🔹 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:

• Visualize variation as a bell curve.

• Estimate tolerances — how wide the natural spread is.

• Predict yield — what percent of parts are likely to fall within spec limits.

• 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:

• Set realistic tolerance limits.

• Understand risk of rejects.

• Make data-driven decisions to improve quality.

🔹 Example: Inside Diameter Results

From your 999-part dataset:

• Mean Inside Diameter = 11.924

• Standard Deviation = 0.048

• Using ±2σ tolerance, 95% of parts are expected within ±0.096 of the mean.

• 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.

🔹 Instructions for Obtaining Monte Carlo Results

1. Prepare Your Data

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• Create a CSV file with two columns:

  • Column 1: Inside Diameter values

  • Column 2: Cross Section values

• Include up to 1000 rows of measurements.

• Example:

   

  11.9520,0.1182

  11.9350,0.1169

  11.8991,0.1195

2. Upload Your File

• On the Monte Carlo Simulation page, click Choose File and select your CSV file.

• The system will automatically check your data for:

  • Non-numeric entries

  • Values outside allowed ranges

  • Outliers (if you select the “Remove Outliers” option).

3. Select Settings

• Tolerance Method: Choose how the achievable tolerance is calculated.

  • ±2σ (95%) — tighter band, captures most values

  • ±3σ (99.7%) — wider band, standard Six Sigma method

  • MAD (±3) — based on Median Absolute Deviation, less affected by outliers

• Spec Limits: Enter your lower and upper spec limits for:

  • Inside Diameter (e.g., 11.875 – 12.000)

  • Cross Section (e.g., 0.115 – 0.121)

4. Run the Simulation

• Click Run Simulation.

• The system will generate 10,000 random samples for each dimension based on your data.

• It will calculate:

  • Mean (average value)

  • Standard Deviation (variation)

  • Achievable Tolerance (spread of values based on chosen method)

  • Yield % (how many parts fall within your spec limits)

5. Review Results

You will see:

• Summary table for Inside Diameter and Cross Section

• Data Cleaning report (how many rows were valid after cleaning)

• Bell Curve charts showing the distribution of results for both dimensions

6. Start Over (Optional)

• 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.