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- 1. Statistical Process ControlSPCISO TS 16949:2002 Lead Auditor Course
- 2. 2Course Objectives• By the end of the course the participantshould be able to identify;1. How to Audit SPC2. Variables SPC charts3. Attribute SPC charts4. When best to apply these charts5. The difference between Ppk and Cpkand understand how to calculate theseindexes
- 3. 3AnISO TS 16949Quality Management Systemis based onPreventionnotDetectionStatistical Process ControlSPCSPC
- 4. 4So what is SPC?• A tool to detect variation• It identifies problems, it does not solve problems•Increases product consistency•Improves product quality•Decreases scrap and rework defects•Increases production output
- 5. 5Statistical Process ControlSPC is a proactive tool which assistsin;• Eliminating waste• Reducing variation• Achieving superior quality productLower unit cost
- 6. 6Types of Variation• Common cause– Due to normal wear and tear e.g. tool wear•Special Cause•Abnormal situation e.g tool broken
- 7. 7Normal Distribution & Standard deviation• Normal distributions are a family of distributions that have the same generalshape. They are symmetric with scores more concentrated in the middle than inthe tails. Normal distributions are sometimes described as bell shaped. Examplesof normal distributions are below.Standard Deviation:Denoted with theGreek symbol Sigma,the standard deviationprovides an estimateof variation. Inmathematical terms, itis the second momentabout the mean. Insimpler terms, youmight say it is how farthe observations varyfrom the mean.σ
- 8. 8Statistical Process Control• There are two types of SPC charts;• Variables– for a variables SPC chart we require variable“number” data such as;• Hole dimension (32.45 mm), Thickness (0.55mm)• Temperature (32 degrees), Weight (38.98grams)
- 9. 9Statistical Process Control• Attributes– for an attributes SPC chart we require attributes(visual) data such as;• Short shot (in an injection moulding operation)• Off color painted spoiler• Incomplete assembly• Insufficient weld
- 10. 10Statistical Process Control• VARIABLES SPC CHARTSThe types of variables charts we will beexamining are;– Average and Range charts (Xbar and R charts)– Average and Standard Deviation charts (Xbar ands charts)– Median charts– Individual and Moving Range chart ( X-MR)
- 11. 11Statistical Process Control• ATTRIBUTES SPC CHARTSThe types of attributes charts we will beexamining are;– Proportion nonconforming (p Chart)– Nonconforming product (np Chart)– Number of nonconformitys (c Chart)– Nonconformitys per unit (u Chart)
- 12. 12What is Six SigmaSix Sigma aims for virtually error free business performance.The Six Sigma standard of 3.4 problemsper million opportunities is a response tothe increasing expectations of customersand the increased complexity of modernproducts.
- 13. 13What is Six Sigma
- 14. 14What other global company’s say• General Electric estimates that the gap between three or four sigma andSix Sigma was costing them between $8 billion and $12 billion peryear in inefficiencies and lost productivity.
- 15. 15The methodologyDesign of Experiments
- 16. SPCVariables
- 17. 17Course Objectives• By the end of the course the participantshould be able to identify;1. Variables SPC charts2. When best to apply these charts3. The difference between Ppk and Cpkand understand how to calculate theseindexes
- 18. 18How to select the correct SPC chartVariablesXbar & S Xbar & R I & MR Mediann =10 or more n= 2 to 9 n=1 n= odd number
- 19. 19X bar and R chart• When to use a X bar and R chart• when there is measured data• to establish process variation• when you can obtain a subgroup of constant size i.e.between 2-9 consecutive pieces• when pieces are produced under similar conditionswith a short interval between production of pieces
- 20. 20• Methodology for the calculation ofparameters for an X bar and R chart– 1. Determine the subgroup size, typically between 2-9 pieces– 2. Establish the frequency of taking measurements– 3. Collect data– 4. Calculate the average for each subgroup and record results– 5. Determine the range for each subgroup and record the result– 6. Plot the average and range onto the chart– 7. Calculate the Upper and Lower Control Lines– 8. Interpret the chartX bar and R chart
- 21. 21X bar and R chartTo calculate the control lines we use thefollowing algorithmwhere k iswhere k isthethenumber ofnumber ofsubgroupssubgroupsRA-X=LCLRA+X=UCLRD=LCLRDUCLandkXXXXkRRRR2x2x3R4Rn21n21=++=+++=
- 22. 22X bar and R chartvalues for D4, D3 and A2n 2 3 4 5 6 7 8 9 10D4 3.27 2.57 2.28 2.11 2 1.92 1.86 1.82 1.78D3 - - - - - 0.08 0.14 0.18 0.22A2 1.88 1.02 0.73 0.58 0.48 0.42 0.37 0.34 0.31
- 23. 23X bar and R chart• Exercise– Using the data in Appendix 1, calculate theUCL and LCL for the average and range ofthe data.– Plot the data onto the charts and identifyany out of control conditions
- 24. 24Average and standard deviation chart Xbar and s chart• When to use a X bar and s chart• when there is measured data recorded on a real timebasis or when operators are proficient is using acalculator• when you require a more efficient indicator ofprocess variability• when you can obtain a subgroup of constant size witha larger sampling size than for Xbar and R charts,n=10 or more• when pieces are produced under similar conditionswith a short interval between production of pieces
- 25. 25X bar and s chart• Methodology for the calculation of Xbar and s chart– 1. Determine the subgroup size, typically 10 or more– 2. Establish the frequency of taking measurements– 3. Collect data– 4. Calculate the average for each subgroup and recordresults– 5. Calculate the standard deviation for each subgroupand record the result– 6. Plot the average and standard deviation onto the chart– 7. Interpret the chart
- 26. 26X bar and s chartTo calculate the control lines we use thefollowing algorithm where n isthe numberof parts inthesubgroupand k is thenumber ofsubgroupssA-X=LCLsA+X=UCLsB=LCLsBUCLKSKXXX1nsnXXXX3x3x3s4sKk21n21=+++=+++=−+++= ∑21s2)(SSXXXi-=
- 27. 27X bar and s chartvalues for B4, B3 and A3n 2 3 4 5 6 7 8 9 10B4 3.27 2.57 2.27 2.09 1.97 1.88 1.82 1.76 1.72B3 - - - - 0.03 0.12 0.19 0.24 0.28A3 2.66 1.95 1.63 1.43 1.29 1.18 1.1 1.03 0.98
- 28. 28X bar and s chart• Exercise– Using the data in Appendix 2 calculate theUCL and LCL for the average andstandard deviation of the data.– Plot the data onto the charts and identifyany out of control conditions
- 29. 29Median charts• When to use a Median chart• 1. When there is measured data recorded• 2. When you require an easy method of processcontrol. This can be a good method to begintraining operators• 3. When you can obtain a subgroup of constantsize - for convenience ensure subgroup size is oddnot even, typically 5• 4. When pieces are produced under similarconditions with a short interval betweenproduction of pieces
- 30. 30Median charts• Methodology for the calculation of Mediancharts– 1. Determine the subgroup size, typically 5, ensure it is anodd number– 2. Establish the frequency of taking measurements– 3. Collect data– 4. Determine the median (middle number) for each subgroupand record results– 5. Determine the range for each subgroup and record theresult– 6. Plot the median and range onto the chart
- 31. 31Median chartsTo calculate the control lines we use thefollowing algorithmA-=LCLA+=UCLD=LCLDUCLkRRRkXXX2X2X3R4Rkk21R~R~RRR~~~~lueLowest va-alueHighest vvalue(middle)Median~~~21XXXRX=+++=+++===Where k is theWhere k is thenumber ofnumber ofsubgroupssubgroups
- 32. 32Median chartsvalues for B4, B3 and A3n 2 3 4 5 6 7 8 9 10D4 3.27 2.57 2.28 2.11 2 1.92 1.86 1.82 1.78D3 - - - - - 0.08 0.14 0.18 0.22A2 1.88 1.19 0.8 0.69 0.55 0.51 0.43 0.41 0.36
- 33. 33Median charts• Exercise– Using the data in Appendix 3calculate the UCL and LCL for themedian chart– Plot the data onto the charts andidentify any out of control conditions
- 34. 34Individuals and moving range chart(X-MR)• When to use a X-MR chart• when there is measured data recorded• when process control is required for individualreadings e.g. a destructive type test which cannotbe repeated frequently because of cost or other
- 35. 35Individuals and moving rangechart• Methodology for the calculation of X-MRchart– 1. Establish the frequency of takingmeasurements– 2. Obtain individual readings– 3. Collect data– 4. Record the individual reading on the chart– 5. Determine the moving range from successivepairs of reading
- 36. 36Individuals and moving rangechartExample of calculating control lines forindividuals and moving range charts (X-MR)where k is thewhere k is thenumber ofnumber ofreadingsreadingsRE-X=LCLRE+X=UCLRD=LCLRDUCLandkXXXX1-kRRRR2x2X3MR4MR21K21 k=++=+++=
- 37. 37Individuals and moving rangechartn 2 3 4 5 6 7 8 9 10D4 3.27 2.57 2.28 2.11 2 1.92 1.86 1.82 1.78D3 - - - - - 0.08 0.14 0.18 0.22E2 2.66 1.77 1.46 1.29 1.18 1.11 1.05 1.01 0.98
- 38. 38Individuals and moving rangechart• Exercise– Using the data in Appendix 4 calculate theUCL and LCL for the X-MR chart– Plot the data onto the charts and identifyany out of control conditions
- 39. 39Process Capability StudiesWhat isPpkand what isCpk
- 40. 40Process Capability Studies• Definition of PpkPreliminary Process Capability Studyfrom 25 or more subgroupsQS 9000 requires Ppk to be greater that orequal to 1.67
- 41. 41Process Capability Studies• Calculation of PpK12)(−−=∑nXXisSSMINZPpkLSL-XZ,X-USLZ)Z,Z(Zmin,3minLSLUSLLSLUSL====
- 42. 42Process Capability Studies• Definition of CpkOngoing Process Capability Studyfor a stable processPPAP requires CpK to be greater that orequal to 1.67, if between 1.33 and 1.67must review with customer
- 43. 43Ongoing Capability Studies• Calculation of CpK n d22 1.1283 1.6934 2.0595 2.3266 2.5347 2.7048 2.8479 2.9710 3.07811 3.17312 3.25813 3.33614 3.40715 3.4722RLSL-XZ,2RX-USLZ)Z,Z(Zmin,3minLSLUSLLSLUSLddMINZCpk====
- 44. 44Standard Deviation Correction factorsn c415 0.982316 0.983517 0.984518 0.985419 0.986220 0.986921 0.987622 0.988223 0.988724 0.989225 0.989630 0.991435 0.992740 0.993645 0.994350 0.99494CSScorrected =To obtain an accurate calculation ofthe standard deviation, at least 60data points are required. If less than60 are available use the followingerror correction factors
- 45. 45Capability study assumptions1. Data is normally distributed2. Process is in statistical controlQuestion: Why is the PpK requirementhigher than the Cpk requirement???
- 46. SPCAttributes
- 47. 47Course Objectives• By the end of the course the participantshould be able to identify;1. Attribute SPC charts2. When best to apply these charts
- 48. 48How to select the correct SPC chartAttributesP chart Np chart U chart C chartCount partsN = fixed orvariedCount partsN = fixedCount occurrencesN = variesCount occurrencesN = fixed
- 49. 49Proportion of Units -Nonconformingp charts• When to use a p chart• when data is of attribute type (an attributethat can be counted)• when you wish to determine the proportion ofnonconforming products in a group beinginspected• from samples of equal or unequal size
- 50. 50p charts• Methodology for the calculation of pcharts– Determine the subgroup size typically >50 units– Establish the frequency of inspection– Collate data - Determine the number ofnonconforming products from that subgroup– Record the number of parts defective onto p-chart– Determine the proportion defective i.e numberdefective/number in subgroup– Plot this onto the p-chart
- 51. 51p charts• Example of calculating control lines forp-chartsNote: nNote: n11pp11 etc..etc..are the numberare the numberofofnonconformingnonconformingproductsproductsdetected and ndetected and n11,,nn22 etc are theetc are thecorrespondingcorrespondingsample sizessample sizesNote: If the LCL is ever calculated to be a negative number, the LCL should then default to a zeroNote: If the LCL is ever calculated to be a negative number, the LCL should then default to a zeronpppLCLpnpppUCLp)1(3)1(3n+n+npn++pn+pn=pp-ingnonconformproportionaveragetheDeterminek21kk2211−×−=−×+=
- 52. 52p charts• Class Exercise– Using the data in Appendix 5 calculate theUCL and LCL for the p chart– Plot the data onto the charts and identifyany out of control conditions
- 53. 53Number of Nonconforming productsnp charts• When to use a np chart• when data is of attribute type (an attributethat can be counted)• when it is more important that you know thenumber of nonconforming products in agroup being inspected• when sample sizes are of equal size
- 54. 54np charts• Methodology for the calculation of np charts– Determine the subgroup size typically >50 units– Establish the frequency of inspection– Collate data - Determine the number ofnonconforming products from that subgroup– Record the number of parts defective onto np-chart– Plot this data onto the np-chart
- 55. 55np charts• Example of calculating control lines fornp-chartsWhere k isWhere k isthe numberthe numberof subgroupsof subgroupsand n is theand n is thesample sizesample sizein each ofin each ofthosethosesubgroups.subgroups.)1(3)1(3np++np+np=pnpn-ingnonconformnumberaveragetheDeterminekk21npnpnpnLCLnpnpnpnpnUCLnp−×−=−×+=
- 56. 56np charts• Class Exercise– Using the data in Appendix 7 calculate theUCL and LCL for the np chart– Plot the data onto the charts and identifyany out of control conditions
- 57. 57Number of Nonconformitysc charts• When to use a c chart• when data is of attribute type (an attributethat can be counted)• when the nonconformitys are distributedthroughout a product e.g. number of defectson a painted part, number of flaws in aassembly operation• when nonconformitys can be found frommultiple sources or attributed to multiplesources
- 58. 58c charts• Methodology for the calculation of c charts– Ensure inspection sample sizes are equal e.g.number of parts, specified area or volume– Establish the frequency of inspection– Determine the number of nonconformitysfound in that sample– Record the number of nonconformitys onto c-chart– Plot this data onto the c-chart
- 59. 59c charts• Example of calculating control lines forc-chartsWhere k is the numberWhere k is the numberof subgroups.of subgroups.c3cc3ckk++2+1=ccitiesnonconformofnumberaveragetheDetermineccc×−=×+=LCLcUCLc
- 60. 60c charts• Class Exercise– Using the data in Appendix 7 calculate theUCL and LCL for the c chart– Plot the data onto the charts and identifyany out of control conditions
- 61. 61Number of Nonconformitys per unitu Chart• When to use a u-chart• when data is of attribute type (an attribute that canbe counted)• when the number of nonconformitys aredistributed throughout a product (e.g. number ofdefects on a painted part, number of flaws in aassembly operation) given varying sample sizes• when nonconformitys can be found from multiplesources or attributed to multiple sources
- 62. 62Number of Nonconformitys per unitu Chart• Methodology for the calculation of ucharts– Define what will be inspected– Establish the frequency of inspection– Determine the number of nonconformitys foundin that sample– Divide the number of nonconformitys found bythe sample size– Record the proportion of nonconformitys onto theu chart– Plot this data onto the u-chart
- 63. 63Number of Nonconformitys per unitu Chart• Example of calculating control lines for u-chartsWhere c1, c2Where c1, c2etc are numberetc are numberofofnonconformitynonconformitys per unit ands per unit andn1, n2 etc isn1, n2 etc isthethecorrespondingcorrespondingsample sizesample sizenu3unu3unk+n2+n1k++2+1=uuunitperitiesnonconformaveragetheDetermineuuu×−=×+=+LCLuUCLu
- 64. 64Number of Nonconformitys per unitu Chart• Class Exercise– Using the data in Appendix 8calculate the UCL and LCL for the uchart– Plot the data onto the charts andidentify any out of control conditions
- 65. 65Auditing SPC1. Are special characteristics being measured usingSPC/Cpk?2. Is their a link from the customer’s designatedspecial characteristics to what the organisation ismonitoring?3. What is the acceptance criteria the organisation isusing?4. How does the organisation determine which SPCchart to use5. What training has been provided to people usingSPC charts6. Is the organisation able to interpret control charts?
- 66. 66Auditing SPC7. Check calculation of a sample of SPC charts8. Does the organisation know what to do when there isan adverse trend or point go outside of the controllines9. How often does the organisation recalculate controllines? And do they follow this process?10. Does the sample size/frequency in the Control Planor other coincide with what the organisation is infact checking?11. Is the IMTE calibrated?

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