1. Overview of Process Capability (Cp) and Process Capability Index (Cpk)
Process Capability is a statistical measure used to determine how well a process produces output within specified limits. It helps identify the reproducibility of a process and its alignment with customer expectations.

Key Terms:
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• Cp: Process Capability, evaluates inherent reproducibility without considering process centering.
• Cpk: Process Capability Index, accounts for both process centering and spread relative to specification limits.
• 6-Sigma Quality: A rigorous standard for minimizing variability and defects in processes.

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2. Process Capability (Cp)

Process Capability (Cp) evaluates how well a process's spread fits within the design limits. It assumes the process is centered and does not consider deviation from the target.

Formula for Cp:
Cp = (SU - SL) / (6s)
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• SU: Upper specification limit
• SL: Lower specification limit
• s: Standard deviation of the process

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Non-Conformance Rate and Cp (when the process is centered):

Specification Limit	Percent Conformance	Non-Conformance Rate (ppm)	Process Capability (Cp)
±1σ	68.7%	317300	0.33
±2σ	95.45%	45500	0.67
±3σ	99.73%	2700	1.00
±4σ	99.9937%	63	1.33
±5σ	99.999943%	0.57	1.67
±6σ	99.999998%	0.002	2.00

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3. Process Capability Index (Cpk)

The Process Capability Index (Cpk) measures both the spread and centering of the process. Unlike Cp, it considers the process mean's alignment with the specification limits.

Formula for Cpk:
Cpk = min((SU - X̄) / (3s), (X̄ - SL) / (3s))
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• X̄: Process mean
• SU, SL, and s: Defined as above

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Non-Conformance Rate and Cpk (when the process is off-center by ±1.5σ):

Specification Limit	Percent Conformance	Non-Conformance Rate (ppm)	Process Capability (Cpk)
±1σ	30.23%	697700	-0.167
±2σ	69.13%	308700	0.167
±3σ	93.32%	66810	0.500
±4σ	99.379%	6210	0.833
±5σ	99.9767%	233	1.167
±6σ	99.996600%	3.4	1.500

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4. The Importance of 6-Sigma Quality

What is 6-Sigma Quality?
6-Sigma is a set of techniques and tools designed for process improvement. Its primary goal is to minimize variation and defects by achieving near-perfect quality levels.

Core Concepts of 6-Sigma:
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• Defects Per Million Opportunities (DPMO): At 6-Sigma, only 3.4 defects per million opportunities occur.
• Process Stability: Achieved through reducing variability in manufacturing or service processes.
• Customer Satisfaction: High-quality output ensures greater satisfaction and lower costs.

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5. Key Takeaways
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• Cp and Cpk Metrics: Cp evaluates process spread, while Cpk considers both spread and centering.
• 6-Sigma Threshold: To meet 6-Sigma quality, a process must have a Cpk of 2.00 when centered or 1.50 with ±1.5σ offset.
• Continuous Improvement: These metrics allow organizations to identify gaps and enhance process performance.

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