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This document provides an overview of statistical process control (SPC). It discusses the objectives of an SPC course, which are to learn how to audit SPC and understand variables and attributes control charts. It then defines SPC and the types of variation it can detect. The document outlines the different types of SPC charts, including variables charts (x-bar and R, x-bar and s), attributes charts (p, np, c, u), and when each is best applied. It also discusses process capability studies and calculating Ppk and Cpk values.

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Statistical Process Control SPC ISO TS 16949:2002 Lead Auditor Course
2 Course Objectives • By the end of the course the participant should be able to identify; 1. How to Audit SPC 2. Variables SPC charts 3. Attribute SPC charts 4. When best to apply these charts 5. The difference between Ppk and Cpk and understand how to calculate these indexes
3 An ISO TS 16949 Quality Management System is based on Prevention not Detection Statistical Process Control SPCSPC
4 So 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 Statistical Process Control SPC is a proactive tool which assists in; • Eliminating waste • Reducing variation • Achieving superior quality product Lower unit cost
6 Types of Variation • Common cause – Due to normal wear and tear e.g. tool wear •Special Cause •Abnormal situation e.g tool broken
7 Normal Distribution & Standard deviation • Normal distributions are a family of distributions that have the same general shape. They are symmetric with scores more concentrated in the middle than in the tails. Normal distributions are sometimes described as bell shaped. Examples of normal distributions are below. Standard Deviation: Denoted with the Greek symbol Sigma, the standard deviation provides an estimate of variation. In mathematical terms, it is the second moment about the mean. In simpler terms, you might say it is how far the observations vary from the mean. σ
8 Statistical 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 (0.55 mm) • Temperature (32 degrees), Weight (38.98 grams)
9 Statistical 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 Statistical Process Control • VARIABLES SPC CHARTS The types of variables charts we will be examining are; – Average and Range charts (Xbar and R charts) – Average and Standard Deviation charts (Xbar and s charts) – Median charts – Individual and Moving Range chart ( X-MR)
11 Statistical Process Control • ATTRIBUTES SPC CHARTS The types of attributes charts we will be examining are; – Proportion nonconforming (p Chart) – Nonconforming product (np Chart) – Number of nonconformity's (c Chart) – Nonconformity's per unit (u Chart)
12 What is Six Sigma Six Sigma aims for virtually error free business performance. The Six Sigma standard of 3.4 problems per million opportunities is a response to the increasing expectations of customers and the increased complexity of modern products.
13 What is Six Sigma
14 What other global company’s say • General Electric estimates that the gap between three or four sigma and Six Sigma was costing them between $8 billion and $12 billion per year in inefficiencies and lost productivity.
15 The methodology Design of Experiments
SPC Variables
17 Course Objectives • By the end of the course the participant should be able to identify; 1. Variables SPC charts 2. When best to apply these charts 3. The difference between Ppk and Cpk and understand how to calculate these indexes
18 How to select the correct SPC chart Variables Xbar & S Xbar & R I & MR Median n =10 or more n= 2 to 9 n=1 n= odd number
19 X 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 conditions with a short interval between production of pieces
20 • Methodology for the calculation of parameters 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 chart X bar and R chart
21 X bar and R chart To calculate the control lines we use the following algorithm where k iswhere k is thethe number ofnumber of subgroupssubgroups RA-X=LCLRA+X=UCL RD=LCLRDUCL and k XXXX k RRRR 2x2x 3R4R n21n21 = ++=+++= 
22 X bar and R chart values for D4, D3 and A2 n 2 3 4 5 6 7 8 9 10 D4 3.27 2.57 2.28 2.11 2 1.92 1.86 1.82 1.78 D3 - - - - - 0.08 0.14 0.18 0.22 A2 1.88 1.02 0.73 0.58 0.48 0.42 0.37 0.34 0.31
23 X bar and R chart • Exercise – Using the data in Appendix 1, calculate the UCL and LCL for the average and range of the data. – Plot the data onto the charts and identify any out of control conditions
24 Average and standard deviation chart X bar and s chart • When to use a X bar and s chart • when there is measured data recorded on a real time basis or when operators are proficient is using a calculator • when you require a more efficient indicator of process variability • when you can obtain a subgroup of constant size with a larger sampling size than for Xbar and R charts, n=10 or more • when pieces are produced under similar conditions with a short interval between production of pieces
25 X bar and s chart • Methodology for the calculation of X bar 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 record results – 5. Calculate the standard deviation for each subgroup and record the result – 6. Plot the average and standard deviation onto the chart – 7. Interpret the chart
26 X bar and s chart To calculate the control lines we use the following algorithm where n is the number of parts in the subgroup and k is the number of subgroups sA-X=LCLsA+X=UCL sB=LCLsBUCL K S K XXX 1n s n XXXX 3x3x 3s4s Kk21 n21 = +++=+++= −+++= ∑   21 s 2)( SSX XXi - =
27 X bar and s chart values for B4, B3 and A3 n 2 3 4 5 6 7 8 9 10 B4 3.27 2.57 2.27 2.09 1.97 1.88 1.82 1.76 1.72 B3 - - - - 0.03 0.12 0.19 0.24 0.28 A3 2.66 1.95 1.63 1.43 1.29 1.18 1.1 1.03 0.98
28 X bar and s chart • Exercise – Using the data in Appendix 2 calculate the UCL and LCL for the average and standard deviation of the data. – Plot the data onto the charts and identify any out of control conditions
29 Median charts • When to use a Median chart • 1. When there is measured data recorded • 2. When you require an easy method of process control. This can be a good method to begin training operators • 3. When you can obtain a subgroup of constant size - for convenience ensure subgroup size is odd not even, typically 5 • 4. When pieces are produced under similar conditions with a short interval between production of pieces
30 Median charts • Methodology for the calculation of Median charts – 1. Determine the subgroup size, typically 5, ensure it is an odd number – 2. Establish the frequency of taking measurements – 3. Collect data – 4. Determine the median (middle number) for each subgroup and record results – 5. Determine the range for each subgroup and record the result – 6. Plot the median and range onto the chart
31 Median charts To calculate the control lines we use the following algorithm A-=LCLA+=UCL D=LCLDUCL k RRR k XXX 2X2X 3R4R kk21 R ~ R ~ RR R ~~~~ lueLowest va-alueHighest v value(middle)Median ~ ~~ 21 XX X R X = +++=+++= = =  Where k is theWhere k is the number ofnumber of subgroupssubgroups
32 Median charts values for B4, B3 and A3 n 2 3 4 5 6 7 8 9 10 D4 3.27 2.57 2.28 2.11 2 1.92 1.86 1.82 1.78 D3 - - - - - 0.08 0.14 0.18 0.22 A2 1.88 1.19 0.8 0.69 0.55 0.51 0.43 0.41 0.36
33 Median charts • Exercise – Using the data in Appendix 3 calculate the UCL and LCL for the median chart – Plot the data onto the charts and identify any out of control conditions
34 Individuals 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 individual readings e.g. a destructive type test which cannot be repeated frequently because of cost or other
35 Individuals and moving range chart • Methodology for the calculation of X-MR chart – 1. Establish the frequency of taking measurements – 2. Obtain individual readings – 3. Collect data – 4. Record the individual reading on the chart – 5. Determine the moving range from successive pairs of reading
36 Individuals and moving range chart Example of calculating control lines for individuals and moving range charts (X-MR) where k is thewhere k is the number ofnumber of readingsreadings RE-X=LCLRE+X=UCL RD=LCLRDUCL and k XXXX 1-k RRRR 2x2X 3MR4MR 21K21 k = ++=+++= 
37 Individuals and moving range chart n 2 3 4 5 6 7 8 9 10 D4 3.27 2.57 2.28 2.11 2 1.92 1.86 1.82 1.78 D3 - - - - - 0.08 0.14 0.18 0.22 E2 2.66 1.77 1.46 1.29 1.18 1.11 1.05 1.01 0.98
38 Individuals and moving range chart • Exercise – Using the data in Appendix 4 calculate the UCL and LCL for the X-MR chart – Plot the data onto the charts and identify any out of control conditions
39 Process Capability Studies What is Ppk and what is Cpk
40 Process Capability Studies • Definition of Ppk Preliminary Process Capability Study from 25 or more subgroups QS 9000 requires Ppk to be greater that or equal to 1.67
41 Process Capability Studies • Calculation of PpK 1 2)( − − = ∑ n XXi s SS MIN Z Ppk LSL-X Z, X-USL Z )Z,Z(Zmin, 3 min LSLUSL LSLUSL == ==
42 Process Capability Studies • Definition of Cpk Ongoing Process Capability Study for a stable process PPAP requires CpK to be greater that or equal to 1.67, if between 1.33 and 1.67 must review with customer
43 Ongoing Capability Studies • Calculation of CpK n d2 2 1.128 3 1.693 4 2.059 5 2.326 6 2.534 7 2.704 8 2.847 9 2.97 10 3.078 11 3.173 12 3.258 13 3.336 14 3.407 15 3.472 2 R LSL-X Z, 2 R X-USL Z )Z,Z(Zmin, 3 min LSLUSL LSLUSL dd MIN Z Cpk == ==
44 Standard Deviation Correction factors n c4 15 0.9823 16 0.9835 17 0.9845 18 0.9854 19 0.9862 20 0.9869 21 0.9876 22 0.9882 23 0.9887 24 0.9892 25 0.9896 30 0.9914 35 0.9927 40 0.9936 45 0.9943 50 0.9949 4C S Scorrected = To obtain an accurate calculation of the standard deviation, at least 60 data points are required. If less than 60 are available use the following error correction factors
45 Capability study assumptions 1. Data is normally distributed 2. Process is in statistical control Question: Why is the PpK requirement higher than the Cpk requirement???
SPC Attributes
47 Course Objectives • By the end of the course the participant should be able to identify; 1. Attribute SPC charts 2. When best to apply these charts
48 How to select the correct SPC chart Attributes P chart Np chart U chart C chart Count parts N = fixed or varied Count parts N = fixed Count occurrences N = varies Count occurrences N = fixed
49 Proportion of Units -Nonconforming p charts • When to use a p chart • when data is of attribute type (an attribute that can be counted) • when you wish to determine the proportion of nonconforming products in a group being inspected • from samples of equal or unequal size
50 p charts • Methodology for the calculation of p charts – Determine the subgroup size typically >50 units – Establish the frequency of inspection – Collate data - Determine the number of nonconforming products from that subgroup – Record the number of parts defective onto p-chart – Determine the proportion defective i.e number defective/number in subgroup – Plot this onto the p-chart
51 p charts • Example of calculating control lines for p-charts Note: nNote: n11pp11 etc..etc.. are the numberare the number ofof nonconformingnonconforming productsproducts detected and ndetected and n11,, nn22 etc are theetc are the correspondingcorresponding sample sizessample sizes Note: 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 zero n pp pLCLp n pp pUCLp )1( 3 )1( 3 n+n+n pn++pn+pn =p p-ingnonconformproportionaveragetheDetermine k21 kk2211 − ×−= − ×+=  
52 p charts • Class Exercise – Using the data in Appendix 5 calculate the UCL and LCL for the p chart – Plot the data onto the charts and identify any out of control conditions
53 Number of Nonconforming products np charts • When to use a np chart • when data is of attribute type (an attribute that can be counted) • when it is more important that you know the number of nonconforming products in a group being inspected • when sample sizes are of equal size
54 np 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 of nonconforming products from that subgroup – Record the number of parts defective onto np-chart – Plot this data onto the np-chart
55 np charts • Example of calculating control lines for np-charts Where k isWhere k is the numberthe number of subgroupsof subgroups and n is theand n is the sample sizesample size in each ofin each of thosethose subgroups.subgroups. )1(3 )1(3 np++np+np =pn pn-ingnonconformnumberaveragetheDetermine k k21 n pn pnpnLCLnp n pn pnpnUCLnp −×−= −×+= 
56 np charts • Class Exercise – Using the data in Appendix 7 calculate the UCL and LCL for the np chart – Plot the data onto the charts and identify any out of control conditions
57 Number of Nonconformity's c charts • When to use a c chart • when data is of attribute type (an attribute that can be counted) • when the nonconformity's are distributed throughout a product e.g. number of defects on a painted part, number of flaws in a assembly operation • when nonconformity's can be found from multiple sources or attributed to multiple sources
58 c 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 nonconformity's found in that sample – Record the number of nonconformity's onto c- chart – Plot this data onto the c-chart
59 c charts • Example of calculating control lines for c-charts Where k is the numberWhere k is the number of subgroups.of subgroups. c3c c3c k k++2+1 =c citiesnonconformofnumberaveragetheDetermine ccc ×−= ×+= LCLc UCLc 
60 c charts • Class Exercise – Using the data in Appendix 7 calculate the UCL and LCL for the c chart – Plot the data onto the charts and identify any out of control conditions
61 Number of Nonconformity's per unit u Chart • When to use a u-chart • when data is of attribute type (an attribute that can be counted) • when the number of nonconformity's are distributed throughout a product (e.g. number of defects on a painted part, number of flaws in a assembly operation) given varying sample sizes • when nonconformity's can be found from multiple sources or attributed to multiple sources
62 Number of Nonconformity's per unit u Chart • Methodology for the calculation of u charts – Define what will be inspected – Establish the frequency of inspection – Determine the number of nonconformity's found in that sample – Divide the number of nonconformity's found by the sample size – Record the proportion of nonconformity's onto the u chart – Plot this data onto the u-chart
63 Number of Nonconformity's per unit u Chart • Example of calculating control lines for u-charts Where c1, c2Where c1, c2 etc are numberetc are number ofof nonconformity'nonconformity' s per unit ands per unit and n1, n2 etc isn1, n2 etc is thethe correspondingcorresponding sample sizesample size n u 3u n u 3u nk+n2+n1 k++2+1 =u uunitperitiesnonconformaveragetheDetermine uuu ×−= ×+= + LCLu UCLu  
64 Number of Nonconformity's per unit u Chart • Class Exercise – Using the data in Appendix 8 calculate the UCL and LCL for the u chart – Plot the data onto the charts and identify any out of control conditions
65 Auditing SPC 1. Are special characteristics being measured using SPC/Cpk? 2. Is their a link from the customer’s designated special characteristics to what the organisation is monitoring? 3. What is the acceptance criteria the organisation is using? 4. How does the organisation determine which SPC chart to use 5. What training has been provided to people using SPC charts 6. Is the organisation able to interpret control charts?
66 Auditing SPC 7. Check calculation of a sample of SPC charts 8. Does the organisation know what to do when there is an adverse trend or point go outside of the control lines 9. How often does the organisation recalculate control lines? And do they follow this process? 10. Does the sample size/frequency in the Control Plan or other coincide with what the organisation is in fact checking? 11. Is the IMTE calibrated?

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Spc la

  • 1.
    Statistical Process Control SPC ISOTS 16949:2002 Lead Auditor Course
  • 2.
    2 Course Objectives • Bythe end of the course the participant should be able to identify; 1. How to Audit SPC 2. Variables SPC charts 3. Attribute SPC charts 4. When best to apply these charts 5. The difference between Ppk and Cpk and understand how to calculate these indexes
  • 3.
    3 An ISO TS 16949 QualityManagement System is based on Prevention not Detection Statistical Process Control SPCSPC
  • 4.
    4 So what isSPC? • 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.
    5 Statistical Process Control SPCis a proactive tool which assists in; • Eliminating waste • Reducing variation • Achieving superior quality product Lower unit cost
  • 6.
    6 Types of Variation •Common cause – Due to normal wear and tear e.g. tool wear •Special Cause •Abnormal situation e.g tool broken
  • 7.
    7 Normal Distribution &Standard deviation • Normal distributions are a family of distributions that have the same general shape. They are symmetric with scores more concentrated in the middle than in the tails. Normal distributions are sometimes described as bell shaped. Examples of normal distributions are below. Standard Deviation: Denoted with the Greek symbol Sigma, the standard deviation provides an estimate of variation. In mathematical terms, it is the second moment about the mean. In simpler terms, you might say it is how far the observations vary from the mean. σ
  • 8.
    8 Statistical 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 (0.55 mm) • Temperature (32 degrees), Weight (38.98 grams)
  • 9.
    9 Statistical 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.
    10 Statistical Process Control •VARIABLES SPC CHARTS The types of variables charts we will be examining are; – Average and Range charts (Xbar and R charts) – Average and Standard Deviation charts (Xbar and s charts) – Median charts – Individual and Moving Range chart ( X-MR)
  • 11.
    11 Statistical Process Control •ATTRIBUTES SPC CHARTS The types of attributes charts we will be examining are; – Proportion nonconforming (p Chart) – Nonconforming product (np Chart) – Number of nonconformity's (c Chart) – Nonconformity's per unit (u Chart)
  • 12.
    12 What is SixSigma Six Sigma aims for virtually error free business performance. The Six Sigma standard of 3.4 problems per million opportunities is a response to the increasing expectations of customers and the increased complexity of modern products.
  • 13.
  • 14.
    14 What other globalcompany’s say • General Electric estimates that the gap between three or four sigma and Six Sigma was costing them between $8 billion and $12 billion per year in inefficiencies and lost productivity.
  • 15.
  • 16.
  • 17.
    17 Course Objectives • Bythe end of the course the participant should be able to identify; 1. Variables SPC charts 2. When best to apply these charts 3. The difference between Ppk and Cpk and understand how to calculate these indexes
  • 18.
    18 How to selectthe correct SPC chart Variables Xbar & S Xbar & R I & MR Median n =10 or more n= 2 to 9 n=1 n= odd number
  • 19.
    19 X bar andR 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 conditions with a short interval between production of pieces
  • 20.
    20 • Methodology forthe calculation of parameters 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 chart X bar and R chart
  • 21.
    21 X bar andR chart To calculate the control lines we use the following algorithm where k iswhere k is thethe number ofnumber of subgroupssubgroups RA-X=LCLRA+X=UCL RD=LCLRDUCL and k XXXX k RRRR 2x2x 3R4R n21n21 = ++=+++= 
  • 22.
    22 X bar andR chart values for D4, D3 and A2 n 2 3 4 5 6 7 8 9 10 D4 3.27 2.57 2.28 2.11 2 1.92 1.86 1.82 1.78 D3 - - - - - 0.08 0.14 0.18 0.22 A2 1.88 1.02 0.73 0.58 0.48 0.42 0.37 0.34 0.31
  • 23.
    23 X bar andR chart • Exercise – Using the data in Appendix 1, calculate the UCL and LCL for the average and range of the data. – Plot the data onto the charts and identify any out of control conditions
  • 24.
    24 Average and standarddeviation chart X bar and s chart • When to use a X bar and s chart • when there is measured data recorded on a real time basis or when operators are proficient is using a calculator • when you require a more efficient indicator of process variability • when you can obtain a subgroup of constant size with a larger sampling size than for Xbar and R charts, n=10 or more • when pieces are produced under similar conditions with a short interval between production of pieces
  • 25.
    25 X bar ands chart • Methodology for the calculation of X bar 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 record results – 5. Calculate the standard deviation for each subgroup and record the result – 6. Plot the average and standard deviation onto the chart – 7. Interpret the chart
  • 26.
    26 X bar ands chart To calculate the control lines we use the following algorithm where n is the number of parts in the subgroup and k is the number of subgroups sA-X=LCLsA+X=UCL sB=LCLsBUCL K S K XXX 1n s n XXXX 3x3x 3s4s Kk21 n21 = +++=+++= −+++= ∑   21 s 2)( SSX XXi - =
  • 27.
    27 X bar ands chart values for B4, B3 and A3 n 2 3 4 5 6 7 8 9 10 B4 3.27 2.57 2.27 2.09 1.97 1.88 1.82 1.76 1.72 B3 - - - - 0.03 0.12 0.19 0.24 0.28 A3 2.66 1.95 1.63 1.43 1.29 1.18 1.1 1.03 0.98
  • 28.
    28 X bar ands chart • Exercise – Using the data in Appendix 2 calculate the UCL and LCL for the average and standard deviation of the data. – Plot the data onto the charts and identify any out of control conditions
  • 29.
    29 Median charts • Whento use a Median chart • 1. When there is measured data recorded • 2. When you require an easy method of process control. This can be a good method to begin training operators • 3. When you can obtain a subgroup of constant size - for convenience ensure subgroup size is odd not even, typically 5 • 4. When pieces are produced under similar conditions with a short interval between production of pieces
  • 30.
    30 Median charts • Methodologyfor the calculation of Median charts – 1. Determine the subgroup size, typically 5, ensure it is an odd number – 2. Establish the frequency of taking measurements – 3. Collect data – 4. Determine the median (middle number) for each subgroup and record results – 5. Determine the range for each subgroup and record the result – 6. Plot the median and range onto the chart
  • 31.
    31 Median charts To calculatethe control lines we use the following algorithm A-=LCLA+=UCL D=LCLDUCL k RRR k XXX 2X2X 3R4R kk21 R ~ R ~ RR R ~~~~ lueLowest va-alueHighest v value(middle)Median ~ ~~ 21 XX X R X = +++=+++= = =  Where k is theWhere k is the number ofnumber of subgroupssubgroups
  • 32.
    32 Median charts values forB4, B3 and A3 n 2 3 4 5 6 7 8 9 10 D4 3.27 2.57 2.28 2.11 2 1.92 1.86 1.82 1.78 D3 - - - - - 0.08 0.14 0.18 0.22 A2 1.88 1.19 0.8 0.69 0.55 0.51 0.43 0.41 0.36
  • 33.
    33 Median charts • Exercise –Using the data in Appendix 3 calculate the UCL and LCL for the median chart – Plot the data onto the charts and identify any out of control conditions
  • 34.
    34 Individuals and movingrange chart (X-MR) • When to use a X-MR chart • when there is measured data recorded • when process control is required for individual readings e.g. a destructive type test which cannot be repeated frequently because of cost or other
  • 35.
    35 Individuals and movingrange chart • Methodology for the calculation of X-MR chart – 1. Establish the frequency of taking measurements – 2. Obtain individual readings – 3. Collect data – 4. Record the individual reading on the chart – 5. Determine the moving range from successive pairs of reading
  • 36.
    36 Individuals and movingrange chart Example of calculating control lines for individuals and moving range charts (X-MR) where k is thewhere k is the number ofnumber of readingsreadings RE-X=LCLRE+X=UCL RD=LCLRDUCL and k XXXX 1-k RRRR 2x2X 3MR4MR 21K21 k = ++=+++= 
  • 37.
    37 Individuals and movingrange chart n 2 3 4 5 6 7 8 9 10 D4 3.27 2.57 2.28 2.11 2 1.92 1.86 1.82 1.78 D3 - - - - - 0.08 0.14 0.18 0.22 E2 2.66 1.77 1.46 1.29 1.18 1.11 1.05 1.01 0.98
  • 38.
    38 Individuals and movingrange chart • Exercise – Using the data in Appendix 4 calculate the UCL and LCL for the X-MR chart – Plot the data onto the charts and identify any out of control conditions
  • 39.
    39 Process Capability Studies Whatis Ppk and what is Cpk
  • 40.
    40 Process Capability Studies •Definition of Ppk Preliminary Process Capability Study from 25 or more subgroups QS 9000 requires Ppk to be greater that or equal to 1.67
  • 41.
    41 Process Capability Studies •Calculation of PpK 1 2)( − − = ∑ n XXi s SS MIN Z Ppk LSL-X Z, X-USL Z )Z,Z(Zmin, 3 min LSLUSL LSLUSL == ==
  • 42.
    42 Process Capability Studies •Definition of Cpk Ongoing Process Capability Study for a stable process PPAP requires CpK to be greater that or equal to 1.67, if between 1.33 and 1.67 must review with customer
  • 43.
    43 Ongoing Capability Studies •Calculation of CpK n d2 2 1.128 3 1.693 4 2.059 5 2.326 6 2.534 7 2.704 8 2.847 9 2.97 10 3.078 11 3.173 12 3.258 13 3.336 14 3.407 15 3.472 2 R LSL-X Z, 2 R X-USL Z )Z,Z(Zmin, 3 min LSLUSL LSLUSL dd MIN Z Cpk == ==
  • 44.
    44 Standard Deviation Correctionfactors n c4 15 0.9823 16 0.9835 17 0.9845 18 0.9854 19 0.9862 20 0.9869 21 0.9876 22 0.9882 23 0.9887 24 0.9892 25 0.9896 30 0.9914 35 0.9927 40 0.9936 45 0.9943 50 0.9949 4C S Scorrected = To obtain an accurate calculation of the standard deviation, at least 60 data points are required. If less than 60 are available use the following error correction factors
  • 45.
    45 Capability study assumptions 1.Data is normally distributed 2. Process is in statistical control Question: Why is the PpK requirement higher than the Cpk requirement???
  • 46.
  • 47.
    47 Course Objectives • Bythe end of the course the participant should be able to identify; 1. Attribute SPC charts 2. When best to apply these charts
  • 48.
    48 How to selectthe correct SPC chart Attributes P chart Np chart U chart C chart Count parts N = fixed or varied Count parts N = fixed Count occurrences N = varies Count occurrences N = fixed
  • 49.
    49 Proportion of Units-Nonconforming p charts • When to use a p chart • when data is of attribute type (an attribute that can be counted) • when you wish to determine the proportion of nonconforming products in a group being inspected • from samples of equal or unequal size
  • 50.
    50 p charts • Methodologyfor the calculation of p charts – Determine the subgroup size typically >50 units – Establish the frequency of inspection – Collate data - Determine the number of nonconforming products from that subgroup – Record the number of parts defective onto p-chart – Determine the proportion defective i.e number defective/number in subgroup – Plot this onto the p-chart
  • 51.
    51 p charts • Exampleof calculating control lines for p-charts Note: nNote: n11pp11 etc..etc.. are the numberare the number ofof nonconformingnonconforming productsproducts detected and ndetected and n11,, nn22 etc are theetc are the correspondingcorresponding sample sizessample sizes Note: 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 zero n pp pLCLp n pp pUCLp )1( 3 )1( 3 n+n+n pn++pn+pn =p p-ingnonconformproportionaveragetheDetermine k21 kk2211 − ×−= − ×+=  
  • 52.
    52 p charts • ClassExercise – Using the data in Appendix 5 calculate the UCL and LCL for the p chart – Plot the data onto the charts and identify any out of control conditions
  • 53.
    53 Number of Nonconformingproducts np charts • When to use a np chart • when data is of attribute type (an attribute that can be counted) • when it is more important that you know the number of nonconforming products in a group being inspected • when sample sizes are of equal size
  • 54.
    54 np charts • Methodologyfor the calculation of np charts – Determine the subgroup size typically >50 units – Establish the frequency of inspection – Collate data - Determine the number of nonconforming products from that subgroup – Record the number of parts defective onto np-chart – Plot this data onto the np-chart
  • 55.
    55 np charts • Exampleof calculating control lines for np-charts Where k isWhere k is the numberthe number of subgroupsof subgroups and n is theand n is the sample sizesample size in each ofin each of thosethose subgroups.subgroups. )1(3 )1(3 np++np+np =pn pn-ingnonconformnumberaveragetheDetermine k k21 n pn pnpnLCLnp n pn pnpnUCLnp −×−= −×+= 
  • 56.
    56 np charts • ClassExercise – Using the data in Appendix 7 calculate the UCL and LCL for the np chart – Plot the data onto the charts and identify any out of control conditions
  • 57.
    57 Number of Nonconformity's ccharts • When to use a c chart • when data is of attribute type (an attribute that can be counted) • when the nonconformity's are distributed throughout a product e.g. number of defects on a painted part, number of flaws in a assembly operation • when nonconformity's can be found from multiple sources or attributed to multiple sources
  • 58.
    58 c charts • Methodologyfor 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 nonconformity's found in that sample – Record the number of nonconformity's onto c- chart – Plot this data onto the c-chart
  • 59.
    59 c charts • Exampleof calculating control lines for c-charts Where k is the numberWhere k is the number of subgroups.of subgroups. c3c c3c k k++2+1 =c citiesnonconformofnumberaveragetheDetermine ccc ×−= ×+= LCLc UCLc 
  • 60.
    60 c charts • ClassExercise – Using the data in Appendix 7 calculate the UCL and LCL for the c chart – Plot the data onto the charts and identify any out of control conditions
  • 61.
    61 Number of Nonconformity'sper unit u Chart • When to use a u-chart • when data is of attribute type (an attribute that can be counted) • when the number of nonconformity's are distributed throughout a product (e.g. number of defects on a painted part, number of flaws in a assembly operation) given varying sample sizes • when nonconformity's can be found from multiple sources or attributed to multiple sources
  • 62.
    62 Number of Nonconformity'sper unit u Chart • Methodology for the calculation of u charts – Define what will be inspected – Establish the frequency of inspection – Determine the number of nonconformity's found in that sample – Divide the number of nonconformity's found by the sample size – Record the proportion of nonconformity's onto the u chart – Plot this data onto the u-chart
  • 63.
    63 Number of Nonconformity'sper unit u Chart • Example of calculating control lines for u-charts Where c1, c2Where c1, c2 etc are numberetc are number ofof nonconformity'nonconformity' s per unit ands per unit and n1, n2 etc isn1, n2 etc is thethe correspondingcorresponding sample sizesample size n u 3u n u 3u nk+n2+n1 k++2+1 =u uunitperitiesnonconformaveragetheDetermine uuu ×−= ×+= + LCLu UCLu  
  • 64.
    64 Number of Nonconformity'sper unit u Chart • Class Exercise – Using the data in Appendix 8 calculate the UCL and LCL for the u chart – Plot the data onto the charts and identify any out of control conditions
  • 65.
    65 Auditing SPC 1. Arespecial characteristics being measured using SPC/Cpk? 2. Is their a link from the customer’s designated special characteristics to what the organisation is monitoring? 3. What is the acceptance criteria the organisation is using? 4. How does the organisation determine which SPC chart to use 5. What training has been provided to people using SPC charts 6. Is the organisation able to interpret control charts?
  • 66.
    66 Auditing SPC 7. Checkcalculation of a sample of SPC charts 8. Does the organisation know what to do when there is an adverse trend or point go outside of the control lines 9. How often does the organisation recalculate control lines? And do they follow this process? 10. Does the sample size/frequency in the Control Plan or other coincide with what the organisation is in fact checking? 11. Is the IMTE calibrated?