Statistical Process Control Tutorial: Control Chart for Xbar

Introduction

• Objective: Construct an Xbar chart from process data and determine if the process is in statistical control.
• Components of a Control Chart:
  • Centerline: X double bar (mean of the sample means)
  • Lower Control Limit (LCL)
  • Upper Control Limit (UCL)

Control Limit Formulas

• Standard Deviation Known: Use specified formula
• Using Range:
  • UCL = X double bar + A2 * R bar
  • LCL = X double bar - A2 * R bar
  • R bar: Average of the sample ranges
  • A2: Found on the control chart factors table

Process Data

• Sample Size: 5
• Collection Period: 10 days
• Objective: Determine if the process mean is in statistical control

Calculations

1. Sample Ranges and Means:
   • Range Formula: Largest minus smallest
   • Example: Day 1 range = 509 - 496 = 13
   • Mean Formula: Sum of values / 5
   • Example: Day 1 mean = 502
2. Calculate R bar and X double bar:
   • R bar:
     • Sum of ranges = 231
     • R bar = 231 / 10 = 23.1
   • X double bar:
     • Sum of sample means = 4978
     • X double bar = 4978 / 10 = 497.8
3. Determine A2:
   • Use Control Limits Factor table
   • For sample size 5, A2 = 0.577
4. Control Limits:
   • UCL: 497.8 + 0.577 * 23.1 = 511.1
   • LCL: 497.8 - 0.577 * 23.1 = 484.5

Xbar Chart Analysis

• Construct the Chart:
  • Plot sample points
  • Draw control limits
  • Complete run chart
• Findings:
  • Sample mean for Day 5 is below LCL
  • Indicates process mean is out of control
• Recommendation:
  • Investigate Day 5 for special cause of variation
  • Implement corrective actions

Conclusion

• Xbar chart completed and analyzed.
• Process found not in statistical control due to Day 5 anomaly.
• Further investigation and corrective measures needed.

Closing

• Thank you for watching.