Implementing Nelson Rules 2 and 3 for Statistical Process Control (SPC) Using Python Data Function in Spotfire

Keywords:
Nelson Rules, Statistical Process Control, SPC, Rule 2, Rule 3, Python, Spotfire, Dashboard, Violation Analysis, Control Limits.

Introduction: This article explains how to implement Nelson Rules 2 and 3 for statistical process control (SPC) using Python and visualize the results in a Spotfire dashboard. The solution helps identify violations of control limits in datasets, enabling better process monitoring and quality control.

Overview: Nelson Rules are a set of eight rules used in SPC to detect out-of-control processes. This article focuses on:

• Rule 2: Two consecutive points outside the control limits (UCL or LCL).
• Rule 3: Four out of five consecutive points beyond one standard deviation from the mean.

The solution uses Python to calculate violations and Spotfire to visualize the results with color-coded tables and summary graphs.

Solution:

1. 1. Python Script for Nelson Rules Analysis

   Code:

   import numpy as np
   import pandas as pd
   
   def check_nelson_rules(cqa, ucl, lcl):
       """
       Check Nelson Rules 2 and 3, returning violation flags.
       """
       cqa = np.array(cqa)
       rule2 = np.zeros_like(cqa, dtype=bool)
       rule3 = np.zeros_like(cqa, dtype=bool)
       
       # Rule 2: Two consecutive points outside control limits
       for i in range(len(cqa) - 1):
           if (cqa[i]  ucl and cqa[i+1]  ucl) or (cqa[i] <lcl): rule2[i]="True" rule2[i+1]="True" #="#" rule="Rule" 3:="3:" four="Four" out="out" of="of" five="five" consecutive="consecutive" points="points" beyond="beyond" limits="limits" for="for" i="i" in="in" range(len(cqa)="range(len(cqa)" -="-" 4):="4):" window="cqa[i:i+5]" above="window"> ucl
           below = window = 4:
               rule3[i:i+5] |= above
           if np.sum(below) = 4:
               rule3[i:i+5] |= below
       return rule2, rule3
   
   # Example usage
   data = {'Column1': [10,12,14,13,15,18,20,25,30,28],
           'Column2': [25,26,24,23,22,20,19,18,17,16]}
   df = pd.DataFrame(data)
   
   UCL = 24
   LCL = 8
   
   # Create violation flags for each column
   combined_df = df.copy()
   for col in df.columns:
       r2, r3 = check_nelson_rules(df[col].values, UCL, LCL)
       combined_df[f"{col}_N2"] = r2  # Rule 2 flags
       combined_df[f"{col}_N3"] = r3  # Rule 3 flags
   
   # Output the combined table
   Output = combined_df
      

   Output:

   • A single table with original data and appended violation flags (_N2 for Rule 2 and _N3 for Rule 3).
   • Flags are True if a violation occurs and False otherwise.

2. 2. Spotfire Dashboard

   Features:

   • Table Visualization: Violating cells are color-coded:
     • Red for Rule 2 violations.
     • Gold for Rule 3 violations.
   • Graph Table: Summarizes the number of violations per column.

   Attached Dashboard: Sample_Nelson_Rules_Analysis.dxp

Nelson Rules Concept:

• Rule 2: Detects shifts in the process mean by identifying two consecutive points outside the control limits.
• Rule 3: Detects trends by identifying four out of five consecutive points beyond one standard deviation from the mean.

References:

• Nelson Rules Documentation
• Spotfire Documentation

Conclusion: This solution provides an easy way to implement Nelson Rules 2 and 3 using Python and visualize the results in Spotfire. The attached dashboard demonstrates how to identify and analyze violations effectively.