Rockford Powertrain Training Workshop Process Capability and Cpk.

Rockford PowertrainTraining Workshop

Process Capability

and Cpk

Training materials, reference documents, and functional SPC templates are available free on the Rockford Powertrain web

site. Go to:

www.rockfordpowertrain.com/supplier

Process Capability

• Enables successful manufacturing and sales

• Prevents scrap, sorting, rework

• Allows jobs to run well

• Has major impact on cost and schedule

“Process Capability”

is the ability of a process to make a feature

within its tolerance.

Everything Varies (and the variation can be seen if we measure precisely enough)

• Heights• Weights• Lengths• Widths• Diameters• Wattage• Horsepower• Miles per Gallon

• Pressure• Roughness• Strength• Conductivity• Loudness• Speed• Torque• Etc. etc. etc.

Eli Whitney in 1798• Won a U.S. Military contract to supply 10,000 guns• Reduced variation and created interchangeable parts for

assembly and service by:– Installing powered factory machinery– Using specialized fixtures, tools, jigs, templates, and end-stops– Creating drawings, routings, operations & training

Manufacturing in the 21st Century• International competition to provide defect-free products

at competitive cost• Reducing variation and providing interchangeable parts

for assembly and service by:– Using machine tools– Using specialized fixtures, tools, jigs, templates, and end-stops– Using drawings, routings, operations & training

Graphing the tolerance and a measurement

It’s useful to see the tolerance and the part measurement on a graph.Suppose that:

.512 .513 .514 .515 . 516 .517 .518 .519 .520 .521 .522 .523 .524 .525 .526 .527 .528



--the tolerance is .515”

SpecificationLimit MIN

.512 .513 .514 .515 . 516 .517 .518 .519 .520 .521 .522 .523 .524 .525 .526 .527 .528



--the tolerance is .515” to .525”

SpecificationLimit MAX


.512 .513 .514 .515 . 516 .517 .518 .519 .520 .521 .522 .523 .524 .525 .526 .527 .528



--the tolerance is .515” to .525”--and an individual part is measured at .520”.



.512 .513 .514 .515 . 516 .517 .518 .519 .520 .521 .522 .523 .524 .525 .526 .527 .528

X

Graphing the tolerance and measurements

Suppose we made and measured several more units, and they were all EXACTLY the same!

We wouldn’t have very many part problems!



.512 .513 .514 .515 . 516 .517 .518 .519 .520 .521 .522 .523 .524 .525 .526 .527 .528

XXXX

Graphing the tolerance and measurements

In the real world, units are NOT EXACTLY the same. Everything VARIES.

The question isn’t IF units vary.It’s how much, when, and why.



.512 .513 .514 .515 . 516 .517 .518 .519 .520 .521 .522 .523 .524 .525 .526 .527 .528

XX XXX XXXXXXXXXXXX

The “normal bell curve”

Widths, heights, depths, thicknesses, weights, speeds, strengths, and many other types of measurements, when charted as a histogram, often form the shape of a bell.*

A “perfect bell,” like a “perfect circle,” doesn’t occur in nature, but many processes are close enough to make the bell curve useful.

(*A number of common industrial measurements, such as flatness and straightness, do NOT tend to distribute in a bell shape; their proper statistical analysis is performed using models other than the bell curve.)

XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX

XX XXX XXXX XXXX XXXXX XXXXX XXXXXX XXXXXX XXXXXXX XXXXXXXX XXXXXXXXX XXXXXXXXXXX

What is a “standard deviation”?

If we measure the DISTANCE from the CENTER of the bellto each individual measurement that makes up the bell curve,we can find a TYPICAL DISTANCE.

The most commonly used statistic to estimate this distance is theStandard Deviation (also called “Sigma”).

Because of the natural shape of the bell curve, the area of +1 to –1 standard deviations includes about 68% of the curve.

XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX

XX XXX XXXX XXXX XXXXX XXXXX XXXXXX XXXXXX XXXXXXX XXXXXXXX XXXXXXXXX XXXXXXXXXXX

Typical distance from the center: +1 standard deviation

Typical distance from the center: -1 standard deviation

How much of the curve is included in how many standard deviations?

From –1 to +1 is about 68% of the bell curve.From –2 to +2 is about 95%From –3 to +3 is about 99.73%From –4 to +4 is about 99.99%

(NOTE: We usually show the bell from –3 to +3 to make it easier to draw, but in concept, the “tails” of the bell get very thin and go on forever.)

-6 -5 -4 -3 -2 -1 +1 +2 +3 +4 +5 +6 0

A

B

What is Cpk? It is a measure of how wella process is within a specification.

Cpk = A divided by BA = Distance from process mean to closest spec limitB = 3 Standard Deviations (also called “3 Sigma”)

A bigger Cpk is better because fewer units will be beyond spec.(A bigger “A” and a smaller “B” are better.)

SpecificationLimit

SpecificationLimit

Cpk = A divided by B

A

B

“Process Capability” is the ability of a process to fit its output within the tolerances.

…a LARGER “A”…and a SMALLER “B”…means BETTER “Process Capability”

SpecificationLimit

SpecificationLimit


A

B

An Analogy

Analogy:The bell curve is your automobile.The spec limits are the edges of your garage door.If A = B, you are hitting the frame of your garage door with your car.

SpecificationLimit

SpecificationLimit


A

B

How can we make Cpk (A divided by B) better?

1. Design the product so a wider tolerance is functional (“robust design”)2. Choose equipment and methods for a good safety margin (“process capability”)3. Correctly adjust, but only when needed (“control”)4. Discover ways to narrow the natural variation (“improvement”)

SpecificationLimit

SpecificationLimit


A

B

What does a very good Cpk do for us?

This process is producing good units with a good safety margin.

Note that when Cpk = 2, our process mean is 6 standard deviations from the nearest spec, so we say it has “6 Sigma Capability.”

SpecificationLimit

SpecificationLimit

This Cpk is about 2. Very good!

Mean

A

B

What does a problem Cpk look like?

This process is in danger of producing some defects.It is too close to the specification limits.

(Remember: the bell curve tail goes further than B……we only show the bell to 3-sigma to make it easier to draw.)

SpecificationLimit

SpecificationLimit

This Cpk is just slightly greater than 1. Not good!

A

B

What does a very bad Cpk look like?

A significant part of the “tail” is hanging out beyond the spec limits.This process is producing scrap, rework, and customer rejects.

Notice that if distance “A” approaches zero… …the Cpk would approach zero, and……the process would become 50% defective!

SpecificationLimit

SpecificationLimit

This Cpk is less than 1. We desire a minimum of 1.33 and ultimately we want 2 or more.

Free software is available to draw a histogramand calculate average, standard deviation, and Cpk.

Located at: www.rockfordpowertrain.com/supplier

What “Six Sigma Philosophy” did Motorolateach its suppliers in the 1980’s?

In the 1980’s, Motorola achieved dramatic quality improvements and won the USA’s Malcolm Baldrige National Quality Award.

Motorola began seminars teaching its “Six Sigma Philosophy” to its suppliers, and to other companies.

The following few slides depict some original messages from that time.

SpecificationLimit

SpecificationLimit

Robust Design – part of the original Six Sigma

The new design above has tolerances set “tight” to a known existing process, while the one below has tolerances that allow “six sigma capability”.

Products have thousands of tolerances. They result from choices about shapes, thicknesses, grades of materials, and grades of components. “Robust design” is NOT about permitting “sloppiness.” It requires very smart engineering to allow ample tolerances AND achieve satisfactory function.

New ProductSpecificationLimit


KnownExistingProcess




Robust Design – part of the original Six Sigma

CAUTION:

Suppliers must negotiate the widening of tolerances BEFORE competitive bids, quotations, and acceptance of orders. Competitive bids are commitments to meet all existing tolerances. Failure to meet customer tolerances means failure to meet contract requirements. Prevent breaches of contract.







Robust Processes – part of the original Six Sigma

The process above varies so much that it “fills” the design tolerance. The different process below has good repeatability for “six sigma capability”.

It’s a false-economy to choose an allegedly lower-cost process that “uses up” all tolerance. The resulting scrap, rework, rejections, recalls, damage to reputation, crisis communications, and fire-fighting cancel out the alleged economy. “Robust Process” requires skillful insight to choose ways to make defect-free product at the lowest real cost.



New Process choice “Y”



New Process choice “X”

6 Sigma Philosophy – Not Just The Shop FloorGetting every person “capable” and in “self control”

Achieving delivery and project deadlinesMeeting budgets & financial goalsAdministrative tasksDesign workPurchasing/sourcingSpecial projectsSecurity and SafetyHealth and EnvironmentalLegal complianceAnything that can be defined and measured

Getting every person “capable” and in “self control”

Defined & Understood Requirements

Ability toMeasure Results

Process Capability and

Ability to Control

The 3Requisites

Of Self-Control

Summary:• To call a process “capable” typically requires at

least a Cpk of 1.33 (+ and - 4 standard deviations within tolerance)

• Many customers desire a Cpk of 2.0 (+ and - 6 standard deviations within tolerance)

• Organizations need:

1. Feasible designs

2. Capable processes

3. Process self-control

Conclusion:Process Capability:

Yes: No:

No:

No:

Yes:

Yes:

potentially capableif re-centered

potentially capableif re-centered

too wide

Review Question 1

What is “Process Capability?”

Review Question 2

How is the “process average” calculated or estimated?

Review Question 3

What is a “Standard Deviation”?

(also known as a “sigma”)

Review Question 4

What is Cpk used for?

Review Question 5

Suppose that a feature tolerance is .750”/.760”,

and the process average is .759”,

and the process standard deviation is .002”

…is the process satisfactory and capable?

Review Question 6

Suppose that a torque tolerance is 25 foot pounds minimum,

and the process average is 26 foot pounds,and the process standard deviation is 3 foot

pounds……is the process capable?

Review Question 7

Suppose that a diameter tolerance is 8.010” to 8.060”,

and the process average is 8.041”,

and the process standard deviation is .002”…

…is the process capable?

Review Question 8Fred is cutting an outside diameter on a lathe

and the diameter is easily adjustable.

The diameter tolerance is 5.050” to 5.090”,

the process average is 5.090”,

and the process standard deviation is .001”…• What is the Cpk?• What should Fred do with the process?

Review Question 9Joe is boring an inside diameter on a lathe.

The diameter tolerance is 1.980” to 2.020”.

Joe has measured three random samples at

2.005”, 2.004”, and 2.006”.• Estimate the process average.• Estimate the standard deviation (best guess).• Estimate whether the process can be

capable.

Review Question 10TechCorp is demonstrating a new “high-precision”

grease dispenser machine.

TechCorp claims that they can “dispense grease all day with an accuracy of plus or minus half an ounce.”

During the demo, ten samples of grease in a row were dispensed (in ounces) as follows:

2.3, 2.0, 2.6, 3.0, 2.1, 2.7, 2.9, 2.5, 2.0, 2.4• Based on the sample data, evaluate TechCorp’s

claim that they can “dispense grease all day with an accuracy of plus or minus half an ounce.”

Quiz Question 1

True or False?

“Process Capability” can be defined as

the ability of a process to make a feature

within its tolerance.

Quiz Question 2

True of False?

We can estimate the process average

by taking a set of sample measurements,

adding them up, and dividing by the number of measurements.

Quiz Question 3

True or False?

A “Standard Deviation” can be thought of as the “typical” distance of the

measurements from the average;

about 68% of the individuals will fall within

+ or – 1 standard deviation of a bell curve.

Quiz Question 4

True or False?

When using Cpk, the goal is to keep the Cpk value as low as possible.

Quiz Question 5True or False?

If the feature tolerance is .350”/.360”,

and the process average is .351”,

and the process standard deviation is .004”

…then the process should be called “capable.”


If a pressure tolerance is 250 PSI minimum,

and the process average is 260 PSI,

and the process standard deviation is 4 PSI,

…then the process is “capable.”

Quiz Question 7

True or False?

If a height tolerance is 7.010” to 7.060”,

and the process average is 7.042”,

and the process standard deviation is .002”…

…then the process is “capable.”


If Larry is cutting an O.D. and the diameter is easily adjustable, the tolerance is 4.055” to 4.095”, the process average is 4.095”, and the standard deviation is .001”…

…then Larry should be able to make the process fully “capable” by adjusting the process.


If Jill is boring an I.D. with a tolerance of 1.475” to 1.525”, and has measured three samples at 1.501”, 1.500”, and 1.499”…

…then the average of the samples is 1.501”, the standard deviation is probably larger than .010”, and the Cpk is probably zero.


If HiTechCo is demonstrating a new “high-precision” surface coating machine, and claims that their machine “can coat all day with an accuracy of plus or minus .010 inches,” and during the demo the coating thickness readings (in inches) were as follows:

.027, .028, .027, .029, .028, .029, .028, .029, .028, .027

…then the sample readings suggest that HiTechCo might be telling the truth about being able to hold plus or minus .010 inches.

Appendix

Cpk and PPM

(Parts Per Million Defective)

Cpk: Avoid confusion and pitfalls

• DOES IT VARY? Cpk varies when sampled, because it’s calculated from the average and the standard deviation, both of which are estimated from samples.

• CARROTS AND STICKS? Giving rewards or reprimands based on minor, short-term fluctuations of Cpk amounts to a lottery. Watch real trends.

• MAKE A “PLANT AVERAGE” CPK? It’s unhelpful to report a plant average Cpk of multiple characteristics and products, because:

1. Cpk values depend on each chosen tolerance

2. An “okay average Cpk” could come from 50% “good” and 50% “bad” numbers -- highly misleading!

A

B

What is PPM (defect Parts Per Million)?

“PPM” is an estimate of the portion that is beyond the spec limit.If we know the Cpk…--we can look up the PPM “out of spec” in a statistics book table, or--we can use software, such as Microsoft Excel, to calculate the PPM.(REMEMBER that the “tail” of the bell goes out further than it is drawn.)

SpecificationLimit

SpecificationLimit

The defect PPM is the area outsidespec limits

What is the “6-Sigma Philosophy”“1.5-Sigma Shift”?

The “6 Sigma Philosophy” includes the premise that real-world processes move around to some extent, and produce more defects than a static process. As an arbitrary convention, this is represented as an “unfavorable shift” of 1.5 sigma in Parts Per Million tables for Six Sigma programs. The intention is to plan conservatively.

(This means that the “PPM vs. Sigma” charts published for “6-Sigma Programs” show

higher defect rates than the similar but traditional “Z-tables” in statistical textbooks.)

SpecificationLimit

SpecificationLimit

Unfavorableprocess shift of 1.5 standard deviations

The following page is a table showing the relationships among the following:

• Cpk,

• “How Many Sigma Capability,”

• Parts Per Million according to traditional statistical tables

• Parts Per Million taking into account the “6-Sigma Philosophy” of an unfavorable shift in the mean of 1.5 Sigma

Cpk (Defined as

distance from process mean to the nearest spec,

divided by 3 Standard

Deviations)

"How Many Sigma

Capability?" Distance of

Process Mean to Spec Limit in

Standard Deviations

Within Spec (Process Perfectly

Centered, Both Tails

Considered)Good Units Per

Million

PPM of the Bell Curve

Out of Spec (Process Perfectly

Centered, Both Tails

Considered)


Out of Spec (Process Not

Centered, Only One Tail Considered)

The column AT LEFT equates to 1 defective out of how

many total?


Out of Spec with Six-Sigma

Philosophy of 1.5 Standard

Deviation Penalty for Anticipated Unfavorable

Process Mean Drift

0 0 0 1,000,000 500,000 2

0.17 0.5 382,925 617,075 308,538 3

0.33 1 682,689 317,311 158,655 6

0.5 1.5 866,386 133,614 66,807 15 500,000

0.67 2 954,500 45,500 22,750 44 308,538

0.83 2.5 987,581 12,419 6,210 161 158,655

1 3 997,300 2,700 1,350 741 66,807

1.17 3.5 999,535 465 233 4,298 22,750

1.33 4 999,937 63 32 31,560 6,210

1.5 4.5 999,993.2 6.8 3.4 294,048 1,350

1.67 5 999,999.4 0.6 0.3 3,483,046 233

1.83 5.5 999,999.96 0.04 0.02 52,530,944 32

2 6 999,999.998 0.002 0.001 1,009,976,693 3.4

2.17 6.5 999,999.99992 0.00008 0.00004 24,778,276,273 0.3

Cpk, PPM, and "Six Sigma"

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Rockford Powertrain Training Workshop Process Capability and Cpk.

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