Process Capability – Technical Guide Without Icons

Process Capability is a statistical tool used to evaluate the ability of a process to produce output within specified limits, or its "potential capability." It ensures that a process can meet customer expectations consistently and efficiently.

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Purpose of Process Capability

• Meet customer requirements/specifications
• Measure and control process spread (variation)
• Define realistic tolerances for product dimensions
• Improve overall process performance

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Influencing Factors

• Machine and equipment condition
• Operational conditions and methods
• Raw material consistency
• Skill levels of operators and inspectors
• Measurement techniques and gauge calibration

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Tools Commonly Used

• Histogram – For data distribution analysis
• Control Chart – To distinguish common vs. special cause variation
• Run Chart – To track process behavior over time
• ANOVA – To evaluate variation across groups

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1. Cp – Process Capability Index

Cp is a measure of the ability of a process to produce output within specification limits, assuming the process is centered.

Key Notes:

• Cp considers spread only
• Does not account for process mean or centering
• Cp ≥ 1.33 is considered capable

Formula:
Cp = (USL - LSL) / 6σ

Example Calculation:
USL = 10, LSL = 2, σ = 1
Cp = (10 - 2) / (6 × 1) = 8 / 6 = 1.33


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2. Cpk – Process Capability Index (Centered Analysis)

Cpk considers both spread and how centered the process is within the specification limits.

Key Notes:

• Cpk reflects both variability and centering
• Cpk ≤ Cp always
• Cpk ≥ 1.33 is considered acceptable

Formula:
Cpk = Min[(USL - X̄) / 3σ, (X̄ - LSL) / 3σ]

Example Calculation:
USL = 10, LSL = 2, X̄ = 6, σ = 1
Cpk = Min[(10 - 6) / (3 × 1), (6 - 2) / (3 × 1)]
Cpk = Min[1.33, 1.33] = 1.33


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Conceptual Analogy – Cp with Car and Garage

Cp > 1 (Excellent Process):
Process width < Specification width
UCL < USL and LCL > LSL
Process is precise and unlikely to produce defects

Cp = 1 (Acceptable Process):
Process width = Specification width
Any shift in the process may lead to defects

Cp < 1 (Poor Process):
Process width > Specification width
High likelihood of defects unless variability is reduced


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Summary Table

Metric	Formula	Interpretation
Cp	(USL - LSL) / 6σ	Spread of the process only
Cpk	Min[(USL - X̄), (X̄ - LSL)] / 3σ	Spread and centering both considered

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Recommendation:
Maintain Cp ≥ 1.33 and Cpk ≥ 1.33 for high-performance, low-defect manufacturing environments like cable production, aerospace, and medical device industries.

Process capability analysis enables proactive control before defects occur. It's essential for predictive quality management and competitive manufacturing.