Overview of Statistical Process Control (SPC)

March 18, 2009

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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

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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.

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The Relationship of Process Limits to Customer Limits (Process Capability)

The process limits are wider than the customer’s limits. The process is not capable. You have three options: Get your customer to relax his requirement, 100% inspect the output of the process, or change the process to meet the customer’s requirements

The process limits are tighter than the customer’s limits. This is a capable process and no significant action is needed other than make sure the process is followed.

The process limits are marginally better than the customer’s limits. The process is centered so variation must be reduced. Great case for six sigma.

The process limits are tighter than the customer’s limits but the process is off target (to high side). Adjust process to target. If the process can’t be adjusted, then reduce variation. Great case for six sigma

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Common Cause and Special Cause Variation

• 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

Upper Process LimitLower Process Limit

99.97%

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2.001.921.841.761.68

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15

10

5

0

Peen Height

Frequency

Histogram of Process Week One

1.981.921.861.801.741.68

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10

8

6

4

2

0

Peen Height

Frequency

Histogram of Process Week Two

2.001.951.901.851.801.751.701.65

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2

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Peen Height

Frequency

Histogram of Process Week Three

1.981.921.861.801.741.68

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12

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8

6

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2

0

Peen Height

Frequency

Histogram of Process Week One

2.001.951.901.851.801.751.701.65

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10

8

6

4

2

0

Peen Height

Frequency

Histogram of Process Week Two

2.001.951.901.851.801.751.701.65

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1

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Peen Height

Frequency

Histogram of Process Week Three

Common Cause Variation

Special Cause Variation

If only common cause variation is present in the process, the histogram will look the same over time

If special cause variation exists, the histogram will change over time in location and/or spread

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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.

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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

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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

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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

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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) shows us where the process is located

– A measure of how much variation is in the process. The range shows us how much variation is in the process.

X

R

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What is a Mean?

• The mean is the center of weight for data. Also called average.

50% Weight

50% Weight

Mean

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How to Calculate a Mean

• Add up the measurements and divide by the number of measurements– Add up measurements:o 1.81+1.81+1.82o Sum=5.44o Number of measurements: 3– Divide sum by the number of

measurements5.44

1.8133

=

Note: Always record the mean to one more decimal place than the original data point

1.82

1.813

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What is a Range?

• The range indicates how similar (or dis-similar) the measurements are in a subgroup

• To calculate the range– Subtract the smallest

measurement from the largest measurement

Largest measurement: 1.80

Smallest measurement: 1.75

Range:

1.80-1.75=0.05

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Exercise #2

• Collect subgroups of data• Calculate mean and range

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Overall Mean

Number of means:10 Sum:2.73+2.71+2.72+2.72+2.72+2.72+2.70.2.72+2.71+2.71

Sum=27.16

Divide sum by number of means

27.162.716

10=

1 2 3 4 5 6 7 8 9 10

X

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Overall Range

• 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+0.04o Sum=0.7o Divide Sum by number of ranges 0.7

0.0710

=

R

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Sections of a Control Chart: Plot of Means and Ranges

Plot of Means

Plot of Ranges

X

R

•The plots show how the process is behaving over time•We expect the points to fall above and below the center line which is the overall mean

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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.

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Exercise #3

• Collect more subgroups and calculate control limits

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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.

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Interpreting Control Charts and Taking Action

Process In Control with Chance Variation

0

5

10

15

• The averages are randomly falling above and below the centerline.

• There are no points outside the upper control limit.

• The variation is common cause variation. No special causes of variation are present

X

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Trends

Trends

0

500

1000

1500

• The plot of averages was behaving randomly but something occurred to make the process start drifting upward.

• The process is no longer behaving randomly. Special cause variation is present

• Find the assignable cause

• Document your actions on the control chart

X

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Jumps in Process Level

Jumps in Process Level

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500

1000

1500

• The process is not exhibiting random behavior

• Special cause variation exists

• Find the assignable cause

• Document your actions on the control chart

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Cyclic Pattern

Recurring Cycles

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200

400

600

• There is a repeating cycle to the data

• This is not random behavior

• Find the assignable cause

• Document your actions on the control chart

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Point Near the Control Limit

0

500

1000

1500• Point at the upper control

limit but not outside the upper control limit

• Proper action to take:– Pull another sample and

plot the average and range. If the average is still near the upper limit, action may be needed

– Document your actions on the control chart

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Point Well Outside the Upper Limit

Process In Control with Chance Variation

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500

1000

1500

• This is a strong signal that an assignable cause exists for this special cause variation

• Find the assignable cause

• Document your actions on the control chart

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Point Just Above or Just Below Control Limit

Process In Control with Chance Variation

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500

1000

1500

• Don’t take the limit so literally. Remember, there is a small probability of a point falling outside the limit. We can expect this to happen less than 1% of the time.

• Proper action to take:– Don’t be so quick to adjust the

machine or process– Pull another sample and plot

the average and range. If the average is still near the upper limit, action may be needed

– Document your action on the control chart

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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

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Exercise #4

• Collect more subgroups and evaluate chart– Change in process level

– OOC point