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**Rockford Powertrain Training Workshop Process Capability and Cpk**

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Training materials, reference documents, and functional SPC templates are available free on the Rockford Powertrain web site. Go to:

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**Process Capability Enables successful manufacturing and sales**

Prevents scrap, sorting, rework Allows jobs to run well Has major impact on cost and schedule

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**“Process Capability” is the ability of a process to make a feature within its tolerance.**

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**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.

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**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

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**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

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**Graphing the tolerance and a measurement**

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

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**Graphing the tolerance and a measurement**

Specification Limit MIN It’s useful to see the tolerance and the part measurement on a graph. Suppose that: --the tolerance is .515”

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**Graphing the tolerance and a measurement**

Specification Limit MIN Specification Limit MAX It’s useful to see the tolerance and the part measurement on a graph. Suppose that: --the tolerance is .515” to .525”

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**Graphing the tolerance and a measurement**

Specification Limit MIN X Specification Limit MAX It’s useful to see the tolerance and the part measurement on a graph. Suppose that: --the tolerance is .515” to .525” --and an individual part is measured at .520”.

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**Graphing the tolerance and measurements**

X X X Specification Limit MIN X Specification Limit MAX Suppose we made and measured several more units, and they were all EXACTLY the same! We wouldn’t have very many part problems!

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**Graphing the tolerance and measurements**

XX XXX XXXXX XXXXXXX Specification Limit MIN Specification Limit MAX 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.

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**The “normal bell curve”**

XX XXX XXXX XXXXX XXXXXX XXXXXXX XXXXXXXX XXXXXXXXX XXXXXXXXXXX XX XXX XXXX XXXXX XXXXXX XXXXXXX XXXXXXXX XXXXXXXXX XXXXXXXXXXX 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”?**

XX XXX XXXX XXXXX XXXXXX XXXXXXX XXXXXXXX XXXXXXXXX XXXXXXXXXXX XX XXX XXXX XXXXX XXXXXX XXXXXXX XXXXXXXX XXXXXXXXX XXXXXXXXXXX Typical distance from the center: -1 standard deviation Typical distance from the center: +1 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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**How much of the curve is included in how many standard deviations?**

-6 -5 -4 -3 -2 -1 +1 +2 +3 +4 +5 +6 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.)

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**A B What is Cpk? It is a measure of how well**

a process is within a specification. A Cpk = A divided by B B Specification Limit Specification Limit 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.)

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

Cpk = A divided by B B Specification Limit Specification Limit …a LARGER “A” …and a SMALLER “B” …means BETTER “Process Capability”

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**A B An Analogy Cpk = A divided by B Analogy:**

Specification Limit Specification Limit 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.

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

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

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**What does a very good Cpk do for us?**

This Cpk is about 2. Very good! B Specification Limit Specification Limit Mean 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.”

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**What does a problem Cpk look like?**

This Cpk is just slightly greater than 1. Not good! B Specification Limit Specification Limit 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.)

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**What does a very bad Cpk look like?**

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

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**Free software is available to draw a histogram**

and calculate average, standard deviation, and Cpk. Located at:

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**What “Six Sigma Philosophy” did Motorola **

teach its suppliers in the 1980’s? Specification Limit Specification Limit 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.

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**Robust Design – part of the original Six Sigma**

Known Existing Process New Product Specification Limit New Product Specification Limit 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. Known Existing Process New Product Specification Limit New Product Specification Limit

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**Robust Design – part of the original Six Sigma**

Known Existing Process New Product Specification Limit New Product Specification Limit 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. Known Existing Process New Product Specification Limit New Product Specification Limit

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**Robust Processes – part of the original Six Sigma**

New Process choice “X” New Product Specification Limit New Product Specification Limit 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 Product Specification Limit New Product Specification Limit

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**6 Sigma Philosophy – Not Just The Shop Floor**

Getting 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

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**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

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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: Feasible designs Capable processes Process self-control

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**Conclusion: Yes: No: Yes: No: Yes: No: Process Capability: too wide**

potentially capable if re-centered Yes: No: potentially capable if re-centered

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**What is “Process Capability?”**

Review Question 1 What is “Process Capability?”

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**How is the “process average” calculated or estimated?**

Review Question 2 How is the “process average” calculated or estimated?

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**Review Question 3 What is a “Standard Deviation”?**

(also known as a “sigma”)

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Review Question 4 What is Cpk used for?

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**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?

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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?

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Review Question 7 Suppose that a diameter tolerance is 8.010” to 8.060”, and the process average is ”, and the process standard deviation is .002”… …is the process capable?

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

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**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.

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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.”

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**Quiz Question 1 True or False? “Process Capability” can be defined as**

the ability of a process to make a feature within its tolerance.

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**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.

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**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.

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

Quiz Question 4 True or False? When using Cpk, the goal is to keep the Cpk value as low as possible.

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**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.”

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**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.”

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**Quiz Question 7 True or False?**

If a height tolerance is 7.010” to 7.060”, and the process average is ”, and the process standard deviation is .002”… …then the process is “capable.”

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**Quiz Question 8 True or False?**

If Larry is cutting an O.D. and the diameter is easily adjustable, the tolerance is ” to 4.095”, the process average is ”, and the standard deviation is .001”… …then Larry should be able to make the process fully “capable” by adjusting the process.

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**Quiz Question 9 True or False?**

If Jill is boring an I.D. with a tolerance of ” 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.

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**Quiz Question 10 True 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.

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**Cpk and PPM (Parts Per Million Defective)**

Appendix Cpk and PPM (Parts Per Million Defective)

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**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: Cpk values depend on each chosen tolerance An “okay average Cpk” could come from 50% “good” and 50% “bad” numbers -- highly misleading!

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**What is PPM (defect Parts Per Million)?**

B The defect PPM is the area outside spec limits Specification Limit Specification Limit “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.)

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**What is the “6-Sigma Philosophy”**

“1.5-Sigma Shift”? Unfavorable process shift of 1.5 standard deviations Specification Limit Specification Limit 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.)

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**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

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