SPC过程能力培训教材(English)

Process Capability (Cp / Cpk / Pp / Ppk)Global Training MaterialCreator Function Approver Document ID Version / Status Location : Global Mechanics Process Manager : Mechanics : Jukka Mehtonen / Global Process Team : DMT00018-EN : V.2.0 / Approved : Notes : \\…\ NMP \ DOCMANR4 \ PCP \ PC Process Library DocManChange History : Issue Date1.0 2.0 21st Dec’01 17th Jun’05Handled ByCommentsJim Christy & Søren Lundsfryd Approved for Global Use Yrjo Saastamoinen Approved for Global UseNOTE – All comments and improvements should be addressed to the creator of this document.1 © NOKIA 2005 T0001802.PPT/ 17-Jun-2005 / Yrjo SaastamoinenCompany ConfidentialContentsSection 1 2 3 4 5 6 7 Heading / Description Page Variation, Tolerances and Dimensional Control 4 Population, Sample and Normal Distribution 15 Cp and Cpk Concept 28 Confidence Interval 37 Process Capability Analysis 47 Mini Cpk Cpk Data Collection Spreadsheet DMM00024 60532© NOKIA 2005 T0001802.PPT/ 17-Jun-2005 / Yrjo SaastamoinenCompany ConfidentialTool Verification ProcessMeasurement System Analysis• Calibration • Variable Gauge R&R •DMY00019, DMT00017, DMM00210Tool Approval – at Tool Maker / Supplier• FAI (DMY00019, DMT00014, DMM00061) • Precontrol: Set-up Rules5 Min Variation Short TermMachine Approval – process capability• 3-10hr Run • Process Capability: Cpk, Ppk •DMY00019, DMT00018, DMM0002410 Hr Variation Long TermProcess Performance• Ongoing production • Process Stability • Process Capability: Cpk, Ppk3 © NOKIA 2005 T0001802.PPT/ 17-Jun-2005 / Yrjo Saastamoinen6 Mo Variation PerformanceCompany ConfidentialProcess Capability - Evaluating Manufacturing Variation4© NOKIA 2005 T0001802.PPT/ 17-Jun-2005 / Yrjo SaastamoinenCompany ConfidentialSection 1 Variation, Tolerances and Dimensional Control5© NOKIA 2005 T0001802.PPT/ 17-Jun-2005 / Yrjo SaastamoinenCompany ConfidentialTwo Types of Product CharacteristicsVariable: A characteristic measured in physical units, e.g. millimetres, volts, amps, decibel and seconds. ly s on le ariab v with deal e i ng w in s tra i In t h Attribute: A characteristic that by comparison to some standard is judged “good” or “bad”, e.g. free from scratches (visual quality).ONOFF6© NOKIA 2005 T0001802.PPT/ 17-Jun-2005 / Yrjo SaastamoinenCompany ConfidentialThe Sources of Process/System VariationEquipment MethodsEnvironment ProcessCustomer SatisfactionOperatorsMaterial7© NOKIA 2005 T0001802.PPT/ 17-Jun-2005 / Yrjo SaastamoinenCompany ConfidentialTwo Types of Processes• All processes have: –Natural (random) variability => due to common causes–Unnatural variability=> due to special causes• Stable Process: A process in which variation in outcomes arises “only" from common causesUSL• Unstable Process: A process in which variation is a result of both common and special causesUSLDefectnominal value nominal valueLSLLSL8© NOKIA 2005 T0001802.PPT/ 17-Jun-2005 / Yrjo SaastamoinenCompany ConfidentialThe Two Causes of VariationUSLNominal value LSL• Common Causes: –Causes that are implemented in the process due to the design of the process, and affect all outcomes of the process –Identifying these types of causes requires methods such as Design of Experiment (DOE), etc.DefectUSLnominal valueLSL• Special Causes: –Causes that are not present in the process all the time and do not affect all outcomes, but arise because of specific circumstances –Special causes can be identified using Statistical Process Control (SPC)Shewhart (1931)9© NOKIA 2005 T0001802.PPT/ 17-Jun-2005 / Yrjo SaastamoinenCompany ConfidentialTolerancesA tolerance is a allowed maximum variation of a dimension.Rejected Part Rejected ProductAcceptable partRejected PartLSL (lower specification limit) 10,7Nominal 10,8±0,1USL (upper specification limit) 10,910© NOKIA 2005 T0001802.PPT/ 17-Jun-2005 / Yrjo SaastamoinenCompany ConfidentialExample of Capability Analysis Data•For some critical dimensions we need to measure more than 1 part•For capability data we usually measure 5 pcs 2times/hour=100 pcs(but sampling plan needs to be made on the basis of production quantity, run duration and cycle time) 1st S u b g ro u p2n d S u b g ro u p3rd S u b g ro u p4th S u b g ro u p118.53118.52118.54118.56118.54118.54118.52118.55118.51118.51118.50118.55118.53118.51118.52118.55118.51118.54118.54118.555th S u b g ro u p6th S u b g ro u p7th S u b g ro u p8th S u b g ro u p118.55118.54118.57118.60118.54118.56118.56118.57118.55118.55118.57118.55118.54118.54118.55118.56118.56118.53118.54118.559th S u b g ro u p10th S u b g ro u p11th S u b g ro u p12th S u b g ro u p118.60118.61118.58118.60118.59118.60118.60118.63118.58118.61118.61118.63118.60118.59118.60118.61118.59118.59118.59118.64Process Capability -What is it?•Process Capability is a measure of the inherent capability of a manufacturing process to be able to consistently produce components that meet therequired design specifications•Process Capability is designated by C p and C pk•Process Performance is a measure of the performance of a process to be able to consistently produce components that meet the required design specifications. Process Performance includes special causes of variation not present in Process Capability•Process Performance is designated P p and P pkSection 2.Population, Sample and Normal Distribution),...,,min(),...,,max(2121N N x x x x x x R −=Example: x 1= 5x 2= 7x 3= 4x 4= 2x 5= 6527)6,2,4,7,5min()6,2,4,7,5max(=−=−=R •The most simple measure of variability is the range . The range of a sample is defined by as the difference between the largest and the smallest observation from samples in a sub-group, e.g. 5 consecutive parts from the manufacturing process.Describe Process variation?DE N T RThe difference between sST and sLT•The difference between sLT and sSTis only in the way that thestandard deviation is calculated•sLT is always the same or larger than sST•If sLT equals sST, then the process control over the longer-term isthe same as the short-term, and the process would not benefit from SPC•If sLT is larger than sST, then the process has lost control over thelonger-term, and the process would benefit from SPC•The reliability of sLT is improved if the data is taken over a longerperiod of time. Alternatively sLT can be calculated on severaloccasions separated by time and the results compared to see whether sLTis stableSection 3.Cp and Cpk ConceptWhat is the Difference Between Cp and Cpk?• The Cp index only accounts for process variability • The Cpk Index accounts for process variability and centering of the process mean to the design nominal • Therefore, Cp ≥ Cpk • NOTE: Same applies also for Pp and PpkNominal Mean Mean = Nominal Reject parts Reject parts Reject partsLSLUSLCp = Cpk (both low)LSLUSLCp high, Cpk low Process should be optimized!Company Confidential31© NOKIA 2005 T0001802.PPT/ 17-Jun-2005 / Yrjo SaastamoinenWhat Do These Indexes Tell Us ??• Simple numerical values to describe the quality of the process >> Thehigher the number the better• Requirement for Cp and Cpk is 1.67 min. • Recommendation for Pp and Ppk is 1.33 min.• •This leaves us some space for the variation, i.e. a safety margin Are we able to improve our process by using SPC?• If index is low, following things should be given a thought: • Is the product design OK? • Are tolerance limits set correctly? • •32Is the process capable of producing good quality products? Process variation? DOE required? Is the measuring system capable? (See Gage R&R)Company Confidential© NOKIA 2005 T0001802.PPT/ 17-Jun-2005 / Yrjo SaastamoinenCpk - With a 2-sigma safety margin• Requirement for Cp and Cpk is 1.67 min.of = 5/3 or 10/6.LSL1.67 is a ratioUSL10 * standard deviation 6 * standard deviation LCL UCL2 * standard deviation2 * standard deviation- 3 sSTMean value = Nominal value or Target+ 3 sST33© NOKIA 2005 T0001802.PPT/ 17-Jun-2005 / Yrjo SaastamoinenCompany ConfidentialAcceptability of Cpk Index•Cpk < 1.67the process NOT CAPABLE•Cpk >= 1.67 •Cpk >= 2.0the process is CAPABLEthe process has reached Six Sigma level34© NOKIA 2005 T0001802.PPT/ 17-Jun-2005 / Yrjo SaastamoinenCompany ConfidentialWhat Do These Indexes Tell Us ??• If Cp = Cpk, • If Pp = Ppk, • If Cpk < Cp, • If Ppk < Pp, • If Cp = Pp, • If Cpk = Ppk, • If Pp < Cp, • If Ppk < Cpk,35… then process perfectly centred… then process not centred (check process mean against design nominal)… then process is not affected by special causes during the study run. SPC would not be effective in this case … then process is affected by special causes. Investigate X-bar/R-chart for out-of-control conditions. SPC may be effectiveCompany Confidential© NOKIA 2005 T0001802.PPT/ 17-Jun-2005 / Yrjo SaastamoinenCp and Cpk Indices and Defects(both tails of the normal distribution)Cpk /Ppk 0.1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.33 1.4 1.5 1.67 2.0 2.5 3.0 4.0 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Cp/Pp 1.0 1.1 1.2 1.33 1.4 1.5 1.67 2.0 2.5 3.0 4.0 % / PPM % % % % % % % % % PPM PPM PPM PPM PPM PPM PPM PPM PPM PPM PPM 76.42 56.61 44.89 40.00 38.56 38.26 38.21 38.21 38.21 38.21 38.21 38.21 38.21 38.21 38.21 38.21 38.21 38.21 38.21 38.21 54.86 38.93 31.02 28.25 27.56 27.44 27.43 27.43 27.43 27.43 27.43 27.43 27.43 27.43 27.43 27.43 27.43 27.43 27.43 36.81 25.09 20.19 18.75 18.45 18.41 18.41 18.41 18.41 18.41 18.41 18.41 18.41 18.41 18.41 18.41 18.41 18.41 23.01 15.10 12.33 11.64 11.52 11.51 11.51 11.51 11.51 11.51 11.51 11.51 11.51 11.51 11.51 11.51 11.51 13.36 8.47 7.19 7.03 4.41 3.57 6.73 3.73 2.13 1.64 6.69 3.61 1.83 0.95 0.69 6.68 3.59 1.79 0.84 0.40 2700 6.68 3.59 1.79 0.82 0.35 1509 967 6.68 3.59 1.79 0.82 0.35 1363 532 318 6.68 3.59 1.79 0.82 0.35 1350 485 165 63 6.68 3.59 1.79 0.82 0.35 1350 484 160 38 27 6.68 3.59 1.79 0.82 0.35 1350 483 159 33 14 7 6.68 3.59 1.79 0.82 0.35 1350 483 159 33 13 3 0.6 6.68 3.59 1.79 0.82 0.35 1350 483 159 32 13 3 0.3 0.0 6.68 3.59 1.79 0.82 0.35 1350 483 159 32 13 3 0.3 0.0 0.0 6.68 3.59 1.79 0.82 0.35 1350 483 159 32 13 3 0.3 0.0 0.0 0.0 6.68 3.59 1.79 0.82 0.35 1350 483 159 32 13 3 0.3 0.0 0.0 0.0 0.0Pp=Ppk=1,33 63 ppm defects = 0,006%Cp=Cpk=1,67 0,6 ppm defects = 0,00006% Note: Ppm reject rates calculated from Cp & Cpk are based on the short term variation which may not represent the long term reject rate36 © NOKIA 2005 T0001802.PPT/ 17-Jun-2005 / Yrjo SaastamoinenCompany ConfidentialThe Effects of Cpk and Cp on FFRCpk Cp Ppm defects Total number of defects for 50,000,000 parts 410,000 67,500 3,150 1,650 350 30 0 Total number of defects if phone has 10 of these parts 4,100,000 675,000 31,500 16,500 3,500 300 10.8 1 1.331.33 1.33 1.331.33 1.50 1.67 2.001.67 1.50 1.67 2.008,200 1,350 63 33 7 1 037© NOKIA 2005 T0001802.PPT/ 17-Jun-2005 / Yrjo SaastamoinenCompany ConfidentialSection 4. Confidence Intervals38© NOKIA 2005 T0001802.PPT/ 17-Jun-2005 / Yrjo SaastamoinenCompany ConfidentialConfidence of Cpk• Cpk values are not definite numbers as they are based on relatively small samples of a population. • The 95% confidence interval determines the interval which includes the true Cpk value with a probability of 95%, i.e. "there is a probability of 5% that Cpk is either lower or higher" than this confidence interval.Cpk lower confidence limit Calculated cpk Cpk upper confidence limit95% confidence interval39© NOKIA 2005 T0001802.PPT/ 17-Jun-2005 / Yrjo SaastamoinenCompany ConfidentialConfidence Intervals95% Confidence Interval on a Cpk of 1.67Cpk.L 3.500 3.000 2.500 Cpk 2.000 1.500 1.000 0.500 0.000 0 50 100 150 200 250 Sam ple Size Cpk.USmall sample sizes gives wide confidence intervalsCompany Confidential40© NOKIA 2005 T0001802.PPT/ 17-Jun-2005 / Yrjo SaastamoinenCpk Confidence Limits with a sample size of 100 and a nominal Cpk of 1.6741© NOKIA 2005 T0001802.PPT/ 17-Jun-2005 / Yrjo SaastamoinenCompany ConfidentialExercise : Cp and Cpk• Determine the approximate Cp and Cpk for the 4 sample populations on the following page • Should actions be made to improve these processes. If yes, which?42© NOKIA 2005 T0001802.PPT/ 17-Jun-2005 / Yrjo SaastamoinenCompany ConfidentialEstimate Cp and Cpk?The width of the normal distributions shown include ±3*sA)B)LSLUSLLSLUSLC)D)LSL43USLLSLUSLCompany Confidential© NOKIA 2005 T0001802.PPT/ 17-Jun-2005 / Yrjo SaastamoinenEstimate Cp and Cpk? - A)Mean and nominalA)LSLUSL - LSL 6*s Mean - LSL USL - MeanUSL3*s44 © NOKIA 2005 T0001802.PPT/ 17-Jun-2005 / Yrjo SaastamoinenCompany ConfidentialEstimate Cp and Cpk? - B)Mean NominalB)LSLUSL - LSL 6*s Mean - LSLUSLUSL - Mean 3*sCompany Confidential45© NOKIA 2005 T0001802.PPT/ 17-Jun-2005 / Yrjo SaastamoinenEstimate Cp and Cpk? - C)Mean NominalC)LSLUSLUSL - LSL 6*s Mean - LSL USL - Mean 3*s46© NOKIA 2005 T0001802.PPT/ 17-Jun-2005 / Yrjo SaastamoinenCompany ConfidentialEstimate Cp and Cpk? - DMean NominalD)LSLUSL - LSL 6*s Mean - LSL 3*s47 © NOKIA 2005 T0001802.PPT/ 17-Jun-2005 / Yrjo SaastamoinenUSLUSL - MeanCompany ConfidentialSection 5. Process Capability Analysis48© NOKIA 2005 T0001802.PPT/ 17-Jun-2005 / Yrjo SaastamoinenCompany ConfidentialProcess Capability Analysis–Used to determine the capability of both the tool and the manufacturing – – – – –process to produce parts consistently to specification. White (and black) diamonds indicate the dimensions used for Cpk analysis Nokia has a standard Data Collection spreadsheet which must be used for ALL White (& black) Diamonds marked on the drawing. Any out of specification data or control conditions need to be investigated and explained. Any Process Capability indices (Cp or Cpk) which are less than 1.67 need to be investigated and explained. Any Process Capability indices (Pp or Ppk) which are less than 1.33 need to be investigated and explained–NMP’s quality requirements must be met PRIOR to Mass Productionrelease (E3 Milestone). ** CONFIDENCE in both the Tool, Process and Supplier **49© NOKIA 2005 T0001802.PPT/ 17-Jun-2005 / Yrjo SaastamoinenCompany Confidential1. Agree how long trial run lasts (3-10hrs) 2. Stabilise process and visual qualityProcess Capability Analysis TrialDepends on program, technology used and needed volumesRequired time depends on part and technology usedRequired time depends on part and technology used Se ion sificat al 6. Fill measurement data into Cpk Data Collection s ction Cla Spreadsheet of Fun teristics Dimension c 9-30 min between samples taken Chara 7. Analyse data3. Note the main parameters for reference 4. Collect and mark (eg. time, date and cavity) 5 consecutive parts out from each cavity at regular intervals for the duration of the trial. (The interval length will be the production run time divided by 20). Total 20 sets of 5 parts from each cavity must be made 5. Collected parts need to stabilize before measurements -EN may begin 00019 d Marking e DMY an8. Send samples and data to Nokia Note: For clarity, only 6 subgroups are shownNumber of subgroups N = 20 Subgroup size n = 5 Time50 © NOKIA 2005 T0001802.PPT/ 17-Jun-2005 / Yrjo SaastamoinenCompany Confidential。