Published on March 19, 2009
Overview of Statistical Process Control (SPC) March 18, 2009
SPC Defined • Basic – Shows the behavior of a characteristic over time – Shows the influence of different variables on the characteristic – Shows where the process is located and how much variation is present in the process – Helps us get a process in a state of control • Advanced – Is the basis for establishing process capability • Process capability defines how well (or not well) our process can meet the needs of our customers – Separates common cause variation from special cause variation 2
Process Limits-Not Customer Limits If the process remains stable and in control, we expect the process’ output to run between these limits almost 100% of the time. 3
The Relationship of Process Limits to Customer Limits (Process Capability) The process limits are wider than the customer’s The process limits are tighter than the customer’s limits. The process is not capable. You have three limits. This is a capable process and no significant options: Get your customer to relax his action is needed other than make sure the process requirement, 100% inspect the output of the is followed. process, or change the process to meet the customer’s requirements The process limits are marginally better than the customer’s The process limits are tighter than the customer’s limits but limits. The process is centered so variation must be the process is off target (to high side). Adjust process to 4 reduced. Great case for six sigma. target. If the process can’t be adjusted, then reduce variation. Great case for six sigma
Common Cause and Special Cause Variation Lower Process Limit Upper Process Limit • Common cause variation is what we expect to happen 99.97% of the time if the process is in control. • Common cause variation exists between the process limits • Special cause variation is not expected to happen and has assignable causes. • Special cause variation occurs outside the process limits 99.97% 5
Common Cause Special Cause Variation Variation Histogram of Process Week One Histogram of Process Week One 20 14 12 15 10 If only common cause Frequency Frequency 8 10 variation is present in 6 5 4 the process, the 2 0 1.68 1.76 1.84 1.92 2.00 0 histogram will look the Peen Height 1.68 1.74 1.80 1.86 1.92 1.98 Peen Height Histogram of Process Week Two Histogram of Process Week Two same over time 12 12 10 10 8 8 Frequency Frequency 6 6 If special cause 4 4 2 2 variation exists, the 0 1.65 1.70 1.75 1.80 1.85 1.90 1.95 2.00 0 1.68 1.74 1.80 1.86 1.92 1.98 Peen Height histogram will change Peen Height Histogramof Process W Three eek 18 over time in location Histogram of Process Week Three 16 4 14 and/or spread 12 3 Frequency 10 Frequency 8 2 6 4 1 2 0 0 1.65 1.70 1.75 1.80 1.85 1.90 1.95 2.00 1.65 1.70 1.75 1.80 1.85 1.90 1.95 2.00 Peen Height Peen Height 6
Examples of Common Cause/Special Cause Variation • Body Temperature – If our body’s processes are in control, we expect temperature to vary slightly above and below 98.6 degrees F. This is the common cause (or expected) variation. – If a virus (special cause) enters our body, a process will be altered and temperature will spike significantly high • Teenage Behavior – Teenagers do teenage things. Always have and always will. Parents must decide what is expected behavior and what is not expected behavior. The former (good or bad) usually warrants a stern lecture while the latter deserves punishment. – Special causes often drive teenage behavior. The breakup by a girlfriend. Being cut from a sports team. Making a bad grade. If they are not acting as expected, we often must find the special cause before acting in return. – An example-My eighteen year old often challenges me on my philosophies and opinions. That is fine. I expect him to do that. I’m glad he does it. Sometimes he goes too far with his mother and can be disrespectful. That’s outside the boundaries of normal behavior and incurs my wrath. 7
Exercise #1 • Run product from machine determine upper and lower process limits • Run product to see how the process limits hold • Introduce special causes – Increased standard deviation – Shift in average 8
The Sections of a Control Chart: Process Information • Process information: This is needed to keep production records to go along with the data. • What you should record: – Date data was collected – Time data was collected – Who collected the data 9
The Sections of a Control Chart: Subgroups • The data is recorded in subgroups • The subgroups are set up to be a certain size. The size of a subgroup is the number of readings recorded. – Typical sizes are three and five • A completed control chart is one with at least twenty completed subgroups on the page 10
The Sections of a Control Chart: Subgroup Statistics • Once the data is recorded in the subgroups, we need to perform calculations for each subgroup – A measure of where the process is located. The mean (or average) X shows us where the process is located – A measure of how much variation is in the process. The range R shows us how much variation is in the process. 11
What is a Mean? • The mean is the center of weight for data. Also called average. 50% 50% Weight Weight Mean 12
How to Calculate a Mean • Add up the measurements and divide by the number of measurements – Add up measurements: o 1.81+1.81+1.82 o Sum=5.44 o Number of measurements: 3 – Divide sum by the number of measurements 5.44 = 1.813 3 Note: Always record the mean to 1.82 one more decimal place than the 1.813 13 original data point
What is a Range? • The range indicates how similar (or dis- Largest similar) the measurement: 1.80 measurements are in Smallest a subgroup measurement: • To calculate the 1.75 range Range: 1.80-1.75=0.05 – Subtract the smallest measurement from the largest measurement 14
Exercise #2 • Collect subgroups of data • Calculate mean and range 15
Overall Mean X 1 2 45 6 78 9 10 3 27.16 Number of means:10 Sum:2.73+2.71+2.72+2.72+2.72+2.72+220.127.116.11+2.71+2.71 = 2.716 10 Sum=27.16 16 Divide sum by number of means
Overall Range R • Number of ranges: 10 • Sum of ranges: o 0.09+0.05+0.05+0.06+0.12+0.08+0.08+0.06+0.07+0.04 o Sum=0.7 o Divide Sum by number of ranges 0.7 = 0.07 10 17
Sections of a Control Chart: Plot of Means and Ranges Plot of X Means Plot of R Ranges •The plots show how the process is behaving over time •We expect the points to fall above and below the 18 center line which is the overall mean
Sections of the Control Chart: Control Limits • Control limits are calculated for means and ranges • Control limits represent the boundaries between normal and abnormal variation or common cause from special cause variation • Common cause variation is: – What we expect to happen the majority of time. – Common cause variation is everything between the limits. You can also call it 50/50 variation. When you flip a coin, there is a 50% chance of getting a head and a 50% chance of getting a tail. Meaning, the only thing driving the outcome is chance. Same with production. If only common cause variation is present, there is a 50% chance of being above the target and a 50% chance of being below the target. The majority of points should fall within the limits. 19
Exercise #3 • Collect more subgroups and calculate control limits 20
Interpreting Charts • There are different pictures you might see in the plots of means and ranges. • Key point: Look for abnormal patterns in the data. Something is causing the abnormal pattern. This “something” is called a assignable cause. 21
Interpreting Control Charts and Taking Action • The averages are randomly falling above Process In Control with Chance Variation and below the centerline. 15 • There are no points outside the upper control 10 limit. • The variation is common 5 cause variation. No X special causes of 0 variation are present 22
Trends • The plot of averages was behaving randomly but Trends something occurred to make the process start drifting upward. 1500 • The process is no longer behaving randomly. 1000 Special cause variation is present • Find the assignable 500 X cause • Document your actions 0 on the control chart 23
Jumps in Process Level • The process is not exhibiting random Jumps in Process Level behavior • Special cause 1500 variation exists 1000 • Find the assignable cause 500 • Document your actions on the control 0 chart 24
Cyclic Pattern • There is a repeating cycle to the data Recurring Cycles • This is not random 600 behavior • Find the assignable 400 cause 200 • Document your actions on the control 0 chart 25
Point Near the Control Limit • Point at the upper control limit but not outside the 1500 upper control limit • Proper action to take: 1000 – Pull another sample and plot the average and range. If the average is still near 500 the upper limit, action may be needed – Document your actions on 0 the control chart 26
Point Well Outside the Upper Limit • This is a strong signal that an assignable Process In Control with Chance Variation cause exists for this special cause 1500 variation • Find the assignable 1000 cause 500 • Document your actions on the control 0 chart 27
Point Just Above or Just Below Control Limit • Don’t take the limit so literally. Remember, there is a small probability of a point falling Process In Control with Chance Variation outside the limit. We can expect this to happen less than 1% of the time. 1500 • Proper action to take: – Don’t be so quick to adjust the 1000 machine or process – Pull another sample and plot the average and range. If the 500 average is still near the upper limit, action may be needed – Document your action on the 0 control chart 28
Taking and Documenting Action • When special cause variation is present, find and eliminate the assignable cause • Document the actions taken on the control chart. Record the date and time for the action 29
Exercise #4 • Collect more subgroups and evaluate chart – Change in process level – OOC point 30
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