1. Process Capability and Capability Index.
Prepared by,
Chandrakant K. Karale

2. Process Capability| Index
Sr. No.
Components 1
Background 2
Common Terminologies 3
Relationship between process variability and specification limit width 4
Calculation of Cpk 5
Interpretation 6
Cpk Value Ranges 7
What if your process not capable 8
Application or Advantages of Cpk

3. Cpk| 1.0 Background Traditional Statistical tools:
Descriptive Statistical Tool
a.) Mean: measure of central tendency
b.) Range: difference between smallest and largest observation in set of data
c.) Standard Deviation: Measures the amount of data dispersion around mean
d.) Data Distribution shape: Normal, Bell shaped or skewed
Normal distribution
Skewed distribution

4. Cpk| 1.0 Background
Control Charts show sample data plotted on a graph with CL, UCL, and LCL

5. Cpk| 2.0 Terminologies Cont..
Definition: “ Process Capability is the measured, inherent variation of the product turned out by a process”
What is Process: To some unique combination of machines, tools, methods, materials & people engaged in production.
Capability: An ability, based on tested performance, to achieve measurable results
Process Capability = +3σ or -3σ ( a total of 6σ) Where, σ shows the standard deviation of Process under a state of statistical control.
Cp: process capability index
Cpk: minimum process capability index
Pp: process performance index
Ppk: minimum process performance index
Cont..

6. Cpk| 2.0 Terminologies Cpk is: Process Capability measure
Simple statistical measure estimate level  process output which will within specified limit
Provides comparison between output of process Vs Process Specification
Process Improvement:
Statistical Process Control tool
monitors process
tells whether capable or not meeting desired level of performance
action to be taken
To investigate concerns
Helps in process improvement and to achieve desired capability levels
Cont..

7. Cpk| 2.0 Terminologies Cp, Cpk Vs Pp, Ppk Cp Cpk Process Capability
Process Performance
Aims
Process Verification
Cp- Potential Capability
What process can do under certain condition
i.e. variation in short run for process in state of statistical control
Cpk- Actual Capability
Estimate of capability what process is doing over extended period of time
-Usage process Sigma for calculation
-K stands for centralizing factor
-For Process Performance
-Process in too new (At development stage)
No historical Data
Sample size is larger from process
Usage sample sigma for calculation
Cpk > Ppk
Anomalies in case of: sample size is small or data represents short amount of time only in that cases Cpk>Ppk is not true
Cont..

8. Cpk 3.0 Relationship between Process
variability and Specification width
Three possible ranges for Cp
Cp = 1, as in Fig. (a), process
variability just meets specifications
Cp ≤ 1, as in Fig. (b), process not capable of producing within specifications
Cp ≥ 1, as in Fig. (c), process
exceeds minimal specifications
One shortcoming, Cp assumes that the process is centered on the specification range
Cp=Cpk when process is centered

9. Cpk| 4.0 Calculations USL: upper specification limit;
LSL: lower specification limit;
Mean: grand average of all the data
Sigma hat: estimated inherent variability (noise) of a stable process
SD: overall variability
𝑪𝒑𝒌= 𝑻𝒐𝒕𝒂𝒍 𝑻𝒐𝒍𝒆𝒓𝒂𝒏𝒄𝒆 𝑷𝒓𝒐𝒄𝒆𝒔𝒔 𝑺𝒑𝒓𝒆𝒂𝒅

10. Cpk| 4.0 Calculation Process Capability analysis Process:
Take representative sample of process output
Statistical analysis of samples (Mathematical tools, Scattered Plot, Pareto Chart, Histogram, (Minitab/Excel/QI Macros for exel)
Calculate mean and Standard Deviation form the sample size
Calculate Cp Value as well as Cpkl and Cpku
Minimum value from Cpkl and Cpku is the value of Cpk
By observing results of statistical analysis one can be explain or determine future expected process capabilities (ex. In response to Productivity or Quality Attribute)
Process Capability provides a single number which has ability to provide details of process consistency output.
Requirement:
Stable Process

11. Cpk| 5.0 Interpretation of Values
Sigma Level
Defect Rate
(DPMO)
Yield
%Goods
Cpk 1σ
691462
30.9
0.33 4σ
6210
99.40%
1.33 2σ
308770
69.10%
0.67 5σ
233
99.98%
1.67 3σ
66811
93.33% 1 6σ
3.44 %
2.0

12. Cpk| 6.0 Cpk Value Ranges

13. Cpk| 7.0 What if process not capable
-Initial action - increase the inspection level and ensure that confidence with respect to the quality of output product is increased.
-Clearly, quality cannot be inspected into a product or process, therefore, the net steps will be to look at how to improve the capability of the process.
-Reviewing the product specifications, as by widening the specifications, the capability can be increased. (This can only be performed, if any proposed specification changes are acceptable per customer needs.)
-Then looking at the process/Actual Operations itself, there will be a need to identify the sources of variation (Ex. Fish Bone i.e. 6M_Man, Material, Machine, Method, Measurement, Mother Nature)

14. Cpk| 7.0 What if process not capable

15. Cpk| 7.0 What if process not capable

16. Cpk| 8.0 Advantages and application
1.) Product/Process Design and Understanding Stage:
-According to experimental design change input material attributes and process parameter
-Allows to Identify special causes and develop control strategy to eliminate or reduce variability
2. Process Scale up and Qualification Stage:
-To establish scientific evidence that the process is reproducible at commercial scale and the process will consistently deliver a product that meets the quality standard established in development stage.
Challenges:
-Limited commercial scale batches
-Higher level of sampling and testing to demonstrate product quality
Once sufficient data points are collected,
– Evaluate if the process reaches a stable state
– Establish control limits for control chart

17. Cpk| 8.0 Advantages and application
3. Routine Commercial Manufacturing Stage –
-Continual assurance that the process remains in a state of control (the validated state) during commercial manufacture
-Traditional sampling and testing to confirm product quality
-Statistical process control tools to monitor the process
-Cpk/Ppk monitoring and trending data of process batches

18. Thank You…!!!