Presentation on theme: "Rockford Powertrain Training Workshop Process Capability and Cpk"— Presentation transcript:
1 Rockford Powertrain Training Workshop Process Capability and Cpk
2 Training materials, reference documents, and functional SPC templates are available free on the Rockford Powertrain web site. Go to:
3 Process Capability Enables successful manufacturing and sales Prevents scrap, sorting, reworkAllows jobs to run wellHas major impact on cost and schedule
4 “Process Capability” is the ability of a process to make a feature within its tolerance.
5 Everything Varies (and the variation can be seen if we measure precisely enough) HeightsWeightsLengthsWidthsDiametersWattageHorsepowerMiles per GallonPressureRoughnessStrengthConductivityLoudnessSpeedTorqueEtc. etc. etc.
6 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 machineryUsing specialized fixtures, tools, jigs, templates, and end-stopsCreating drawings, routings, operations & training
7 Manufacturing in the 21st Century International competition to provide defect-free products at competitive costReducing variation and providing interchangeable parts for assembly and service by:Using machine toolsUsing specialized fixtures, tools, jigs, templates, and end-stopsUsing drawings, routings, operations & training
8 Graphing the tolerance and a measurement It’s useful to see the tolerance and the part measurement on a graph.Suppose that:
9 Graphing the tolerance and a measurement SpecificationLimit MINIt’s useful to see the tolerance and the part measurement on a graph.Suppose that:--the tolerance is .515”
10 Graphing the tolerance and a measurement SpecificationLimit MINSpecificationLimit MAXIt’s useful to see the tolerance and the part measurement on a graph.Suppose that:--the tolerance is .515” to .525”
11 Graphing the tolerance and a measurement SpecificationLimit MINXSpecificationLimit MAXIt’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”.
12 Graphing the tolerance and measurements XXXSpecificationLimit MINXSpecificationLimit MAXSuppose we made and measured several more units, and they were all EXACTLY the same!We wouldn’t have very many part problems!
13 Graphing the tolerance and measurements XXXXXXXXXXXXXXXXXSpecificationLimit MINSpecificationLimit MAXIn 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.
14 The “normal bell curve” XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXWidths, 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.)
15 What is a “standard deviation”? XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXTypical distance from the center: -1 standard deviationTypical distance from the center: +1 standard deviationIf 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.
16 How much of the curve is included in how many standard deviations? -6-5-4-3-2-1+1+2+3+4+5+6From –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.)
17 A B What is Cpk? It is a measure of how well a process is within a specification.ACpk =A divided byBBSpecificationLimitSpecificationLimitCpk = 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.)
18 “Process Capability” is the ability of a process to fit its output within the tolerances. Cpk =A divided byBBSpecificationLimitSpecificationLimit…a LARGER “A”…and a SMALLER “B”…means BETTER “Process Capability”
19 A B An Analogy Cpk = A divided by B Analogy: SpecificationLimitSpecificationLimitAnalogy: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.
20 A B How can we make Cpk (A divided by B) better? Cpk = A divided by B SpecificationLimitSpecificationLimitDesign 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”)
21 What does a very good Cpk do for us? This Cpk is about 2. Very good!BSpecificationLimitSpecificationLimitMeanThis 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.”
22 What does a problem Cpk look like? This Cpk is just slightly greater than 1. Not good!BSpecificationLimitSpecificationLimitThis 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.)
23 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.BSpecificationLimitSpecificationLimitA 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!
24 Free software is available to draw a histogram and calculate average, standard deviation, and Cpk.Located at:
25 What “Six Sigma Philosophy” did Motorola teach its suppliers in the 1980’s?SpecificationLimitSpecificationLimitIn 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.
26 Robust Design – part of the original Six Sigma KnownExistingProcessNew ProductSpecificationLimitNew ProductSpecificationLimitThe 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.KnownExistingProcessNew ProductSpecificationLimitNew ProductSpecificationLimit
27 Robust Design – part of the original Six Sigma KnownExistingProcessNew ProductSpecificationLimitNew ProductSpecificationLimitCAUTION: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.KnownExistingProcessNew ProductSpecificationLimitNew ProductSpecificationLimit
28 Robust Processes – part of the original Six Sigma New Process choice “X”New ProductSpecificationLimitNew ProductSpecificationLimitThe 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 ProductSpecificationLimitNew ProductSpecificationLimit
29 6 Sigma Philosophy – Not Just The Shop Floor Getting 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 bedefined and measured
30 Getting every person “capable” and in “self control” Defined & UnderstoodRequirementsAbility toMeasure ResultsProcess Capability and Ability to ControlThe 3RequisitesOf Self-Control
31 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 designsCapable processesProcess self-control
32 Conclusion: Yes: No: Yes: No: Yes: No: Process Capability: too wide potentially capableif re-centeredYes:No:potentially capableif re-centered
33 What is “Process Capability?” Review Question 1What is “Process Capability?”
34 How is the “process average” calculated or estimated? Review Question 2How is the “process average” calculated or estimated?
35 Review Question 3 What is a “Standard Deviation”? (also known as a “sigma”)
37 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?
38 Review Question 6Suppose 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?
39 Review Question 7Suppose 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?
40 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 ”,and the process standard deviation is .001”…What is the Cpk?What should Fred do with the process?
41 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 at2.005”, 2.004”, and 2.006”.Estimate the process average.Estimate the standard deviation (best guess).Estimate whether the process can be capable.
42 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, 2.4Based 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.”
43 Quiz Question 1 True or False? “Process Capability” can be defined as the ability of a process to make a feature within its tolerance.
44 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.
45 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.
46 When using Cpk, the goal is to keep the Cpk value as low as possible. Quiz Question 4True or False?When using Cpk, the goal is to keep the Cpk value as low as possible.
47 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.”
48 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.”
49 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.”
50 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.
51 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.
52 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.
53 Cpk and PPM (Parts Per Million Defective) AppendixCpk and PPM(Parts Per Million Defective)
54 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 toleranceAn “okay average Cpk” could come from 50% “good” and 50% “bad” numbers -- highly misleading!
55 What is PPM (defect Parts Per Million)? BThe defect PPM is the area outsidespec limitsSpecificationLimitSpecificationLimit“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.)
56 What is the “6-Sigma Philosophy” “1.5-Sigma Shift”?Unfavorableprocess shift of 1.5 standard deviationsSpecificationLimitSpecificationLimitThe “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.)
57 The following page is a table showing the relationships among the following: Cpk,“How Many Sigma Capability,”Parts Per Million according to traditional statistical tablesParts Per Million taking into account the “6-Sigma Philosophy” of an unfavorable shift in the mean of 1.5 Sigma
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