1. Step M2 – Variable Process Capability
Capability analysis (Cp, Cpk, Pp, Ppk) indices is a set of statistical calculations used to assess the performance of a system, process, or part compared to its specification limits.
Capability analysis has predictive value only if certain priori assumptions are met.
Capability Analysis uses specification limits (Spec limits). Spec limits are not the same as control limits. Spec limits are set by the customer, engineering, or management, and control limits are based on the data collected to make a control chart.
The capability analysis reveals the percent of product which may lie outside the specification limits and describes how capable the system is. It draws a picture of the distribution to the specifications limits.

2. Step M2 – Variable Process Capability
Priori Assumptions for Calculating Process Capability
The process is stable
The process is in statistical control
The data sample used for the analysis is normally distributed
There are enough samples to describe the process – more data results in greater accuracy, greater precision and greater confidence in the results. At least 30 samples but more is better.

3. Step M2 – Variable Process Capability
Process Capability Steps
1 Select output variable for improvement
2. Verify measurement system (MSA)
3. Verify
customer
requirements
4. Validate
Specification
Limits
5. Collect sample data
6. Check data
for
normality
7. Calculate
Capability
8. Estimate LT Capability

4. Step M2 – Variable Process Capability
Process Capability Steps
1. Select output variable for improvement. This is your Y (Primary or a secondary metric) of interest and directly linked to your charter business case.
2. Verify measurement system (MSA). Make sure the measurement system is capable GR&R: %Cont <10%, %Study<30%, Dist. Cat. >4
3. Verify customer requirements. Consult customer and/or engineering. Determine if requirements are RUMBA: Reasonable, Understandable, Measurable, Believable, Achievable.
4. Validate specification limits. Check drawings, engineering, SOPs, Control plans, speak with operations.

5. Step M2 – Variable Process Capability
Process Capability Steps
5. Collect sample data. Determine a rational sampling plan and collect short term (ST) or long term data (LT). ST data captures only a small portion of the total variation a process may exhibit. Gather data from more than one shift, one lot, or one operator. LT captures the majority of variation and may include all shifts, many lots, many operators over a longer time than ST data.
6. Check data for normality. Minitab: Stat>Basic Statistics>Normality test. P>0.05 = Normal data. P<0.05 ≠ non-normal data
7. Calculate capability. Calcualte Z-Score, PPM, Yield, or Capability Cp, Cpk. Minitab: Stat>Quality Tools>Capability Analysis
8. Estimate LT capability. As appropriate, estimate LT capability by shifting ST 1.5 sigma, or using Pp and Ppk, LT Z-score, PPM, Yield

6. Standard Deviation calculated
Step M2 – Variable Process Capability
Basic Components
Lower and upper specification limits supplied by customer or engineering
LSL
USL Cp
Cp is the allowable width versus process spread
Sample data from process
CPL
CPU
Cpk is how centered the process is compared to the mean
Mean
and
Standard Deviation calculated
This slide represents
±6σ

7. If the process is centered the Cp and Cpk will be the same
Step M2 – Variable Process Capability
Two Standard Deviations (s = standard deviation) (plus one and minus one from the mean) is the average distance from the mean for all the sample data. It comprises 68.26% of all the data
Four Standard Deviations contains 95.44% of all data
Six Standard Deviations captures 99.73% of the process sample data
Thus. We use 6s
(99.73% of data) to calculate Cp
And 3s (1/2 the data) to calculate Cpk upper or
Cpk lower
depending on which value is smaller
68.26%
95.44%
99.73%
If the process is centered the Cp and Cpk will be the same

8. Step M2 – Variable Process Capability
Why we care about Cp and Cpk
Cp describes process spread and the % DEFECTS that result
Cpk describes process centering and resulting % DEFECTS
Both Cp and Cpk are required to describe the process
LSL
USL Cp
CPL
CPU
This slide represents
±3σ

9. Step M2 – Variable Process Capability
Cp is a ratio between the width of specification limits (allowable width) to the natural variation of a process
Cp = USL – LSL
6 * S
process spec limits
Natural process variation
Cp = Upper Spec Limit – Lower Spec limit
6 * Sample Standard deviation
Cp = Width between your spec limits
Width of your samples

10. Step M2 – Variable Process Capability
Cp is a ratio between the width of the specification limits (allowable spread) versus the actual width of the process
Cp = Upper Spec Limit – Lower Spec limit
6 * Sample Standard deviation
Which Is
Cp = The Width Between Spec Limits
Width of your samples 20 50 70
30 Samples
Mean of = 50
Std Dev = 5
EXAMPLE
Cp = (70 – 20)
6 * 5 (std dev)
Cp = 50 30
Cp = 1.67

11. Step M2 – Variable Process Capability
Cpk is a ratio between the distance from the MEAN of your sample and the closest specification limit (LSL or USL) to the width of ½ your process variation 60
LSL 20
USL 70 10 10
3 * 5
30 Samples
Mean of = 50
Std Dev = 5 10 15
6 Std Dev
Cpk = USL - Mean( )
3 * Std Dev 50
Cpk = .67
½ of the data
Use USL or LSL - whichever is smaller
because that is the direction of our problem

12. Step M2 – Variable Process Capability
If your data set is not a normal distribution there are ways to transform the data in Minitab, otherwise, the calculation is invalid. If you transform the data you have to transform the spec limits as well.
Pp and Ppk are the same as Cp and Cpk except Pp and Ppk are predicting long term capability. The long term calculations use overall standard deviation as opposed to calculating the standard deviation of each sub-group.
2 Cpk = 6 σ so be skeptical of capability calculations greater than 2
Short Term (ST)
Sigma Level
ST Cpk
ST Probability
ST PPM
ST % area under the curve
LT Probability
LT PPM
Ppk 1
.33
-0.16 2
.67
0.16 3
1.00
1350.0
0.50 4
1.33
31.7
6209.7
0.83 5
1.67
.03
232.7
1.16 6
2.00
0.0
3.4
1.50
This slide represents

13. Step M2 – Variable Process Capability
Determine % defective
If one tail is out of spec use the appropriate formula. If both tails are out use both formulas and add the results together (ZUSL + Z LSL). If a Z value is over 4 consider Z equal to zero.
_ _
Z USL = USL - X AND/OR Z LSL = X - LSL
σ σ
Z = Z value USL = Upper Spec Limit
LSL = Lower Spec Limit X = Process Sample Mean
σ = Sample Standard deviation
Using Z table in the Memory Jogger (p. 246) to find each Z value and then multiply that value by 100 to get % outside the spec limit.

14. Step M2 – Variable Process Capability
Calculating Sample Size
If Minitab is not available use this rough sample size calculation
n = Z2 * S2 h2
n = Minimum sample size (round up)
Z = confidence interval (default is 1.96 = 95% confidence)
S = Population standard deviation. If unknown use sample standard deviation
h = Smallest change you want to detect as measured in the same units as S If in doubt start by taking total tolerance/10.
If still in doubt use 30 or more as a sample size to start.

15. Step M2 – Variable Process Capability
Capability Analysis Using Non-normal Data
If the distribution is not normally distributed the capability calculations will not be valid. To use non-normal data use Minitab.
STATS > BASIC STATS > NORMALITY TEST P value must be ≥ .05
STATS > QUALITY TOOLS > INDIVIDUAL DISTRIBUTION IDENTIFICATION
The output will indicate which distribution most closely fits your data based upon the P value of each distribution. Pick the highest P value.
STATS > QUALITY TOOLS > CAPABILITY ANALYSIS > NONNORMAL Choose the distribution indicated from the previous operation.
Your output is a graph quoting Pp and Ppk