Process Capability Calculator Skill

Process Capability Calculator

Overview

The Process Capability Calculator skill provides comprehensive capabilities for analyzing process capability against specification limits. It supports multiple capability indices, normality testing, and defect rate estimation for both short-term and long-term performance assessment.

Capabilities

Capability index calculation (Cp, Cpk, Pp, Ppk)
Specification limit analysis
Process performance metrics
Normality testing
Non-normal data transformation
Capability histogram generation
PPM defect rate estimation

Used By Processes

SIX-003: Process Capability Analysis
SIX-002: Statistical Process Control Implementation
QMS-004: Cost of Quality Analysis

Tools and Libraries

Statistical software APIs
Quality analysis libraries
Data transformation tools
Visualization libraries

Usage

skill: process-capability-calculator
inputs:
  data: [10.2, 10.1, 10.3, 10.0, 10.2, 10.4, 10.3, 10.2, 10.5, 10.3]
  specification_limits:
    usl: 10.8
    lsl: 9.2
    target: 10.0
  analysis_type: "short_term"  # short_term | long_term
  normality_test: true
outputs:
  - capability_indices
  - ppm_estimates
  - sigma_level
  - histogram_with_specs
  - normality_assessment
  - recommendations

Capability Index Formulas

Short-Term (Potential) Capability

Cp = (USL - LSL) / (6 * sigma_within)

Cpk = min[(USL - mean) / (3 * sigma_within), (mean - LSL) / (3 * sigma_within)]

Long-Term (Actual) Performance

Pp = (USL - LSL) / (6 * sigma_overall)

Ppk = min[(USL - mean) / (3 * sigma_overall), (mean - LSL) / (3 * sigma_overall)]

Capability Interpretation

| Cp/Cpk Value | Interpretation | Sigma Level | |--------------|----------------|-------------| | < 0.67 | Very poor | < 2 sigma | | 0.67 - 1.00 | Poor | 2 - 3 sigma | | 1.00 - 1.33 | Marginal | 3 - 4 sigma | | 1.33 - 1.67 | Good | 4 - 5 sigma | | 1.67 - 2.00 | Very good | 5 - 6 sigma | | > 2.00 | Excellent | > 6 sigma |

PPM Defect Rate Estimation

| Cpk | PPM (one-sided) | % Yield | |-----|-----------------|---------| | 1.00 | 1,350 | 99.865% | | 1.33 | 32 | 99.997% | | 1.67 | 0.3 | 99.99997% | | 2.00 | 0.001 | 99.9999999% |

Integration Points

Quality Management Systems
Statistical analysis software
SPC platforms
Customer reporting systems

Agent Skills: Process Capability Calculator

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