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# Process-capability

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• 1. 1 PROCESS CAPABILITY Muhammad Asif
• 2. 2 The Normal Distribution 99.73 % 95.46 % µ µ+1σ µ+2σ µ+3σµ-1σµ-2σµ-3σ At 3-sigma away from process mean expect 99.73% of observations fall within these limits. At +2σ expect 95.46% X +1 S.D, 68% of population +2 S.D, 95% of population+3 S.D, 99.7% of population
• 3. 3 Z-DISTRIBUTIONTABLE
• 4. 4 Process Capability The ability of a process to meet product design/technical specifications Conducted only when the process is normally distributed
• 5. HOW TO MEASURE Cp -4 3σ3σ LTL UTL σ6 )( LTLUTL Cp − = X 1 6 6 == σ σ pC
• 6. 6 Process Capability Index: Cp -- Measure of Potential Capability σ6variationprocess variationprocess LSLUSL actual allowable Cp − == Cp > 1 LSL USL Cp = 1 Cp < 1
• 7. 2 6 12 == σ σ pC -4 6σ6σ LTL UTL X SIX SIGMA PROCESS
• 8. 8 What value of cp is acceptable Cp<1.0 poor process Cp=1.0 so ok Cp1.3 - 1.5 good Cp=2 Excellent, that is 6 sigma
• 9. 9 Process Capability Index Example A manufacturing process produces a certain part with a mean diameter of 2 inches and a standard deviation of 0.03 inches. The lower and upper engineering specification limits are 1.90 inches and 2.05 inches. 83.0 )03.0(6 90.105.2 6 = − = − = σ LSLUSL Cp Process is not a capable process since Cp<1.0
• 10. 10 Process Capability Index: Cpk -- Measure of Actual Capability ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ −− = σσ 3 , 3 min XUSLLSLX Cpk σ is the standard deviation of the process
• 11. 11 WHY Cpk IS NEEDED? IS Cp NOT ENOUGH?
• 12. 12 Impact of Process Location on Process Capability σ = 2 5044 56 6238 5044 56 6238 5044 56 6238 5044 56 6238 LSL USL 53 Cp = 2.0 Cpk = 2.0 Cp = 2.0 Cpk = 1.5 Cp = 2.0 Cpk = 1.0 Cp = 2.0 Cpk = 0
• 13. 13 WHY Cpk IS NEEDED? IS Cp NOT ENOUGH? Cp TELLS U ONLY ABOUT THE SMARTNESS OF CURVE Cpk TELLS U ABOUT THE POSITIONING / LOCATION OF THE CURVE
• 14. 14 Process Capability Index Example A manufacturing process produces a certain part with a mean diameter of 2 inches and a standard deviation of 0.03 inches. The lower and upper engineering specification limits are 1.90 inches and 2.05 inches. 56.0]56.0,11.1min[ )03.0(3 205.2 , )03.0(3 90.12 min 3 , 3 min == ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ −− =⎥ ⎦ ⎤ ⎢ ⎣ ⎡ −− = σσ XUSLLSLX Cpk Therefore, the process is not capable (the variation is too large and the process mean is not on target)
• 15. 15 Process Capability LowerLower specificationspecification MeanMean UpperUpper specificationspecification Nominal valueNominal value Six sigmaSix sigma Four sigmaFour sigma Two sigmaTwo sigma
• 16. 16 Six Sigma Is the relentless and rigorous pursuit of the reduction of variation in all critical processes to achieve continuous and breakthrough improvements that impact the bottom line of the organization and increase customer satisfaction. It is an organizational initiative designed to create manufacturing, service and administrative processes that produce approximately 3.4 defects per million. Opportunities (DPMO).
• 17. 17 WITH OUT ANY DEVIATION -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 68.27 % 95.45 % 99.73 % 99.9937 % 99.999943 % result: 317300 ppm outside (deviation) 45500 ppm 2700 ppm 63 ppm 0.57 ppm between + / - 1σ between + / - 2σ between + / - 3σ between + / - 4σ between + / - 5σ σ 99.9999998 % 0.002 ppmbetween + / - 6σ
• 18. 18 Distribution shifted ± 1.5
• 19. 19 DMAIC Model The model that is used to improve a process in Six Sigma management is called the DMAIC model. This stands for: Define Measure Analyze Improve Control
• 20. 20 LEADERSHIP Six Sigma must be implemented from the top-down.
• 21. 21 Green Belt. Green Belts are project leaders who receive two weeks of training on the Six Sigma roadmap and essential elements of Statistical methodologies supporting Six Sigma projects. Successful Green Belts are able to allocate 50% of their time to their four to six month Six Sigma Project.
• 22. 22 CHAMPIONS An executive level business leader who facilitates the leadership, implementation, and deployment of Six Sigma philosophies.
• 23. 23 Black Belt. Black Belts are project leaders who receive four weeks of training focusing on the Six Sigma Road map and extensive statistical methodologies Successful Black Belts normally dedicate at least 75% of their time to 4 -6 month Six Sigma Project.
• 24. 24 Master Black Belt. Master Black Belt provides technical leadership to Six Sigma program. The mentor and teacher of the of Six Sigma Black Belt and Six Sigma Green Belt.
• 25. 25 6 Sigma Support Personnel
• 26. 26 Process capability calculation using Minitab Please refer to the examples discussed in class
• 27. 27 601.50600.75600.00599.25598.50597.75 LSL Target USL Process Data Sample N 100 StDev(Within) 0.576429 StDev(Overall) 0.620865 LSL 598 Target 600 USL 602 Sample Mean 599.548 Potential (Within) Capability Overall Capability Pp 1.07 PPL 0.83 PPU 1.32 Ppk 0.83 Cpm Cp 0.87 1.16 CPL 0.90 CPU 1.42 Cpk 0.90 Observed Performance PPM < LSL 10000.00 PPM > USL 0.00 PPM Total 10000.00 Exp. Within Performance PPM < LSL 3621.06 PPM > USL 10.51 PPM Total 3631.57 Exp. Overall Performance PPM < LSL 6328.16 PPM > USL 39.19 PPM Total 6367.35 Within Overall Process Capability of Supp1
• 28. 28 604.5603.0601.5600.0598.5597.0 LSL Target USL Process Data Sample N 100 StDev(Within) 1.67231 StDev(Overall) 1.87861 LSL 598 Target 600 USL 602 Sample Mean 600.23 Potential (Within) Capability Overall Capability Pp 0.35 PPL 0.40 PPU 0.31 Ppk 0.31 Cpm Cp 0.35 0.40 CPL 0.44 CPU 0.35 Cpk 0.35 Observed Performance PPM < LSL 110000.00 PPM > USL 180000.00 PPM Total 290000.00 Exp. Within Performance PPM < LSL 91186.50 PPM > USL 144933.01 PPM Total 236119.51 Exp. Overall Performance PPM < LSL 117604.95 PPM > USL 173049.32 PPM Total 290654.27 Within Overall Process Capability of Supp2
• 29. 29 SampleMean 191715131197531 602 600 598 __ X=600.23 UCL=602.474 LCL=597.986 SampleRange 191715131197531 8 4 0 _ R=3.890 UCL=8.225 LCL=0 Sample Values 2015105 604 600 596 604.5603.0601.5600.0598.5597.0 LSL USL Specifications LSL 598 USL 602 605600595 Within Overall Specs Within StDev 1.67231 Cp 0.4 Cpk 0.35 Overall StDev 1.87861 Pp 0.35 Ppk 0.31 Cpm * 1 1 Process Capability Sixpack of Supplier 2 Xbar Chart R Chart Last 20 Subgroups Capability Histogram Normal Prob Plot AD: 0.287, P: 0.615 Capability Plot