process-capability-calculator

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