influence the current value has on the new EWMA (z) value, which makes it easier to detect a small shift. If lambda = 1.0, then it would be equivalent to the traditional Shewhart chart, since 100% of the current value would be used, and 0% of the prior values would be used. = (0.9*9.945) + (0.1*7.99) Sample Date x z 1 1-Oct 9.45 9.945 2 2-Oct 7.99 9.7495 3 3-Oct 9.29 9.7035 4 4-Oct 11.66 9.899 9.899 = (0.9*9.7035) + (0.1*11.6)

11 total defects found on 6 documents
c chart Plots the quantity of defects in a sample Each part can have more than one defect Requires same number of parts within each sample Finally, we discuss the c-chart. Similar to how the np-chart is a simplified version of the p-chart, so is the c-chart to the u-chart. Instead of having a different quantity of documents each time, we keep our sample consistent to 6 documents, then just plot the number of defects found within each sample. Again, there is no calculations involved. 11 total defects found on 6 documents c = 11 defects per sample

Decision Tree for Control Charts
What type of data: Attribute or Variable? Attribute Variable How are defects counted: Defectives (Y/N), or Count of Defects? How large are the subgroups? 1 2 to 5 5 or more Defectives Count Constant Sample Size? Constant Sample Size? Use the X-bar and moving range for subgroup sizes from 2 to 5, and switch to the X-bar and Standard Deviation chart when the subgroup increase beyond 5, although either Range or Standard Deviation can be used for subgroups sizes between 5 and 10. Subgroups of size 10 or larger should use Standard Deviation charts. Defectives are also called binary (0/1) or Pass/Fail, since it is either good or bad. Count of defects has no limit to the number of defects that can be found. It can be converted to Defectives by taking all samples with at least one defect and calling it “Bad” or a “Fail” Individuals and Moving Range X-bar and Range X-bar and Std Dev Yes No Yes No np chart (number defective) P chart (proportion defective) c chart (defects per sample) u chart (defects per unit)

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Additional Resources Quality Management Systems Solutions Contact us at if you have any questions about this course, or would like some information about our training and/or consulting options This training material references Introduction to Statistical Quality Control, Douglas Montgomery, 5th Edition, which can be found online at

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