Statistical Process Control (SPC) Series: Constructing an R-Chart

Introduction to Control Charts

• Purpose: Monitor process changes over time to assess stability or variability
• Types of Variations:
  • Random/Natural Variations: Present in every system
  • Assignable Variations: Special causes needing identification and elimination
• Control Chart Components:
  • Lower Control Limit (LCL)
  • Center Line (CL)
  • Upper Control Limit (UCL)

Process Control Evaluation

• A process is in control if:
  1. No sample points are outside the control limits
  2. Sample points are randomly distributed (no trends or unusual patterns)
• Out of control examples:
  • Sample points outside control limits
  • Positive trends or increasing variation

Types of Control Charts Discussed

• R-Chart
• X-bar Chart
• P-Chart
• C-Chart
• R & X-bar Charts: Monitor quantitative variables (variability and central tendency)
• P & C Charts: Monitor qualitative variables (attributes or characteristics)

Constructing an R-Chart

• Objective: Determine if process variability is in control using sample data
• Data Example: Weights of a snack pack (500 grams), samples of size 5 over 10 days
• Range Calculation:
  • Range = Largest - Smallest value in a sample
  • Example: First sample range is 13 (509-496), second is 29 (521-492)
• Centerline (R-bar) Calculation:
  • Sum of ranges = 231
  • Mean of ranges (R-bar) = 231/10 = 23.1

Control Limits Calculation

• Formulas:
  • LCL = D3 * R-bar
  • UCL = D4 * R-bar
• Control Limit Constants:
  • From table: Sample size 5, D3 = 0, D4 = 2.114
  • LCL = 0 * 23.1 = 0
  • UCL = 2.114 * 23.1 = 48.83

Drawing the R-Chart

• Plot control limits and sample ranges
• Connect sample points with lines
• Conclusion: Process is within statistical control if points are random and within limits

Additional Resources

• Links for drawing control charts in Excel are available in the video description