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SPC

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Statistical Process Control - try to make little bit more descriptive

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SPC

  1. 1. STATISTICAL PROCESSSTATISTICAL PROCESSSTATISTICAL PROCESSSTATISTICAL PROCESS CONTROLCONTROLCONTROLCONTROL ---- SPCSPCSPCSPCCONTROLCONTROLCONTROLCONTROL ---- SPCSPCSPCSPC 1
  2. 2. SPC • What is Statistical Process Control • History of SPC • Activities of SPC • Control Charts 2 • Control Charts • Control Chart Patterns • Process Capability • Process Capability Ratio (Cp) • Process Capability Index (Cpk) • Advantages of SPC • Quiz Questions
  3. 3. SPC • Is the application of Statistical Methods to monitor and control a process to ensure that it operates at its full potential to produce conforming product. OR •Is an analytical decision making tool which allows you to see when a process is working correctly and when it is not. 3 process is working correctly and when it is not. • Statistical process control is a collection of tools that when used together can result in process stability and variance reduction
  4. 4. SPC •Was Pioneered By Walter .A. Shewhart In The Early 1920s. •W. Edwards Deming Later Applied SPC Methods In The US During World war II, Successfully Improved Quality In The Manufacture Of Munitions And Other Strategically Important Products. 4 Munitions And Other Strategically Important Products. •Deming introduced SPC Methods to Japanese Industry After The War Had Ended. •Resulted high quality of Japanese products. •Shewhart Created The Basis For The Control Chart And The Concept Of A State Of Statistical Control By Carefully Designed Experiments.
  5. 5. SPC Statistical process control - broadly broken down into 3 sets of activities 5 1. Understanding the process 2. Understanding the causes of variation 3. Elimination of the sources of special cause variation.
  6. 6. SPC Understanding the process • Process is typically mapped out and the process is monitored using control charts. Understanding the causes of variation • Control charts are used to identify variation that may be due to special 6 • Control charts are used to identify variation that may be due to special causes, and to free the user from concern over variation due to common causes. • It is a continuous, ongoing activity. • When a process is stable and does not trigger any of the detection rules for a control chart, a process capability analysis may also be performed to predict the ability of the current process to produce conforming product in the future.
  7. 7. SPC •When excessive variation is identified by the control chart detection rules, or the process capability is found lacking, additional effort is exerted to determine causes of that variance. • The tools used include Understanding the Causes of Variation 7 • Ishikawa diagrams •Designed experiments •Pareto charts •Designed experiments are critical -only means of objectively quantifying the relative importance of the many potential causes of variation.
  8. 8. SPC Elimination of the sources of special cause variation •Once the causes of variation have been quantified, effort is spent in eliminating those causes that are both statistically and practically significant. 8 •includes development of standard work, error-proofing and training. •Additional process changes may be required to reduce variation or align the process with the desired target, especially if there is a problem with process capability.
  9. 9. SPC • Random – Common causes – In herent in a process • Non-Random – Special causes – Due to identifiable factors – Does not affect every part 9 In herent in a process – Affects every part – Examples: gravity, air pressure, tool wear – Can be eliminated only through improvements in the system – Does not affect every part – Examples: tool breakage, start up, change of operators – Can be modified through operator or management action
  10. 10. SPC 10
  11. 11. SPC • Machine Warm-up • Operator Breaks• Operator Breaks • Material Changes • Tool Breakage • Operator Changes • Training
  12. 12. SPC Process is said to be ‘in control’ and stable • If common cause is the only type of variation that exists in the process • It is also predictable within set limits i.e. the probability of any future outcome falling within the limits can be stated approximately. Process is said to be ‘out of control’ and unstable exists 12 Results Index > 1.67 1.33≤ Index ≤ 1.67 Index ≤ 1.33 Interpretation Meets acceptance criteria May be acceptable Does not meet acceptance criteria Special cause variation exists within the process
  13. 13. SPC • Attribute – a product characteristic that can be evaluated with a discrete response – good – bad; yes - no 13 – good – bad; yes - no • Variable – a product characteristic that is continuous and can be measured – weight - length
  14. 14. SPC TOTAL VARIANCE σσσσσσσσ22 TT = σ2 Tool Wear + σ2 Measurement Error + 14 σσσσσσσσ22 TT = σ2 Tool Wear + σ2 Measurement Error + σ2 Gage Error + σ2 Material + σ2 Temperature + σ2 Operator + σ2 Other
  15. 15. To measure the process, we take samples andTo measure the process, we take samples and analyze the sample statistics following these stepsanalyze the sample statistics following these steps (b)(b) After enough samples areAfter enough samples are The solid lineThe solid line represents therepresents the SPC (b)(b) After enough samples areAfter enough samples are taken from a stabletaken from a stable process, they form aprocess, they form a pattern called apattern called a distributiondistribution represents therepresents the distributiondistribution FrequencyFrequency WeightWeight
  16. 16. To measure the process, we take samples andTo measure the process, we take samples and analyze the sample statistics following these stepsanalyze the sample statistics following these steps (c)(c) There are many types of distributions, including the normal (bellThere are many types of distributions, including the normal (bell--shaped)shaped) SPC (c)(c) There are many types of distributions, including the normal (bellThere are many types of distributions, including the normal (bell--shaped)shaped) distribution, but distributions do differ in terms of central tendency (mean),distribution, but distributions do differ in terms of central tendency (mean), standard deviation or variance, and shapestandard deviation or variance, and shape WeightWeight Central tendencyCentral tendency WeightWeight VariationVariation WeightWeight ShapeShape FrequencyFrequency
  17. 17. To measure the process, we take samples andTo measure the process, we take samples and analyze the sample statistics following these stepsanalyze the sample statistics following these steps SPC (d)(d) If only natural causes ofIf only natural causes of variation are present, thevariation are present, the output of a process formsoutput of a process forms a distribution that is stablea distribution that is stable over time and isover time and is predictablepredictable WeightWeight FrequencyFrequency PredictionPrediction
  18. 18. To measure the process, we take samples andTo measure the process, we take samples and analyze the sample statistics following these stepsanalyze the sample statistics following these steps ???? ?? SPC (e)(e) If assignable causes areIf assignable causes are present, the process output ispresent, the process output is not stable over time and isnot stable over time and is not predicablenot predicable WeightWeight FrequencyFrequency PredictionPrediction ?????? ?? ?? ?? ?? ?????? ???? ?? ?? ?? ?? ??????
  19. 19. Constructed from historical data, the purpose of controlConstructed from historical data, the purpose of control charts is to help distinguish between natural variations andcharts is to help distinguish between natural variations and variations due to assignable causesvariations due to assignable causes SPC variations due to assignable causesvariations due to assignable causes
  20. 20. FrequencyFrequency Lower control limitLower control limit Upper control limitUpper control limit (a) In statistical control(a) In statistical control and capable ofand capable of producing withinproducing within control limitscontrol limits SPC (weight, length, speed, etc.)(weight, length, speed, etc.) SizeSize Lower control limitLower control limit Upper control limitUpper control limit (b) In statistical control(b) In statistical control but not capable ofbut not capable of producing within controlproducing within control limitslimits (c) Out of control(c) Out of control
  21. 21. SPC • Enables successful manufacturing and sales • Prevents scrap, sorting, rework • Allows jobs to run well 21 • Allows jobs to run well • Has major impact on cost and schedule “Process Capability” is the ability of a process to make a feature within its tolerance.
  22. 22. SPC Everything Varies (and the variation can be seen if we measure precisely enough) • Heights • Weights • Pressure • Roughness 22 • Weights • Lengths • Widths • Diameters • Wattage • Horsepower • Miles per Gallon • Roughness • Strength • Conductivity • Loudness • Speed • Torque • Etc. etc. etc.
  23. 23. SPC XX XXX XXXX XXXX XXXXX XXXXX XXXXXX XXXXXX XXXXXXX XX XXX XXXX XXXX XXXXX XXXXX XXXXXX XXXXXX XXXXXXX Typical distance from the center: +1 standard deviation Typical distance from the center: -1 standard deviation 23 If we measure the DISTANCE from the CENTER of the bell to 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 the Standard 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. XXXXXXX XXXXXXXX XXXXXXXXX XXXXXXXXXXX XXXXXXX XXXXXXXX XXXXXXXXX XXXXXXXXXXX
  24. 24. SPC How much of the curve is included in how many standard deviations? ----6666 ----5555 ----4444 ----3333 ----2222 ----1111 +1+1+1+1 +2+2+2+2 +3+3+3+3 +4+4+4+4 +5+5+5+5 +6+6+6+60000 24 From –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.) ----6666 ----5555 ----4444 ----3333 ----2222 ----1111 +1+1+1+1 +2+2+2+2 +3+3+3+3 +4+4+4+4 +5+5+5+5 +6+6+6+60000
  25. 25. • To compute the mean we simply sum all the observations and divide by the total no. of observations. SPC 25
  26. 26. • Range, which is the difference between the largest and smallest observations. SPC smallest observations. 26
  27. 27. • Standard deviation is a measure of dispersion of a curve. • It measures the extent to which these values are scattered around the central mean. SPC scattered around the central mean. 27
  28. 28. SPC Control Charts for Variables Mean chart ( x -Chart ) uses average of a sample Range chart ( R-Chart ) uses amount of dispersion in a sample 28
  29. 29. SPC xx == xx11 ++ xx22 + ...+ ... xxkk kk == 29 UCL =UCL = xx ++ AA22RR LCL =LCL = xx -- AA22RR == == wherewhere xx = average of sample means= average of sample means ==
  30. 30. SPC OBSERVATIONS (SLIP- RING DIAMETER, CM) SAMPLE k 1 2 3 4 5 x R 1 5.02 5.01 4.94 4.99 4.96 4.98 0.08 2 5.01 5.03 5.07 4.95 4.96 5.00 0.12 3 4.99 5.00 4.93 4.92 4.99 4.97 0.08 30 3 4.99 5.00 4.93 4.92 4.99 4.97 0.08 4 5.03 4.91 5.01 4.98 4.89 4.96 0.14 5 4.95 4.92 5.03 5.05 5.01 4.99 0.13 6 4.97 5.06 5.06 4.96 5.03 5.01 0.10 7 5.05 5.01 5.10 4.96 4.99 5.02 0.14 8 5.09 5.10 5.00 4.99 5.08 5.05 0.11 9 5.14 5.10 4.99 5.08 5.09 5.08 0.15 10 5.01 4.98 5.08 5.07 4.99 5.03 0.10 50.09 1.15
  31. 31. SPC x = = = 5.01 cm= ∑x k 50.09 10 31 UCL = x + A2R = 5.01 + (0.58)(0.115) = 5.08 LCL = x - A2R = 5.01 - (0.58)(0.115) = 4.94 = = Retrieve Factor Value A2
  32. 32. SPC UCL = 5.08 Mean 5.10 – 5.08 – 5.06 – 5.04 – x = 5.01= 32 LCL = 4.94 Mean Sample number | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 5.02 – 5.00 – 4.98 – 4.96 – 4.94 – 4.92 – x = 5.01=
  33. 33. SPC UCL =UCL = DD44RR LCL =LCL = DD33RR ∑∑RR 33 RR == ∑∑RR kk wherewhere RR = range of each sample= range of each sample kk = number of samples= number of samples
  34. 34. SPC OBSERVATIONS (SLIPOBSERVATIONS (SLIP--RING DIAMETER, CM)RING DIAMETER, CM) SAMPLESAMPLE kk 11 22 33 44 55 xx RR 11 5.025.02 5.015.01 4.944.94 4.994.99 4.964.96 4.984.98 0.080.08 22 5.015.01 5.035.03 5.075.07 4.954.95 4.964.96 5.005.00 0.120.12 34 22 5.015.01 5.035.03 5.075.07 4.954.95 4.964.96 5.005.00 0.120.12 33 4.994.99 5.005.00 4.934.93 4.924.92 4.994.99 4.974.97 0.080.08 44 5.035.03 4.914.91 5.015.01 4.984.98 4.894.89 4.964.96 0.140.14 55 4.954.95 4.924.92 5.035.03 5.055.05 5.015.01 4.994.99 0.130.13 66 4.974.97 5.065.06 5.065.06 4.964.96 5.035.03 5.015.01 0.100.10 77 5.055.05 5.015.01 5.105.10 4.964.96 4.994.99 5.025.02 0.140.14 88 5.095.09 5.105.10 5.005.00 4.994.99 5.085.08 5.055.05 0.110.11 99 5.145.14 5.105.10 4.994.99 5.085.08 5.095.09 5.085.08 0.150.15 1010 5.015.01 4.984.98 5.085.08 5.075.07 4.994.99 5.035.03 0.100.10 50.0950.09 1.151.15
  35. 35. SPC OBSERVATIONS (SLIP-RING DIAMETER, CM) SAMPLE k 1 2 3 4 5 x R 1 5.02 5.01 4.94 4.99 4.96 4.98 0.08 2 5.01 5.03 5.07 4.95 4.96 5.00 0.12 3 4.99 5.00 4.93 4.92 4.99 4.97 0.08 4 5.03 4.91 5.01 4.98 4.89 4.96 0.14 5 4.95 4.92 5.03 5.05 5.01 4.99 0.13 6 4.97 5.06 5.06 4.96 5.03 5.01 0.10 7 5.05 5.01 5.10 4.96 4.99 5.02 0.14 35 7 5.05 5.01 5.10 4.96 4.99 5.02 0.14 8 5.09 5.10 5.00 4.99 5.08 5.05 0.11 9 5.14 5.10 4.99 5.08 5.09 5.08 0.15 10 5.01 4.98 5.08 5.07 4.99 5.03 0.10 50.09 1.15 ∑R k R = = = 0.115 1.15 10 UCL = D4R = 2.11(0.115) = 0.243 LCL = D3R = 0(0.115) = 0 Retrieve Factor Values DRetrieve Factor Values D33 and Dand D44
  36. 36. SPC Sample SizeSample Size Mean FactorMean Factor Upper RangeUpper Range Lower RangeLower Range nn AA22 DD44 DD33 22 1.8801.880 3.2683.268 00 33 1.0231.023 2.5742.574 00 36 33 1.0231.023 2.5742.574 00 44 .729.729 2.2822.282 00 55 .577.577 2.1152.115 00 66 .483.483 2.0042.004 00 77 .419.419 1.9241.924 0.0760.076 88 .373.373 1.8641.864 0.1360.136 99 .337.337 1.8161.816 0.1840.184 1010 .308.308 1.7771.777 0.2230.223 1212 .266.266 1.7161.716 0.2840.284
  37. 37. SPC UCL = 0.243 0.28 – 0.24 – 0.20 – R-Chart Example (cont.) 37 LCL = 0 Range Sample number R = 0.115 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 0.16 – 0.12 – 0.08 – 0.04 – 0 –
  38. 38. SPC Upper control limitUpper control limit 38 Normal behavior. Process is “inNormal behavior. Process is “in control.”control.” TargetTarget Lower control limitLower control limit
  39. 39. SPC Upper control limitUpper control limit 39 TargetTarget Lower control limitLower control limit One plot out above (or below).One plot out above (or below). Investigate for cause. Process isInvestigate for cause. Process is “out of control.”“out of control.”
  40. 40. SPC Upper control limitUpper control limit 40 TargetTarget Lower control limitLower control limit Trends in either direction, 5 plots.Trends in either direction, 5 plots. Investigate for cause ofInvestigate for cause of progressive change.progressive change.
  41. 41. SPC Upper control limitUpper control limit 41 TargetTarget Lower control limitLower control limit
  42. 42. SPC Upper control limitUpper control limit 42 TargetTarget Lower control limitLower control limit Run of 5 above (or below) centralRun of 5 above (or below) central line. Investigate for cause.line. Investigate for cause.
  43. 43. SPC Upper control limitUpper control limit 43 TargetTarget Lower control limitLower control limit Erratic behavior. Investigate.Erratic behavior. Investigate.
  44. 44. SPC CCpp == Upper SpecificationUpper Specification -- Lower SpecificationLower Specification 66σσ 44 A capable process must have aA capable process must have a CCpp of at leastof at least 1.01.0 Does not look at how well the process is centered in the specificationDoes not look at how well the process is centered in the specification rangerange Often a target value ofOften a target value of CCpp = 1.33= 1.33 is used to allow for offis used to allow for off--centercenter processesprocesses Six Sigma quality requires aSix Sigma quality requires a CCpp = 2.0= 2.0
  45. 45. SPC Insurance claims processInsurance claims process Process mean xProcess mean x = 210.0= 210.0 minutesminutes 45 CCpp == Upper SpecificationUpper Specification -- Lower SpecificationLower Specification 66σσ Process mean xProcess mean x = 210.0= 210.0 minutesminutes Process standard deviationProcess standard deviation σσ = .516= .516 minutesminutes Design specificationDesign specification = 210= 210 ±± 33 minutesminutes == = 1.938= 1.938213213 -- 207207 6(.516)6(.516) Process is capable
  46. 46. SPC Net weight specification = 9.0 oz ± 0.5 oz Process mean = 8.80 oz Process standard deviation = 0.12 oz Cp = = = 1.39 upper specification limit - lower specification limit 6σ 9.5 - 8.5 6(0.12)
  47. 47. SPC New Cutting MachineNew Cutting Machine New process mean xNew process mean x = .250 inches= .250 inches Process standard deviationProcess standard deviation σσ = .0005 inches= .0005 inches Upper Specification LimitUpper Specification Limit = .251 inches= .251 inches Lower Specification LimitLower Specification Limit = .249 inches= .249 inches 47 Lower Specification LimitLower Specification Limit = .249 inches= .249 inches CCpkpk = == = 0.670.67 .001.001 .0015.0015 New machine is NOT capable CCpkpk = minimum of ,= minimum of , (.251)(.251) -- .250.250 (3).0005(3).0005 .250.250 -- (.249)(.249) (3).0005(3).0005 Both calculations result inBoth calculations result in
  48. 48. SPC Net weight specification = 9.0 oz ± 0.5 oz Process mean = 8.80 oz Process standard deviation = 0.12 oz x - lower specification limit 48 Cpk = minimum = minimum , = 0.83 x - lower specification limit 3σ = upper specification limit - x 3σ = , 8.80 - 8.50 3(0.12) 9.50 - 8.80 3(0.12)
  49. 49. SPC A B What is Cpk? It is a measure of how well a process is within a specification. Cpk = A divided by B 49 Cpk = A divided by B A = Distance from process mean to closest spec limit B = 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.) Specification Limit Specification Limit
  50. 50. SPC A B “Process Capability” is the ability of a process to fit its output within the tolerances. Cpk = A divided by B 50 …a LARGER “A” …and a SMALLER “B” …means BETTER “Process Capability” Specification Limit Specification Limit B
  51. 51. SPC A B How can we make Cpk (A divided by B) better? Cpk = A divided by B 51 1. Design the product so a wider tolerance is functional (“robust design”) 2. Choose equipment and methods for a good safety margin (“process capability”) 3. Correctly adjust, but only when needed (“control”) 4. Discover ways to narrow the natural variation (“improvement”) Specification Limit Specification Limit
  52. 52. SPC A B What does a very good Cpk do for us? This Cpk is about 2. Very good! 52 This process is producing good units with a good safety margingood units with a good safety margingood units with a good safety margingood 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.”“6 Sigma Capability.”“6 Sigma Capability.”“6 Sigma Capability.” Specification Limit Specification Limit Mean
  53. 53. SPC A B What does a problem Cpk look like? This Cpk is just slightly greater than 1. Not good! 53 This 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.) Specification Limit Specification Limit
  54. 54. SPC A B 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. 54 A 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! Specification Limit Specification Limit want 2 or more.
  55. 55. SPC • Reduces waste • Lead to a reduction in the time required to produce the product or service from end to end due to a diminished likelihood that the final product will have 55 due to a diminished likelihood that the final product will have to be reworked, identify bottlenecks, wait times, and other sources of delays within the process. •A distinct advantage over other quality methods, such as inspection - its emphasis on early detection and prevention of problems •Cost reduction •Customer satisfaction
  56. 56. SPC True or False? 1. “Process Capability” can be defined as the ability of a process to make a feature within its tolerance. 56 to make a feature within its tolerance. 2. We can estimate the process average by taking a set of sample measurements, adding them up, and dividing by the number of measurements. 3. 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.
  57. 57. SPC True or False? 1. When using Cpk, the goal is to keep the Cpk value as low as possible. 2. If a pressure tolerance is 250 PSI minimum, and the process 57 2. 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.” 3. 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.” 4. If a height tolerance is 7.010” to 7.060”, and the process average is 7.042”,and the process standard deviation is .002”……then the process is “capable.”
  58. 58. SPC True or False? 1. If Larry is cutting an O.D. and the diameter is easily adjustable, the tolerance is 4.055” to 4.095”, the process average is 4.095”, and the standard deviation is .001”……then Larry should be able to make the process fully “capable” by adjusting the process. 2. If Jill is boring an I.D. with a tolerance of 1.475” to 1.525”, and has 58 2. If Jill is boring an I.D. with a tolerance of 1.475” 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. 3. 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.
  59. 59. THANKS 59 THANKS

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