Six Sigma Green Belt Part 5

Transcription

1 Six Sigma Green Belt Part 5 Process Capability 2013 IIE and Aft Systems, Inc. 5-1

2 Process Capability Is the measured, inherent reproducibility of the product turned out by the process. It can be quantified from data which, in turn, are the result of measurements of work performed by the process. It defines limits we would normally expect virtually all individuals to fall within. By definition a process is capable when it is operating at the three sigma level IIE and Aft Systems, Inc. 5-2

3 Process Capability Is the range over which the natural variation of a process occurs as determined by the system of common causes. It is the ability of the combination of people, machines, methods, materials, and measurements to produce a product or service that will consistently meet design specifications IIE and Aft Systems, Inc. 5-3

4 Measuring Process Capability Process capability is measured by the proportion of output that can be produced within design specifications-it is a long term prediction. It is a measure of the uniformity of the process. It can be measured only if all special causes have been eliminated and the process is in a state of statistical control IIE and Aft Systems, Inc. 5-4

5 Components of Process Capability Design specifications Centering of natural variation Range or spread of variation 2013 IIE and Aft Systems, Inc. 5-5

6 Capability Measures Short term measures show the capability at a specific instance in time, e.g., 5 out of 90 samples did not meet customer requirements Long term measures show the expected capability of the process based on statistical projections using inherent process variability 2013 IIE and Aft Systems, Inc. 5-6

7 Frequency Establishing Process Capability Histogram Control Chart These must be performed prior to calculating any process capability measures Weight If a process is not in control it is not predictable IIE and Aft Systems, Inc. 5-7

8 Statistics Green Belts are expected to be able to calculate the following: Percent or proportion Non-Conforming Cp Index Cpk Index 2013 IIE and Aft Systems, Inc. 5-8

9 Percent Non-Conforming Reflects the proportion of the population that we normally expect not to meet the process specifications. Corresponds to the tail areas on the normal curve sketch USL LSL LSL Acceptable 2013 IIE and Aft Systems, Inc. 5-9

10 Calculating Use z transform. Values in Normal Curve Table z u x Uspec- x is also called the mean z l Lspec- x ' R d or MR 2 d 2 Process must be centered somewhere between the customer requirements IIE and Aft Systems, Inc. 5-10

11 Z Value Tail Proportion Z Value Tail Proportion Z Value Tail Proportion Z Value Tail Proportion IIE and Aft Systems, Inc. 5-11

12 Z Value Tail Proportion Z Value Tail Proportion Z Value Tail Proportion Z Value Tail Proportion IIE and Aft Systems, Inc. 5-12

13 Z Value Tail Proportion Z Value Tail Proportion Z Value Tail Proportion Z Value Tail Proportion IIE and Aft Systems, Inc. 5-13

14 Example A process has a mean of 600 and a standard deviation of 6. Spec limits are 585 and What is the percent nonconforming? (The total proportion in both tails.) 2. What is the DPMO? 3. What is the sigma level? (The sigma level is the smaller of the two z values.) Unacceptable LSL USL Unacceptable 2013 IIE and Aft Systems, Inc. 5-14

15 Example Unacceptable LSL LSL USL Unacceptable A process has a mean of 100 and a standard deviation of 4. Spec limits are 95 and What is the percent nonconforming? 2. What is the sigma level? 3. What is the DPM? 2013 IIE and Aft Systems, Inc. 5-15

16 Example Continued In the preceding example if each incorrect transaction costs $4 and annual volume is 400,000, what is the cost of the incorrect transactions? 2013 IIE and Aft Systems, Inc. 5-16

17 Example Continued If in the preceding example the standard deviation were reduced to 2 via a DMAIIC Green Belt project. If this were done at a cost of $100,000 would it be worth it? (One year payback.) 2013 IIE and Aft Systems, Inc. 5-17

18 Example Continued What would it take (or be worth) to now reduce the standard deviation to 1? 2013 IIE and Aft Systems, Inc. 5-18

19 More Practice A process has a mean of 200 and and a standard deviation of 2. Upper specification limit is 212. Lower specification limit is 188. Determine Proportion non conforming DPMO Sigma Level Motorola Shift 2013 IIE and Aft Systems, Inc. 5-19

20 Another Problem What is the capability of the process, in terms of proportion defective or sigma level or dpmo, we collected data on earlier in the course? (page 4-12) 2013 IIE and Aft Systems, Inc. 5-20

21 Capability Indices Show the relationship between the process capability and the process specifications Cp measures potential capability assuming that the process average is equal to the midpoint of the specification limits and the process is operating in statistical control. This will be the maximum proportion of output that meets specifications. Cpk reflects the current process mean s proximity to either specification limit. (When the process is centered Cp = Cpk.) Although the indices are calculated differently, the interpretation is the same 2013 IIE and Aft Systems, Inc. 5-21

22 Cp or Cpk Less than 1.0 Cp or Cpk Value Sigma Level IIE and Aft Systems, Inc. 5-22

23 Cp or Cpk Equal to 1.0 Cp or Cpk Value Sigma Level IIE and Aft Systems, Inc. 5-23

24 Cp or Cpk Greater than 1.0 Cp or Cpk Value Sigma Level No Motorola Shift 2013 IIE and Aft Systems, Inc. 5-24

25 Calculating Cp Cp = (Uspec Lspec)/6 Process must be centered at the midpoint of the specification limits IIE and Aft Systems, Inc. 5-25

26 C pk Calculation Smaller of the following: C pku = (Uspec Mean) / 3 C pkl = (Mean Lspec) / 3 C pk also is equal to the sigma level divided by 3 Note: Can also use these for one sided requirements 2013 IIE and Aft Systems, Inc. 5-26

27 Capability What is the capability index for the process we analyzed earlier? (page 4-12) 2013 IIE and Aft Systems, Inc. 5-27

28 Interpretation Capability Measure Not Capable Capable More than Capable Proportion Non Conforming More than Less than.0027 DPMO More than Less than 2700 Sigma Level Less than Cpk Less than More than 3.0 More than IIE and Aft Systems, Inc. 5-28

29 Another Cost Study (Optional) A process has customer requirements of 50 and 75. It is in control with an adjustable mean and a known standard deviation (based on the Shewhart approximation) of 8. Accounting tells us that a defect on the low side will cost of $10 and on the high side $5. (Scrap vs. rework.) Engineering has not been able to figure out a way to reduce variation. What is the optimum location for the process centering in order to minimize cost? 2013 IIE and Aft Systems, Inc. 5-29

30 Optional Homework Exercise U-Bolts On the following page is data on U-bolts for the dimension shown at the right. Determine the capability of the process regarding the indicated dimension. (Specs are ) 2013 IIE and Aft Systems, Inc. 5-30

31 Sample Observations Average Range IIE and Aft Systems, Inc. 5-31

32 Statistics Mean Average Range.2021 x Shewhart Standard Deviation.0869 R Calculated Standard Deviation IIE and Aft Systems, Inc. 5-32

33 Frequency IIE and Aft Systems, Inc. 5-33

34 Sample ID Averages Ranges 2013 IIE and Aft Systems, Inc. 5-34

35 # Observations Histogram Solution starts here to <= to <= to <= to <= to <= to <= to <= to <= to <= to <= 10.9 Class IIE and Aft Systems, Inc. 5-35

36 Xbar Chart UCL= CEN= LCL= R Chart UCL= CEN= LCL= IIE and Aft Systems, Inc. 5-36

37 Mean = StdDev = USL = LSL = Sigma Level = Process Capability Cpk Analysis Cpk =.5600 DPM = 84, IIE and Aft Systems, Inc. 5-37