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Calcimator

Control Chart Calculator

Calculate Upper Control Limit (UCL), Lower Control Limit (LCL), and center line for X-bar, R, and S control charts using process statistics and sample size.

Inputs

Results

Upper Control Limit (UCL)

52.68

Center Line (CL)

50

Lower Control Limit (LCL)

47.32

Chart TypeX-bar Chart
+2σ Zone Boundary51.79
-2σ Zone Boundary48.21
+1σ Zone Boundary50.89
-1σ Zone Boundary49.11
Control Range (UCL - LCL)5.37
How to Use This Calculator
  1. Enter Process Mean (X̄), Process Std Dev (σ), and Sample Size (n).
  2. Set Chart Type, X-bar Chart, and R Chart (Range).
  3. Adjust S Chart (Std Dev) as needed.
  4. Review Upper Control Limit (UCL), Center Line (CL), and Lower Control Limit (LCL).
  5. Use Chart Type and +2σ Zone Boundary to inform your decision.

How the result changes with Process Mean (X̄)

Process Mean (X̄)Upper Control Limit (UCL)Center Line (CL)Lower Control Limit (LCL)
-800,000-799,997.32-800,000-800,002.68
-300,000-299,997.32-300,000-300,002.68
300,000300,002.68300,000299,997.32
800,000800,002.68800,000799,997.32

What each input means

Process Mean (X̄)
The overall process mean — average of all subgroup means.
Process Std Dev (σ)
The process standard deviation estimated from historical data.
Sample Size (n)
Number of observations per subgroup. Typically 4-6 for manufacturing processes.
Chart Type
X-bar monitors process mean shifts. R chart monitors variability (range). S chart monitors variability (std dev).

How this is calculated

Worked example, using the default values

  1. Identify Input Parameters
    4 parameters
    Process Mean (X̄) = 50, Process Std Dev (σ) = 2, Sample Size (n) = 5, Chart Type = 1 = 4 input(s) provided
  2. Calculate Upper Control Limit
    Upper Control Limit
    52.6842 = 52.6842
  3. Calculate Center Line
    Center Line
    50 = 50
  4. Calculate Lower Control Limit
    Lower Control Limit
    47.3158 = 47.3158
  5. Calculate Chart Type
    X-bar Chart = X-bar Chart
  6. Calculate +2σ Zone Boundary
    +2σ Zone Boundary
    51.7895 = 51.7895

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