PROCESS CAPABILITY

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



Suppose that:

--the tolerance is .515”

Specification

Limit MIN

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



Suppose that:

--the tolerance is .515” to .525”

Specification

Limit MAX

Specification

Limit MIN

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



Suppose that:

--the tolerance is .515” to .525”

--and an individual part is measured at .520”.

Specification

Limit MAX

Specification

Limit MIN

.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!

Specification

Limit MAX

Specification

Limit MIN

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

X

X

X

X

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.

Specification

Limit MAX

Specification

Limit MIN

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

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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.)

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What is a “standard deviation”?

If we measure the DISTANCE from the CENTER of the bell

to 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 the

Standard 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.

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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 +60

A

B

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

Cpk = A divided by B

A = Distance from process mean to closest spec limit

B = 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.)

Specification

Limit

Specification

Limit

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”

Specification

Limit

Specification

Limit

Cpk =

A divided by

B

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.

Specification

Limit

Specification

Limit

Cpk =

A divided by

B

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”)

Specification

Limit

Specification

Limit

Cpk =

A divided by

B

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.”

Specification

Limit

Specification

Limit

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.)

Specification

Limit

Specification

Limit

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!

Specification

Limit

Specification

Limit

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 histogram

and calculate average, standard deviation, and Cpk.

Located at: www.rockfordpowertrain.com/supplier

What “Six Sigma Philosophy” did Motorola

teach 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.

Specification

Limit

Specification

Limit

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 Product

Specification

Limit

New Product

Specification

Limit

Known

Existing

Process

New Product

Specification

Limit

New Product

Specification

Limit

Known

Existing

Process

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.

New Product

Specification

Limit

New Product

Specification

Limit

Known

Existing

Process

New Product

Specification

Limit

New Product

Specification

Limit

Known

Existing

Process

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 Product

Specification

Limit

New Product

Specification

Limit

New Process

choice “Y”

New Product

Specification

Limit

New Product

Specification

Limit

New Process

choice “X”

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

Achieving delivery and project deadlines

Meeting budgets & financial goals

Administrative tasks

Design work

Purchasing/sourcing

Special projects

Security and Safety

Health and Environmental

Legal compliance

Anything that can be

defined and measured

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

Defined & Understood

Requirements

Ability to

Measure Results

Process

Capability and

Ability to Control

The 3

Requisites

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 capable

if re-centered

potentially capable

if 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 8

Fred 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”,


• What is the Cpk?

• What should Fred do with the process?

Review Question 9

Joe 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 10

TechCorp 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 5

True 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.”

Quiz Question 6

True or False?

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”,


…then the process is “capable.”

Quiz Question 8

True or False?

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.

Quiz Question 9

True or False?

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.

Quiz Question 10True or False?

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.)

Specification

Limit

Specification

Limit

The defect PPM is

the area outside

spec 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.)

Specification

Limit

Specification

Limit

Unfavorable

process 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)

PPM of the Bell

Curve

Out of Spec

(Process Not

Centered,

Only One Tail

Considered)

The column AT

LEFT equates to 1

defective out of how

many total?

PPM of the Bell

Curve

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"

Documents

PROCESS CAPABILITY