copq-estimator

name	copq-estimator
description	Deterministic Cost of Poor Quality (COPQ) financial estimator over the PAF (Prevention-Appraisal-Failure) model.

Cost of Poor Quality (COPQ) Financial Estimator

Overview

The Cost of Poor Quality (COPQ) Estimator provides deterministic financial quantification of quality nonconformances, defects, and appraisal/prevention activities using the classical Prevention-Appraisal-Failure (PAF) cost accounting model.

Developed originally by Armand Feigenbaum and Joseph Juran and codified in the ASQ Certified Six Sigma Green Belt (CSSGB) Body of Knowledge and the Council for Six Sigma Certification (CSSC) Lean Six Sigma Manual (2018), Cost of Quality (CoQ) categorizes quality-related expenditures into four distinct quadrants:

1. Prevention Costs: Investments made to avoid nonconformances, errors, and defects upstream (e.g., APQP quality planning, DFM reviews, poka-yoke error-proofing, operator training, supplier capability audits).
2. Appraisal Costs: Expenses incurred to measure, audit, or evaluate products and processes to assure conformance to standards (e.g., receiving inspection, CMM dimensional checks, in-process AOI testing, gage calibration, laboratory analysis).
3. Internal Failure Costs: Waste and losses resulting from defects identified prior to delivery or transfer to the customer (e.g., scrap, rework labor and added materials, sorting/containment, retesting, production downtime).
4. External Failure Costs: Losses and liabilities resulting from defects identified after shipment or customer delivery (e.g., warranty claims, customer returns, product recalls, field service, price concessions / deviations).

Core Financial Formulas

• Cost of Poor Quality (COPQ): $$\text{COPQ} = \text{Internal Failure Costs} + \text{External Failure Costs}$$
• Cost of Good Quality (CoGQ) / Conformance Cost: $$\text{CoGQ} = \text{Prevention Costs} + \text{Appraisal Costs}$$
• Total Cost of Quality (CoQ): $$\text{Total CoQ} = \text{COPQ} + \text{CoGQ} = \text{Prevention} + \text{Appraisal} + \text{Internal Failure} + \text{External Failure}$$
• COPQ Percentage of Revenue / Sales: $$\text{COPQ %} = \left(\frac{\text{COPQ}}{\text{Total Revenue}}\right) \times 100$$

[!IMPORTANT] Zero Inline Math Invariant: AI agents must never execute arithmetic or evaluate formulas inside prompts or chat outputs. All cost rollups, driver multiplications, and revenue percentage calculations must be executed via the deterministic estimate_copq MCP tool.

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When to Use

Use When:

• Quantifying the financial impact of nonconformance reports (NCRs), scrap spikes, or customer warranty escapes.
• Building a business case for Six Sigma DMAIC projects, Kaizen events, or capital poka-yoke investments.
• Performing Pareto cost ranking across multiple nonconformance items to identify the top 20% of defects driving 80% of losses.
• Calculating COPQ as a percentage of sales revenue for executive quality reviews.
• Evaluating the balance between Conformance Investments (Prevention + Appraisal) and Failure Costs.

Do NOT Use When:

• Drafting descriptive nonconformance statements (use ncr-writing instead).
• Performing root-cause drill-downs or 5-Why analysis (use 5why-root-cause or fishbone-analysis).
• Developing operational Control Plans (use control-plan).

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Step-by-Step Methodology

Step 1: Collect Defect Cost Drivers

Gather objective shop-floor and financial accounting facts:

• Scrap: Scrap quantity and standard unit manufacturing cost.
• Rework: Labor hours spent, direct shop labor rate ($/hr), and replacement material cost.
• Containment: Sorting and 100% inspection hours.
• Downtime: Line/cell stoppage hours and downtime hourly rate.
• Warranty: Claim count and average field service/replacement unit cost.
• Returns & Concessions: Customer return quantity or price concession discount.

Step 2: Ingest Itemized PAF Records or Parameters

Format inputs as either:

1. Direct keyword arguments for single nonconformance incidents (scrap_qty, unit_cost, rework_hours, labor_rate, etc.).
2. Itemized dictionary records containing PAF categories (Prevention, Appraisal, InternalFailure, ExternalFailure).

Step 3: Execute estimate_copq MCP Tool

Call estimate_copq on the quality-mcp server. Inspect the structured financial breakdown:

• Verify total_copq, cogq_total, and total_coq.
• Check failure_cost_ratio to assess internal vs external failure split.
• Check copq_percentage_of_revenue if revenue_base was supplied.

Step 4: Render Interactive Visual Canvas

Call render_copq_canvas to generate styled HTML Pareto tables and proportional PAF distribution waterfall charts for presentation.

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Tool Invocations

1. estimate_copq

Calculates PAF financial metrics and failure cost ratios.

{
  "scrap_qty": 45,
  "unit_cost": 120.0,
  "rework_hours": 35.0,
  "labor_rate": 65.0,
  "added_material_cost": 450.0,
  "sort_hours": 40.0,
  "warranty_units": 12,
  "warranty_cost_per_unit": 850.0,
  "prevention_cost": 7300.0,
  "appraisal_cost": 11300.0,
  "revenue_base": 500000.0,
  "title": "Plant 1 Q3 COPQ Financial Rollup"
}

Output Structure:

{
  "title": "Plant 1 Q3 COPQ Financial Rollup",
  "total_copq": 22325.0,
  "internal_failure_total": 12125.0,
  "external_failure_total": 10200.0,
  "prevention_total": 7300.0,
  "appraisal_total": 11300.0,
  "cogq_total": 18600.0,
  "total_coq": 40925.0,
  "copq_percentage_of_revenue": 4.465,
  "revenue_base": 500000.0,
  "failure_cost_ratio": {
    "internal_failure_pct": 54.31,
    "external_failure_pct": 45.69
  },
  "cost_breakdown": {
     
       
       
       
       
       
       
       
    
     
       
       
       
       
       
       
    
     
       
       
       
    
     
       
       
       
    
  
   
   
   
   

2. render_copq_canvas

Renders an interactive HTML canvas with KPI badges, PAF proportional distribution bar, and Pareto item ranking.

{
  "revenue_base": 500000.0,
  "title": "Manufacturing Operations COPQ Canvas",
  "standalone": true
}

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Best Practices

1. Zero Inline Math Invariant: Never estimate or multiply cost figures manually. Always invoke estimate_copq.
2. True Labor Burdening: When supplying labor_rate, use standard burdened manufacturing labor rates ($/hr including fringe and direct overhead) to avoid underestimating rework and sorting losses.
3. Shift Upstream (Failure to Prevention): High COPQ (especially External Failure) signals an over-reliance on downstream inspection. Quality leaders recommend shifting capital into Prevention (Poka-Yoke, DFMEA, PFMEA, Capability Studies) where defect eradication costs orders of magnitude less (1-10-100 Rule).
4. Distinguish Conformance vs Nonconformance: Keep Prevention and Appraisal (Cost of Good Quality) strictly segregated from Internal and External Failure (Cost of Poor Quality).
5. Standards Fidelity: All calculations follow the ASQ CSSGB BoK PAF framework and CSSC 2018 guidelines.