1. Process Capability ASQ Section 1404
Ken Fredryk
March 10, 2015

2. Process Capability
We continually gather data on our process but can we emphatically answer this question: “How well can the process produce products to meet costumer specifications?” Gathering and analyzing data to answer that question is called a Capability Study
So how do we know if our process is capable? A capability study is analyzing data from our processes to see if our process is capable of producing defect-free products.

3. Process Capability Definition
The degree to which a process is able to meet defined tolerance limits (aka specification limits)
A measurable property of a process related to customer specifications and process output
Based on statistical evaluation of a process to measure inherent variability compared to the specification/tolerance limits
We’ve talked a lot about the voice of the customer—what we see in our control charts. Now we’re going to merge the voice of the customer with the voice of the process. And we’ll do that with a Capability Study.
What does it mean when we say something of someone else is “capable?” Encourage class participation.
Capability of a process indicates whether the process can produce products that meet specs. Capability studies can help us see how to improve capability to give us better centering and to reduce variation or spread. Remember where we talked about centering and spread? In SPC Control Charts!

4. Process Capability Components
Two factors of process capability
Measurement of inherent process characteristics
Location of the mean
Variation in terms of standard deviation
Specification Limits
Expressed as a process capability performance index
CP or CPK
PP or PPK
We’ve talked a lot about the voice of the customer—what we see in our control charts. Now we’re going to merge the voice of the customer with the voice of the process. And we’ll do that with a Capability Study.
What does it mean when we say something of someone else is “capable?” Encourage class participation.
Capability of a process indicates whether the process can produce products that meet specs. Capability studies can help us see how to improve capability to give us better centering and to reduce variation or spread. Remember where we talked about centering and spread? In SPC Control Charts!

5. Process Capability – Another View
Quantifiable comparison of Voice of Customer (spec limits) to Voice of the Process (control limits)
Most process measures have some target value and acceptable limits of variation around the target
The extent to which the “expected” values fall within tolerance limits determines how capable the process is of meeting its requirements

6. Process Capability Consider key measures of process performance in:
Help Desk Responsiveness
Customer Queue Time
Service Cost / Order
Revenue / Employee
Proposal Acceptance Rate
Service Complaints
On-Time Delivery
Days On-Hand Inventory

7. Why Conduct a Capability Study?
Process capability is a tool evaluate how well a process can produce products or services that meet customer specifications
May be required to a secure a contract
Validate new equipment
Provides direction about how to improve process performance
We’ve talked a lot about the voice of the customer—what we see in our control charts. Now we’re going to merge the voice of the customer with the voice of the process. And we’ll do that with a Capability Study.
What does it mean when we say something of someone else is “capable?” Encourage class participation.
Capability of a process indicates whether the process can produce products that meet specs. Capability studies can help us see how to improve capability to give us better centering and to reduce variation or spread. Remember where we talked about centering and spread? In SPC Control Charts!

8. Uses of Capability Analysis
Performed on existing processes as a means of establishing a baseline of current operations
Provide verification that processes meet contractual requirements
When done periodically is a means of monitoring deterioration of a process (system, equipment, environment, etc.)

9. Rationale of a Capability Study
Optimize process performance by minimizing variation and centering around the target
Non-Capable Process
Process target
Capable Process
Process target
from this
to this
We’ve talked a lot about the voice of the customer—what we see in our control charts. Now we’re going to merge the voice of the customer with the voice of the process. And we’ll do that with a Capability Study.
What does it mean when we say something of someone else is “capable?” Encourage class participation.
Capability of a process indicates whether the process can produce products that meet specs. Capability studies can help us see how to improve capability to give us better centering and to reduce variation or spread. Remember where we talked about centering and spread? In SPC Control Charts! m m
Not a silver bullet!!

10. Causes of Low Process Capability
Excess variation resulting from:
Process design
Poor design, lacking SOP, people, equipment, training, measurement, material
Remember the 6 M’s
Unreasonably tight specifications
Process not centered
What causes defects in your process? We looked at this graphic earlier in the week. Many things can contribute to a process being incapable of producing good parts.

11. Process Capability Requirements
Type of data determines how to conduct the study
Attribute/discrete data
Continuous/variable data
Process must be stable and in control
Need to identify distribution characteristics of data
CP and CPK are sensitive to data normality
Reliable measurement system
Measurement system must be verified prior to conducting a Capability Study
aka MSA

12. Process Capability – 30,000 ft. View
What Type of Data Do You Have?
Attribute Data
Variables Data
Collect Data on Process
Analyze Data in Excel
Analyze Data in Minitab/Excel
State Capability DPU, Sigma Quality
Level, PPM
State Capability DPU, Sigma, PPM, Cp, Cpk, Pp, Ppk
We can analyze capability with either attribute or variables data. With attribute data we use an Excel spreadsheet to calculate capability. You have a copy of the attribute sigma calculator on your data disc. If we have variables data, we use Minitab to get information on both short-term and long-term capability—Cp and Cpk being short-term and Pp and Ppk being long-term.

13. Process Stability Is Crucial
Stability is needed for process capability
Process output will be predictable
Nearly all outcomes (99.7%) will lie within ±3s of the process mean for Normal Data
Capability ratios will be meaningful
When there is no stability, there is NO capability
Process output will not be predictable
The rule of ±3s does not apply
Capability ratios will be meaningless
When we do a capability study, it only makes sense when the process is stable. How do we know when a process is stable? (Stable is the same thing as “in-control;” i.e., our control chart shows common-cause variation only.
If our process is not in control (is not stable), there is no capability. If we have assignable causes (which make a process not stable or out-of-control), we should be able to find the reasons for the assignable causes, fix them and bring the process into control.
Then do a capability study.

14. A Stable Process May Not Be Capable
The process has too much variation
Without decreasing process variation, some out of specification product is inevitable
The process is not centered
The specification limits are too close together
The process does not have enough room to move. Without a decrease in process variation or a widening of the specifications, some out of specification product is inevitable
Why could a process be stable and non-capable? Stability has nothing to do with capability, but there is no capability without stability.

15. Voice of the Process
The normal distribution is the voice of the process—it’s how the process behaves.

16. Voice of the Customer
The goal posts are the voice of the customer. They’re our spec limits.

17. Process Capability Ratios “Merge the Voices”
When we overlay the voice of the process on the voice of the customer, we have our process capability study.

18. Normal Distribution
The area under sections of the curve can be used to estimate the cumulative probability of a certain event occurring m

19. Process Capability: The Two Voicesm
LSL
USL
+3
-3
99.73% of values
Natural Process Variation
When we merge the natural process variation with the specification tolerance interval we have defined process capability.
And we want to have some elbow room. Over time, processes tend to shift by up to 1.5 sigma or standard deviations; so it is desirable to have some “elbow room” for the process to shift and to still remain capable.
We can control our processes—or at least use six sigma to make process improvements, but do we have control of our customer’s specs? In an ideal situation, you can establish specification limits based on your process variation. This is not always possible, however; but in Eaton we have application engineers who work with our customers to establish specs. And if we can establish specs based on our products, we can often have a competitive advantage over our competitors.

20. Process Capability Voice of the Process
Always estimated by (±) 3 standard deviations from the mean (the “Natural Process Limits”)
Therefore, six standard deviations in total

21. Visualizing Process Capability
This helps to visualize the difference between a process that is marginally capable (Cp = 1) and one that is six sigma capable (Cp = 2). Much easier to park the motorcycle in the garage than it is the car without scraping the sides.

22. Examples of Capable Processes
Process is barely capable as long as it remains centered within the specification limits 3 s
LSL
USL
Process is capable and will remain so, even if the process average is moved. Often called process shift 3 s
LSL
USL m m
You can see why both centering and spread are critical components of capability. What do you think would happen if the process on the left shifted over time? (It would become non-capable.)
If your process is just inside the spec limits, it does not have the ability to shift over time while remaining within the spec limits. The second distribution has room to shift.

23. Examples of Non-Capable Processes
Product produced beyond both upper and lower spec limits. 3s
LSL
USL
Product produced above the upper spec limit. 3s
LSL
USL 3s
LSL
USL m m m
Here are some examples of non-capable processes. (They are not capable because the curves are wider that the LSL/USL.) The second and third curves are shifted to the right and left, respectively. (It would be possible to be shifted and still be capable—if the width of the curve is less than the LSL/USL—even if it is shifted.
Taguchi stressed the concept of variation reduction, driving the point home by hypothesizing that there is a cost to society as the product reaches the upper and lower spec limits.
Product produced below the lower spec limit.

24. Capability Study Options1 5 4 3 2 9 O b s e r v a t i o n N u m I d l V P c D f C o2 X = . 6 U L 8
A short-term capability study covers a relative short period of time during which extraneous sources of variation have been excluded. (Guideline: data points.) A long-term capability study covers a longer period of time in which there is more chance for a process shift. (Guideline: data points.) 1 5 4 3 2 9 O b s e r v a t i o n N u m I d l V P c D f C X = . 6 U L 8
We’re using these two graphs to show a short time frame and a longer time frame. We can do both short- and long-term capability studies, based on the timeframe we select.
Do you notice anything about these control charts? In these examples capabilities studies would be meaningless. Why? Because the process is out-of-control. The illustration is used to show the difference in timeframe only.
Why would you ever want a short-term study? When you are just starting up a new process, you may not be able to collect enough data points to do a long-term capability study.
GM ran a study that proved that by taking readings on 10 consecutive parts, 6s=2R (six times the sample standard deviation = two times the range), so a large number of parts were not required to get a true representation of their process.

25. Steps of a Capability Study
Set the process to run as it normally would and record the values of the input variables
Execute the process over a period of time suitable
to the purpose of the study
Have all sources of variation been accounted for?
Take plenty of notes
Measure and record values of the output
How do you do a capability study?
1. First, set the process to its best known settings and record the input values.
2. If we have a lot of data, I.e., we are making lots of parts, we can use an Xbar-R chart. If I have a natural subgroup size of one or my process does not produce parts rapidly, there may not be the part-to-part dependence we have in the world of lots of parts. Hence, as a result of the slower speed (or higher cost of getting more parts) we may not be able to look at subgroups. In that case, an I-MR chart would be used.
is only a rule of thumb. A sample size of 30 is good for an estimate of the standard deviation. If you only had 25 samples, you wouldn’t have to worry too much. 100, again, is only a target sample size.

26. Steps of a Capability Study (continued)
5. Conduct Analysis (e.g. Minitab, Excel) to study: • Stability • Normal Plot • Histogram • Capability Ratios 6. Develop an action plan based on diagnostics.
4. We want to learn about our process. So you need to take plenty of notes. Watch the process over the course of the study. Just as we asked questions while walking the process for our process map, we need to take plenty of notes here, too. Get to know the process operator.
5. What we’re not doing here is going out and grabbing a bunch of historical data not knowing where it came from or how it was collected. The cycle time for producing a product—a piece of switchgear, for example—may be 40 days, so it may not always be practical to “wait” for new data as you begin your process. But remember: you may not know where historical data came from or how it was collected. As you begin to collect new data use this strategy so that you can learn about the process and the data you are collecting.
6. Use Minitab to study stability and capability.
7. And develop a plan of attack.

27. Sigma Level - s Definition:
The number of total standard deviations (+/–) that would fit within the spec limits
For example, a 3s level would mean 6 standard deviations can fit within the specification limits
Sigma Level is a measure of the process performance

28. Compare % Defective With and Without Shift
Calculated using a “shift” factor
Calculated as the area under the curve

29. Process Capability versus PPM Defects
s level:
A 6s level is  standard deviations or sigmas from the mean
This would be standard deviations, or 12s!
PPM: number of defects per million opportunities
We talked about the concept of capability in our overview earlier this week. It was our sigma level. You’ll remember that a sigma level correlates to parts per million defective.

30. Compare PPM Defects With and Without Shift

31. Graphical View of Sigma Levels
LSL USL
+1 s
+3 s
+2 s
LSL USL m m

32. Process Capability – Cp
Ratio of total variation allowed by the specification to the total variation actually measured from the process
Typical targets for Cp are greater than 1.33 (or 1.67 for safety items)
If Cp < 1, then the variability of the process is greater than the specification limits
Cp takes into account only process spread and not
location

33. Process Capability – Cp
Cp = Allowable variation (spec width)
Process Variation
Cp = USL – LSL 6 OR
Typical values:
Marginal Cp = 1.00
Acceptable Cp=1.33
Good Cp = 1.67
Six Sigma level Cp = 2.00

34. One-Sided Capability Ratios
If a process has just one spec (either USL or LSL), a
one-sided capability ratio (CPU or CPL) is calculated
It takes into account process spread and location
CPL = Xbar - LSL 3
CPU = USL – Xbar 3
Typical Values (when the “shift” is taken into consideration)
Marginal CPU or CPL = 1
Good CPU or CPL = 1.33
Six Sigma CPU or CPL = 1.5
If a spec is one-sided, the capability ratio is one-sided, too. Can you think of a one-sided spec? Cycle time (can’t be less than 0), distance to the window in an airline seat, flatness (can’t be flatter than “flat”). CPU and CPL take both center and spread into account.
This is assuming that the process ‘shifts’ and does not remain centered. In other words, the mean shifts from 0 to 1.5. If the shift was not taken into account, these numbers would be the same as the Cp

35. Centered Capability Ratio, CPK
If the spec is two-sided, the centered capability ratio can be calculated
It is the smaller of CPU and CPL
CPK = Minimum (CPU or CPL)
If a spec is two-sided, pick the smaller of the two.

36. Relationship Between CP and CPK
CPK = CP (1-K)
K ³ 0 is a “shift factor”
CPK is always less than, or equal to CP
Typical values (when the “shift” is taken into consideration):
Marginal CPK = 1
Acceptable CPK = 1.33
Six Sigma CPK = 1.5
Cpk takes centering, as well as spread, into consideration; whereas, Cp only factors in spread.
If the mean is outside the spec limits, the Cpk could be negative. In this case K would be greater than one.
Note for instructor:
k = [absolute value of (midpoint - mean)]/(USL - LSL)/2
where the midpoint is the point between the USL and LSL
soverall= total process variation = s/c4(n)
where n = total # of observations and the denominator is an unbiasing constant
swithinl= total process variation = sp/c4(d + 1)
where sp is the pooled standard deviation using all the data; it is the same as the usual s calculation, except that the denominator is (ni - 1) instead of n-1. (It subtracts 1 from each observation, rather than only from the total n.) m

37. Process mean is outside the specification limit
Negative Cpk
Process mean is outside the specification limit 3s
LSL
USL
Negative Cpk occurs when the mean is outside the USL or LSL
e.g. Cpk = -0.5
Cpk takes centering, as well as spread, into consideration; whereas, Cp only factors in spread.
If the mean is outside the spec limits, the Cpk could be negative. In this case K would be greater than one.
Note for instructor:
k = [absolute value of (midpoint - mean)]/(USL - LSL)/2
where the midpoint is the point between the USL and LSL
soverall= total process variation = s/c4(n)
where n = total # of observations and the denominator is an unbiasing constant
swithinl= total process variation = sp/c4(d + 1)
where sp is the pooled standard deviation using all the data; it is the same as the usual s calculation, except that the denominator is (ni - 1) instead of n-1. (It subtracts 1 from each observation, rather than only from the total n.)

38. Capability versus Performance
Capability Ratios (CP and CPK)
use a short-term estimate of sigma (s) obtained from the within-subgroup variation
show what the process would be capable of if it did not have shifts and drifts between subgroups
Performance Ratios (PP and PPK)
use a long-term estimate of sigma (s) obtained from within-subgroup plus between-subgroup variation
Show what the overall variation is
Performance ratios will be worse (smaller) than the corresponding capability ratios if the process has shifts and drifts
There may be confusion (especially w/automotive) with the short term and long term - Cpk was taken from production and the Ppk was often taken from prototypes (which would not have been actually ‘long term’).
We’ve talked about capability ratios—short-term measures of sigma—Cp and Cpk.
Pp and Ppk are performance ratios. Performance ratios use long-term estimates of sigma. We expect our short-term numbers to be higher because there is less chance of variability.

39. Over time, a process tends to shift by approximately 1.5 
The Dynamic Process
LSL
USL
Process Capability
Process Performance
Why do we care? There are natural shifts and drifts in the process. Remember the 1.5 sigma we talked about earlier? This is the amount by which a natural process varies.
Over time, a process tends to shift by approximately 1.5 

40. Capability Example Sample data of pin diameters
Data collected over 27 days
Sub-group size 5
Tolerance is –
P G A Approach (aka KFred rule of thumb: Always do PGA)

41. Capability Example Data

42. Control Chart by Subgroup

43. Capability Analysis 1

44. Normality Test

45. Capability Analysis by Subgroup

46. Capability Analysis 1

47. Capability Analysis 1

48. Capability Analysis 2

49. Capability Analysis 2
Excel Based
Cap_Study_.xls.xlsx

50. Capability Analysis Comparison
Original Data (Non-Normal)
Minitab
Transformed Data
Minitab
Original Data (Non-Normal)
Excel
Potential (Within) Capability
Cp 1.77
CPL 1.94
CPU 1.61
Cpk 1.61
Overall Capability
Pp 1.72
PPL 1.88
PPU 1.56
Ppk 1.56
Potential (Within) Capability
Cp 1.77
CPL 1.48
CPU 2.06
Cpk 1.48
Overall Capability
Pp 1.71
PPL 1.43
PPU 2.00
Ppk 1.43

51. Capability Analysis Comparison
Original Data Subgroup Size 5
Original Data Subgroup Size 1
Potential (Within) Capability
Cp 1.77
CPL 1.94
CPU 1.61
Cpk 1.61
Overall Capability
Pp 1.72
PPL 1.88
PPU 1.56
Ppk 1.56
Potential (Within) Capability
Cp 1.92
CPL 2.09
CPU 1.75
Cpk 1.75
Overall Capability
Pp 1.72
PPL 1.88
PPU 1.57
Ppk 1.57

52. Results Is the process stable? YES
Are the data normally distributed? No
What is the standard deviation (within) of the process? Approximately
What are CP and CPK? 1.77 and 1.61, respectively
What are the PPM (use the “within” performance)? Approximately 1

53. But what if we have only attribute data?

54. Attribute & Continuous Data Comparison

55. Process Capability from Count Data
Process capability for count data is assessed differently from continuous data
Summary of process capability using count data
Control Chart (I-MR)
DPU, DPMO and Sigma Level metrics
Ability to meet customer requirement
Process must be stable; otherwise, there is no capability

56. Attribute Capability Example
Customer spec is sigma quality level > 3.5
Last month 16,810 units were produced over 18 days
231 were defective
Did we meet customer requirements?
You know how to look at a control chart to see if the process is stable. Let’s do that.

57. Attribute Capability Analysis
Does the control chart show a stable process?
What are DPU?
What are DPMO?
What is the sigma level?
Does the process meet customer requirements?
You know how to look at a control chart to see if the process is stable. Let’s do that.

58. Attribute Capability Analysis
You know how to look at a control chart to see if the process is stable. Let’s do that.

59. I and MR Chart for Rate Is the process stable? Avg. Defect Rate
Is the process stable? If so, go on. If not, fix the assignable cause variation. You would know where to work based on your sampling strategy.
Now let’s look at how to calculate the other metrics.
(could use a p chart)
Is the process stable?

60. What Are the Defects per Unit (DPU)?
Formula: Example:
DPU = Total # Defects
Total Units Produced
DPU = =
16810
You can calculate defects per unit by simply dividing total number of defects by the total number of units produced. This example uses our data set for brakes. How would you know the total number of defects? (You count them—or run a total of the column.) And the total number of units produced? (Count them, or total them, again.) Then you simply divide the total number of defects by the total number of units produced.

61. What Are the Defects per Million Opportunities (DPMO)?
Formula: Example:
DPMO = DPU X 1,000,000
Total Opportunities for a Defect in One Unit
Another statistic you’ll want to calculate for attribute data is defects per million opportunity. How do you know how many opportunities you have for defects in one unit? Your team decides. How many do you have in a brake? (It either works or it doesn’t.) What happens if your team selects more than one opportunity for defects? (The denominator gets larger and the total number of defects goes down.) You influence the numbers!
DPMO = (1M) = 13,741.8
16810

62. What Is the Process Sigma Level?
Procedure: Use the Excel file sigmacalc.xls

63. Another Example Attribute Capability Study
Process: Bank Loan Application Review
Objective: Determine the capability of completed loan applications
Inspect completed loan applications for defects
What is a defect?
Need operational definition of a defect
Validate measurement system
Conduct attribute MSA
Tally defects
Calculate sigma level

64. Another Example Attribute Capability Study
Process: Bank Loan Application Review
500 random applications reviewed
5 fields per form are required to be completed by the applicant
Operational definition of a defect
Missing, illegible or wrong format fields
260 defects identified

65. Capability Summary
Capability ratios are used to compare the VOC (specs) to the VOP (natural process limits)
For a capability ratio to be a good predictor of future performance, the process must be stable
The two key ways to improve process capability are to reduce variation and to improve centering
A capability ratio should never be interpreted without a histogram of the process to ensure normality
Because these indices are unit-less, you can use capability statistics to compare the capability of one process to another

66. Questions? References Dean Cristolear iSixSigma.org 6Sigma.org ASQ.org
Cap_Study.xls
iSixSigma.org
6Sigma.org
ASQ.org
Six Sigma Forum Magazine May 2005:
Capability Indexes: Mystery Solved
Questions?