🔹 What is a Monte Carlo Simulation?
A Monte Carlo Simulation is a way of using random numbers and repeated trials to predict how a process or measurement will behave in the real world.
Instead of relying on just a handful of measurements, the simulation generates thousands of possible outcomes based on the variation we see in your data.
This lets us:
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Visualize variation as a bell curve.
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Estimate tolerances — how wide the natural spread is.
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Predict yield — what percent of parts are likely to fall within spec limits.
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Test “what if” scenarios — e.g., what happens if we tighten specs or reduce variation.
🔹 Why it’s Useful
Every manufacturing process has variation. A Monte Carlo Simulation shows you the probability of success or failure instead of a single “pass/fail” number. This helps you:
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Set realistic tolerance limits.
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Understand risk of rejects.
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Make data-driven decisions to improve quality.
🔹 Example: Inside Diameter Results
From your 999-part dataset:
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Mean Inside Diameter = 11.924
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Standard Deviation = 0.048
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Using ±2σ tolerance, 95% of parts are expected within ±0.096 of the mean.
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With your chosen spec window (11.875 – 12.000), the simulation shows a yield of ~79%.
👉 In plain terms: about 8 out of 10 parts meet spec, and 2 out of 10 fall outside.
✅ So, in just a few clicks, the Monte Carlo Simulation lets you see whether your process can consistently hit your targets — or if adjustments are needed.
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Monte Carlo Tolerance Simulation
🔹 Instructions for Obtaining Monte Carlo Results
1. Prepare Your Data
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Create a CSV file with two columns:
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Column 1: Inside Diameter values
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Column 2: Cross Section values
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Include up to 1000 rows of measurements.
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Example:
2. Upload Your File
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On the Monte Carlo Simulation page, click Choose File and select your CSV file.
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The system will automatically check your data for:
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Non-numeric entries
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Values outside allowed ranges
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Outliers (if you select the “Remove Outliers” option).
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3. Select Settings
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Tolerance Method: Choose how the achievable tolerance is calculated.
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±2σ (95%) — tighter band, captures most values
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±3σ (99.7%) — wider band, standard Six Sigma method
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MAD (±3) — based on Median Absolute Deviation, less affected by outliers
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Spec Limits: Enter your lower and upper spec limits for:
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Inside Diameter (e.g., 11.875 – 12.000)
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Cross Section (e.g., 0.115 – 0.121)
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4. Run the Simulation
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Click Run Simulation.
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The system will generate 10,000 random samples for each dimension based on your data.
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It will calculate:
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Mean (average value)
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Standard Deviation (variation)
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Achievable Tolerance (spread of values based on chosen method)
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Yield % (how many parts fall within your spec limits)
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5. Review Results
You will see:
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Summary table for Inside Diameter and Cross Section
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Data Cleaning report (how many rows were valid after cleaning)
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Bell Curve charts showing the distribution of results for both dimensions
6. Start Over (Optional)
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Click Clear to reset the form, upload a new dataset, and run again.
👉 These steps ensure you can consistently obtain accurate tolerance, control limits, and yield predictions from your real-world measurement data.