1. Process Capability 1 There are 6 different “measures” that can be used to define how capable a process is of meeting customer requirements These measures are all related to each other and can be mathematically converted from one measure to another measure
2. Short and Long Term Capability 2 Data and the six measures of process capability can represent Short-term capability Long-term capability The Differences between short and long-term capability will be covered after an explanation of the different measures of process capability
3. Measures of Process Capability 3 Z values Sigma % Out of Spec DPMO 1 Defect per # of Opportunities Cpk
4. Z Values 4 Z value is simply the number of standard deviations the customer specification is away from the process mean The Z value assumes the normal distribution Example: mean = 50 standard deviation = 5 specification limit = 60 Z value = 2
5. Sigma 5 Sigma is another term for the Z value and is often used interchangeably with Z values In the context of a Six Sigma program, Sigma is defined as equal to the Z value that represents the short-term capability of the process (short and long-term capability are explained later)
6. % Out of Spec 6 The % Out of Spec represents the percentage of the data that does not meet customer specifications It is the probability of obtaining a higher Z value than the current Z value (this is the case of an upper spec. For a lower spec it would be the probability of obtaining a lower value)
7. % Out of Spec 7 Example from Z value: Z = 2 Probability of getting a Z value > 2 = 0.02275 0.02275 / 100 = 2.275 % out of Spec Example of calculating directly from the data: 2,275 shipments were late total # of shipments was 100,000 (2,275 / 100,000) * 100 = 2.275 % Out of Spec probability of 0.02275 = Z value of 2
8. DPMO 8 DPMO stands for “Defects Per Million Opportunities” DPMO is related to the Z value and the % out of spec numbers
9. DPMO 9 Example from Z probability: Z = 2 and probability = 0.02275 DPMO = 0.02275 * 1,000,000 = 22,750 Example from % Out of Spec % Out of Spec = 2.275 DPMO = 2.275 * 10,000 = 22,750
10. 1 Defect per # of Opportunities 10 Sometimes people wish to express process capability by saying a defect will occur, on average, every X # of opportunities This value can be estimated by 1,000,000 / DPMO Example: DPMO = 22,750 1,000,000 / 22,750 = 43.956 = 44 Process will have, on average, 1 defect every 44 opportunities
11. Cpk 11 Cpk for a process can be estimated by using the standard formulas available in any textbook or Dow publication Relationship between Cpk and Z values is Cpk = Z / 3
12. Cpk 12 Example from “textbook calculations” mean = 50 standard deviation = 5 specification limit = 60 Cpk = (USL - Mean) / ( 3 * standard deviation) Cpk = (60 - 50) / (3*5) = 10 / 15 = 0.66666667
13. Cpk 13 Example from “Z value” mean = 50 standard deviation = 5 specification limit = 60 Z value = 2 Cpk = Z / 3 Cpk = 2 / 3 = 0.66666667
14. Summary of Process Measurements 14 For a process with mean = 50, standard deviation = 5 and a customer specification = 60 Z value = 2 Sigma =2 (depending on if data is short or long-term) % Out of Spec = 2.275 DPMO = 22,750 One defect per # of opportunities = 44 Cpk = 0.66666667 The six process capability measurements are all equivalent to each other
15. Short and Long Term Capability 15 Data and the six measures of process capability can represent Short-term capability Long-term capability
16. Guidelines 16 If data is collected over several cycles/time intervals/batches/campaigns then it is considered long-term If data is collected over just one cycle/time interval/batch/campaign then it is considered short-term If it is felt that both random and nonrandom influences were present when data was collected, then data is considered long-term
17. Short-term Capability 17 Describes how precise the process is at any given moment in time It represents the true potential of the process technology to meet the given performance specifications What the process can do if everything is controlled to such an extent that only random variation (background noise) is present Assumes that the process is perfectly centered
18. Long-Term Capability 18 Describes the sustained reproducibility of a process Process will drift over time Drift reflects the influence of time related sources of error which tend to upset process centering (mean changes over time) any static offset present in the process mean (mean is not perfectly centered)
22. Short and Long Term Capability 22 Short-Term Capability Effect of random variation only Process is centered Long-Term Capability Effect of random variation Effect of time related sources of error (drifting mean) Effect of static offset in process mean (mean is not centered)
23. Correction Factor or Shift 23 How do we go between long-term and short-term capability ? Apply a correction factor or shift Experience show that a shift of 1.5 sigma is typical for most processes Once the sigma or Z value is adjusted, related values such as DPMO, % Out of Spec, 1 defect per # of Opportunities, and Cpk can be calculated from the Z values
24. Correction Factor or Shift 24 Lower Spec Limit Target Upper Spec Limit m 3.4 DPMO 1.5s 6s 6s
25. Converting from Long-Term to Short-Term 25 Assume the calculated value for Z = 2.00 If data was long-term then Zlt = 2.00 ZShort-Term = Zlt + shift Zst = 2.00 + 1.5 Zst = 3.50 % Out of Spec, DPMO, 1 defect per # of opportunities, and Cpk can now be estimated for short-term data by using Zst = 3.50 and the equivalent long-term measures can be estimated by using Zlt = 2.00 Sigma = Zst = 3.50
26. Converting from Short-Term to Long-Term 26 Assume the calculated value for Z = 3.50 If data was short-term then Zst = 3.50 ZLong-Term = Zst - shift Zlt= 3.50 - 1.5 Zlt = 2.00 The other process capability measures can be estimated in the same manner as the previous example (by using Zlt = 2.00 and Zst = 3.50 and then converting those values to the equivalent DPMO, Cpk, etc.)
28. “Equivalent Values” 28 For the previous example when Z long-term = 2.00 the equivalent values for the other process capability measures are:
29. Six Sigma Reporting Convention 29 In the context of the Six Sigma Program Use Zst to reference the SIGMA of a process this is what the process is capable of, if everything is perfect [no drift, no off center mean, nothing but random variation (background noise)] Use the long-term DPMO to estimate the expected defects in your process you know that the process will tend to drift and shift over time, so this is a more realistic estimate of the number of defects you will get over a long time frame
30. Six Sigma Reporting Convention 30 For the previous example when Z long-term = 2.00 the equivalent values for the other process capability measures and the “standard report” are:
31. Using the Sigma Calculator 31 Sigma Calculator is an Excel Spreadsheet It makes use of the fact that once 1 process capability measure is known, the other process capability measurements can be calculated Reports data in “Standard Six Sigma Reporting Format” Enables user to focus on reducing defects instead of calculating numbers
32. Which Measure to Calculate First ? 32 It is generally recommended to calculate the % Out of Spec value first Sigma, Z, and Cpk numbers all assume the normal distribution which may not be true at all Some manufacturing data follows the exponential distribution (some reasons are that it is impossible to get less than 0 ppm, plus laws of how chemical reactions occur) Transactional data may follow the Poisson distribution (discrete events that have a small probability of occurring and large sample sizes)
33. Steps in Calculating Process Capability 33 Collect Data Determine % Out of Spec Determine if data is long or short-term data Choose % Out of Spec in the Sigma Calculator drop down box for either long or short-term data Enter in % Out of Spec See what the “Sigma” and DPMO are for the process Take action to reduce the number of defects
34. Example 34 Over a long time period 2,500 customer shipments were tracked to see if they arrived at the customer’s location on time 5 shipments did not arrive on time
35. Collect Data 35 The 2,500 shipments were tracked and 5 were found to have arrived late
36. Determine % Out of Spec 36 (5 / 2,500) * 100 = 0.2 percent out of spec
37. Determine if Data is long or short-term 37 Since problem said over a long time and it was felt that both random and nonrandom events occurred in this time period the data was determined to be long-term Note that the main goal is to get a benchmark value and reduce it no matter if it is long or short-term
38. Choose % Out of Spec (long-term data) from Drop Down Box 38
