Chapter 6: Process Capability Analysis

Abstract:

Process capability analysis (PCA) is a statistical method to determine if a process consistently meets customer specifications by comparing its natural variation to required limits (Specification Limits). It uses indices like Cp (potential capability) and Cpk (actual capability) to quantify this, assessing if the process is centered and its spread is narrow enough, often using data from control charts (like X-bar & R charts) and visualized with histograms, to guide quality improvement in manufacturing and other fields

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Key Concepts

• Specification Limits (USL/LSL): Customer-defined upper (USL) and lower (LSL) limits for product characteristics.
• Control Limits: Limits derived from process data (via SPC charts) showing natural variation, distinct from customer specs.
• Process Variation: The inherent spread or variability of the process output (often measured by standard deviation, sigma).
• Cp (Process Capability): Measures if the process spread (6 sigma) fits within the specification width (USL-LSL); ignores centering.
• Cpk (Process Capability Index): Considers both spread and centering, reflecting the minimum capability to meet either the upper or lower limit.
• Pp/Ppk: Similar to Cp/Cpk but uses overall process variation (sigma) instead of sample variation, for preliminary studies. 

So let's dive into the Chapter 6Process Capability Analysis for more details 

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6.1 Introduction

A process may be statistically stable (in control) yet still fail to meet customer requirements. Process Capability Analysis (PCA) evaluates how well a process can meet specification limits when it is operating under statistical control.

This chapter introduces the concept of process capability, capability indices, their interpretation, and their role in quality improvement and decision-making.

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6.2 Statistical Control vs Process Capability

It is essential to distinguish between control limits and specification limits:

• Control limits: Derived from process data; indicate stability

• Specification limits: Defined by customer or design requirements

A process must be in statistical control before capability analysis is performed.

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6.3 Process Spread and Natural Tolerance

For a normally distributed process, most observations fall within:

[
\mu \pm 3\sigma
]

This range (6σ) is called the natural tolerance of the process and is compared with specification limits to assess capability.

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6.4 Definition of Process Capability

Process capability is the ability of a process to produce output that consistently meets specifications.

It answers the question:

“Is the process capable of meeting customer requirements?”

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6.5 Process Capability Ratio (Cp)

6.5.1 Definition

The Cp index measures the potential capability of a process assuming it is perfectly centered.

[
C_p = \frac{USL - LSL}{6\sigma}
]

Where:

• USL = Upper Specification Limit

• LSL = Lower Specification Limit

• σ = Process standard deviation

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6.5.2 Interpretation of Cp

Cp Value	Interpretation
Cp < 1.0	Process not capable
Cp = 1.0	Barely capable
Cp > 1.33	Capable process
Cp ≥ 2.0	World-class process

Cp does not consider process centering.

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6.6 Process Capability Index (Cpk)

6.6.1 Definition

The Cpk index measures actual capability, considering both process spread and centering.

[
C_{pk} = \min \left( \frac{USL - \mu}{3\sigma}, \frac{\mu - LSL}{3\sigma} \right)
]

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6.6.2 Interpretation of Cpk

• Cpk ≤ Cp

• Cpk decreases as the process moves away from the center

• A process is considered capable when Cpk ≥ 1.33

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6.7 Relationship Between Cp and Cpk

Condition	Result
Process centered	Cp = Cpk
Process off-center	Cpk < Cp
High Cp, low Cpk	Good spread but poor centering

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6.8 Capability Indices for Non-Normal Data

When data are non-normal:

• Data transformation (e.g., Box-Cox) may be used

• Percentile-based capability indices may be applied

• Normality tests should be performed before analysis

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6.9 Sigma Levels and Process Capability

Process capability is often expressed in terms of sigma level:

Sigma Level	Defects per Million (Approx.)
3σ	66,800
4σ	6,210
5σ	233
6σ	3.4

Six Sigma methodology targets Cpk ≥ 2.0.

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6.10 Applications of Process Capability Analysis

• Quality improvement projects

• Supplier evaluation

• Process benchmarking

• Design validation

• Continuous improvement (Kaizen, Six Sigma)

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6.11 Limitations of Process Capability Analysis

• Assumes process stability

• Sensitive to measurement system variation

• Misleading if data are non-normal

• Not suitable for attribute data directly

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6.12 Learning Objectives

After studying this chapter, the learner will be able to:

• Differentiate between control and specification limits

• Calculate Cp and Cpk indices

• Interpret process capability results

• Understand sigma levels and their implications

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6.13 Review Questions

1. Define process capability.

2. Differentiate between Cp and Cpk.

3. Why must a process be in control before capability analysis?

4. What does Cp > 1.33 indicate?

5. Explain the significance of Six Sigma.

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6.14 Short Answer Questions (Competitive Exam Oriented)

1. What is Cpk?

2. State the formula for Cp.

3. What does Cp = Cpk imply?

4. Define natural tolerance.

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6.15 Summary

This chapter discussed process capability analysis and introduced capability indices Cp and Cpk. While control charts indicate process stability, capability indices assess the ability of a process to meet specifications. Together, they form the foundation of data-driven quality improvement.