gage-rr-analyzer

name	gage-rr-analyzer
description	Measurement System Analysis skill for Gage R&R studies with variance component analysis.
allowed-tools	Bash(*) Read Write Edit Glob Grep WebFetch
metadata	{"author":"babysitter-sdk","version":"1.0.0","category":"quality-engineering","backlog-id":"SK-IE-016"}
graph	{"domains":["domain:industrial-engineering"],"skillAreas":["skill-area:statistical-analysis","skill-area:organizational-design","skill-area:data-analysis"],"roles":["role:operations-analyst","role:research-engineer"]}

gage-rr-analyzer

You are gage-rr-analyzer - a specialized skill for conducting Measurement System Analysis (MSA) and Gage R&R studies.

Overview

This skill enables AI-powered MSA including:

• Gage R&R study design (crossed, nested)
• ANOVA variance decomposition
• Repeatability (equipment variation) calculation
• Reproducibility (appraiser variation) calculation
• Part-to-part variation analysis
• %GRR and %Contribution metrics
• Number of distinct categories (ndc)
• Measurement decision analysis
• Acceptance criteria evaluation (< 10%, 10-30%, > 30%)

Prerequisites

• Python 3.8+ with numpy, scipy, pandas
• Measurement data from designed study
• Understanding of MSA principles

Capabilities

1. Gage R&R Study Design

from dataclasses import dataclass
from typing import List
import numpy as np

@dataclass
class GageRRStudyDesign:
    """
    Design parameters for Gage R&R study
    """
    num_parts: int = 10  # Typically 10
    num_operators: int = 3  # Typically 2-3
    num_trials: int = 3  # Typically 2-3 measurements per part per operator

    def total_measurements(self):
        return self.num_parts * self.num_operators * self.num_trials

    def randomized_run_order(self):
        """Generate randomized measurement order"""
        runs = []
        for part in range(1, self.num_parts + 1):
            for operator in range(1, self.num_operators + 1):
                for trial in range(1, self.num_trials + 1):
                    runs.append({
                        : part,
                        : operator,
                        : trial
                    })

        np.random.shuffle(runs)
         runs

 ():
    
    runs = design.randomized_run_order()

    worksheet = {
        : {
            : ,
            : ,
            : ,
            : ,
            : ,
            : 
        },
        : [  i  (, design.num_operators + )],
        : [  i  (, design.num_parts + )],
        : runs,
        : []
    }

     worksheet

2. ANOVA Method (Crossed Study)

import pandas as pd
from scipy import stats

def gage_rr_anova(data, parts_col='Part', operators_col='Operator', measurement_col='Measurement'):
    """
    Gage R&R analysis using ANOVA method

    data: DataFrame with Part, Operator, and Measurement columns
    """
    df = pd.DataFrame(data)

    # Get design parameters
    n_parts = df[parts_col].nunique()
    n_operators = df[operators_col].nunique()
    n_trials = len(df) // (n_parts * n_operators)

    # Calculate means
    grand_mean = df[measurement_col].mean()
    part_means = df.groupby(parts_col)[measurement_col].mean()
    operator_means = df.groupby(operators_col)[measurement_col].mean()
    cell_means = df.groupby([parts_col, operators_col])[measurement_col].mean()

    # Sum of Squares
    SS_total = ((df[measurement_col] - grand_mean) ** 2).sum()

    SS_part = n_operators * n_trials * ((part_means - grand_mean) ** 2).sum()

    SS_operator = n_parts * n_trials * ((operator_means - grand_mean) ** 2).sum()

    # SS Interaction
    SS_cell = n_trials * ((cell_means - grand_mean) ** 2).sum()
    SS_interaction = SS_cell - SS_part - SS_operator

    # SS Error (repeatability)
    SS_error = SS_total - SS_part - SS_operator - SS_interaction

    # Degrees of freedom
    df_part = n_parts - 1
    df_operator = n_operators - 1
    df_interaction = df_part * df_operator
    df_error = n_parts * n_operators * (n_trials - 1)
    df_total = len(df) - 1

    # Mean Squares
    MS_part = SS_part / df_part
    MS_operator = SS_operator / df_operator
    MS_interaction = SS_interaction / df_interaction if df_interaction >   
    MS_error = SS_error / df_error

    
    F_part = MS_part / MS_interaction  MS_interaction >   MS_part / MS_error
    F_operator = MS_operator / MS_interaction  MS_interaction >   MS_operator / MS_error
    F_interaction = MS_interaction / MS_error  MS_interaction >   

    
    p_part =  - stats.f.cdf(F_part, df_part, df_interaction  MS_interaction >   df_error)
    p_operator =  - stats.f.cdf(F_operator, df_operator, df_interaction  MS_interaction >   df_error)
    p_interaction =  - stats.f.cdf(F_interaction, df_interaction, df_error)  F_interaction >   

    anova_table = {
        : {: SS_part, : df_part, : MS_part, : F_part, : p_part},
        : {: SS_operator, : df_operator, : MS_operator, : F_operator, : p_operator},
        : {: SS_interaction, : df_interaction, : MS_interaction, : F_interaction, : p_interaction},
        : {: SS_error, : df_error, : MS_error},
        : {: SS_total, : df_total}
    }

     anova_table, {
        : n_parts,
        : n_operators,
        : n_trials,
        : grand_mean
    }

3. Variance Components Calculation

def calculate_variance_components(anova_table, design_params):
    """
    Extract variance components from ANOVA
    """
    n = design_params['n_trials']
    k = design_params['n_operators']
    p = design_params['n_parts']

    MS_part = anova_table['Part']['MS']
    MS_operator = anova_table['Operator']['MS']
    MS_interaction = anova_table['Part*Operator']['MS']
    MS_error = anova_table['Repeatability']['MS']

    # Variance components
    var_repeatability = MS_error

    # Check if interaction is significant (p < 0.25 typically)
    if anova_table['Part*Operator']['p'] < 0.25:
        var_interaction = max(0, (MS_interaction - MS_error) / n)
        var_operator = max(0, (MS_operator - MS_interaction) / (n * p))
    else:
        # Pool interaction with error
        var_interaction = 0
        pooled_ms = (anova_table['Part*Operator']['SS'] + anova_table['Repeatability']['SS']) / \
                    (anova_table['Part*Operator']['df'] + anova_table['Repeatability']['df'])
        var_operator = max(0, (MS_operator - pooled_ms) / (n * p))
        var_repeatability = pooled_ms

    var_part = max(0, (MS_part - MS_operator) / (n * k)) if MS_part > MS_operator else \
               (, (MS_part - MS_error) / (n * k))

    
    var_reproducibility = var_operator + var_interaction

    
    var_grr = var_repeatability + var_reproducibility

    
    var_total = var_grr + var_part

     {
        : var_repeatability,
        : var_reproducibility,
        : var_operator,
        : var_interaction,
        : var_grr,
        : var_part,
        : var_total
    }

4. %GRR and Metrics Calculation

def calculate_grr_metrics(variance_components, tolerance=None):
    """
    Calculate Gage R&R metrics

    tolerance: specification range (USL - LSL) for %Tolerance calculation
    """
    vc = variance_components

    # Standard deviations (6*sigma for 99.73% spread)
    std_repeatability = np.sqrt(vc['repeatability'])
    std_reproducibility = np.sqrt(vc['reproducibility'])
    std_grr = np.sqrt(vc['gage_rr'])
    std_part = np.sqrt(vc['part_to_part'])
    std_total = np.sqrt(vc['total'])

    # Study variation (6 * sigma)
    sv_repeatability = 6 * std_repeatability
    sv_reproducibility = 6 * std_reproducibility
    sv_grr = 6 * std_grr
    sv_part = 6 * std_part
    sv_total = 6 * std_total

    metrics = {
        "study_variation": {
            "repeatability": sv_repeatability,
            "reproducibility": sv_reproducibility,
            "gage_rr": sv_grr,
            "part_to_part": sv_part,
            "total": sv_total
        },
        "percent_contribution": {
            "repeatability": vc['repeatability'] / vc['total'] * 100,
            "reproducibility": vc['reproducibility'] / vc['total'] * 100,
            "gage_rr": vc['gage_rr'] / vc['total'] * 100,
            "part_to_part": vc['part_to_part'] / vc['total'] * 100
        },
        : {
            : sv_repeatability / sv_total * ,
            : sv_reproducibility / sv_total * ,
            : sv_grr / sv_total * ,
            : sv_part / sv_total * 
        }
    }

    
     tolerance:
        metrics[] = {
            : sv_repeatability / tolerance * ,
            : sv_reproducibility / tolerance * ,
            : sv_grr / tolerance * 
        }

    
    ndc = ( * (std_part / std_grr))  std_grr >   np.inf
    metrics[] = (, ndc)

     metrics

5. Acceptance Criteria Evaluation

def evaluate_measurement_system(metrics):
    """
    Evaluate measurement system against acceptance criteria
    """
    grr_pct_sv = metrics['percent_study_variation']['gage_rr']
    grr_pct_tol = metrics.get('percent_tolerance', {}).get('gage_rr', grr_pct_sv)
    ndc = metrics['ndc']

    evaluation = {
        "grr_percent": grr_pct_sv,
        "ndc": ndc,
        "assessment": "",
        "recommendations": []
    }

    # AIAG guidelines
    if grr_pct_sv < 10:
        evaluation["assessment"] = "ACCEPTABLE"
        evaluation["recommendations"].append("Measurement system acceptable for use")
    elif grr_pct_sv < 30:
        evaluation["assessment"] = "MARGINAL"
        evaluation["recommendations"].append("May be acceptable depending on application")
        evaluation["recommendations"].append("Consider improvement opportunities")
    else:
        evaluation["assessment"] = "UNACCEPTABLE"
        evaluation["recommendations"].append("Measurement system requires improvement")
        evaluation["recommendations"].append("Do not use for process control until improved")

    # NDC evaluation
    if ndc < 2:
        evaluation["ndc_assessment"] = "Cannot distinguish between parts"
        evaluation[].append()
     ndc < :
        evaluation[] = 
        evaluation[].append()
    :
        evaluation[] = 

    
    pct_repeat = metrics[][]
    pct_reprod = metrics[][]

     pct_repeat > pct_reprod * :
        evaluation[] = 
        evaluation[].append()
     pct_reprod > pct_repeat * :
        evaluation[] = 
        evaluation[].append()
    :
        evaluation[] = 
        evaluation[].append()

     evaluation

6. Gage R&R Report Generation

def generate_grr_report(data, parts_col, operators_col, measurement_col,
                        tolerance=None, characteristic_name=""):
    """
    Generate complete Gage R&R report
    """
    # Run analysis
    anova_table, design_params = gage_rr_anova(data, parts_col, operators_col, measurement_col)
    variance_components = calculate_variance_components(anova_table, design_params)
    metrics = calculate_grr_metrics(variance_components, tolerance)
    evaluation = evaluate_measurement_system(metrics)

    report = {
        "study_info": {
            "characteristic": characteristic_name,
            "tolerance": tolerance,
            "parts": design_params['n_parts'],
            "operators": design_params['n_operators'],
            "trials": design_params['n_trials'],
            "total_measurements": len(data)
        },
        "anova_table": anova_table,
        "variance_components": variance_components,
        "metrics": metrics,
        "evaluation": evaluation,
        "conclusion": {
            "grr_result": evaluation['assessment'],
            "grr_percent": round(metrics['percent_study_variation']['gage_rr'], 2),
            "ndc": metrics['ndc'],
            "primary_contributor": evaluation['primary_issue']
        }
    }

    return report

Process Integration

This skill integrates with the following processes:

• statistical-process-control-implementation.js
• design-of-experiments-execution.js

Output Format

{
  "study_info": {
    "characteristic": "Diameter",
    "tolerance": 0.05,
    "parts": 10,
    "operators": 3,
    "trials": 3
  },
  "metrics": {
    "percent_study_variation": {
      "repeatability": 8.5,
      "reproducibility": 12.3,
      "gage_rr": 15.2,
      "part_to_part": 98.8
    },
    "ndc": 9
  },
  "evaluation": {
    "assessment": 
     
  
   
    
    
  

Best Practices

1. Proper study design - Minimum 10 parts, 3 operators, 2-3 trials
2. Representative parts - Select parts spanning expected range
3. Blind measurements - Operators shouldn't know which part
4. Randomize order - Prevent systematic bias
5. Same conditions - Control environmental factors
6. Trained operators - Ensure consistent technique

Constraints

• Use parts representing production range
• Document measurement procedure
• Report all variance components
• Follow AIAG MSA guidelines