Calibration Interval and Measurement Uncertainty
A digital micrometer is used to measure the diameter of a precision shaft with a tolerance of ±0.01 mm. The micrometer has a resolution of 0.001 mm and a calibration certificate that states the expanded uncertainty (k=2) is ±0.002 mm. The calibration was performed 10 months ago with a recommended interval of 12 months. The inspector measures a shaft and obtains a reading of 25.003 mm. The specification limits are 25.000 ± 0.010 mm. The inspector also has a gauge block set that is used as a reference standard; the gauge blocks have a calibration uncertainty of ±0.001 mm (k=2) and are calibrated every 2 years. The inspector must decide if the shaft is acceptable, considering measurement uncertainty, and whether the micrometer is due for recalibration.
1. Determine if the shaft is acceptable, taking into account measurement uncertainty. Show the decision rule and calculations.
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The specification limits are 24.990 mm to 25.010 mm. The measured value is 25.003 mm. The measurement uncertainty (k=2) is ±0.002 mm. To make a decision with uncertainty, we can use a simple acceptance rule: if the measured value plus or minus the expanded uncertainty falls entirely within the specification limits, the item is conforming. Here, the upper bound of the measurement is 25.003 + 0.002 = 25.005 mm, which is below the upper limit of 25.010 mm. The lower bound is 25.003 - 0.002 = 25.001 mm, which is above the lower limit of 24.990 mm. Therefore, the shaft is acceptable because the entire uncertainty interval is within the specification limits. Alternatively, if using a guard band, we would compare the measured value to the specification limits reduced by the uncertainty; but in this case, it is clearly within. So the shaft is acceptable.
2. Evaluate the calibration status of the micrometer and the gauge blocks. What actions are required?
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The micrometer was calibrated 10 months ago with a 12-month interval, so it is still within its calibration period. No immediate recalibration is required, but the inspector should monitor its performance and consider recalibration if there is any suspicion of drift. The gauge blocks are calibrated every 2 years; the inspector should check the calibration date to ensure they are within their interval. If they are, they can be used as reference standards. However, the inspector should also consider the uncertainty of the gauge blocks when using them for calibration or verification. The combined uncertainty of the micrometer and gauge blocks might affect the measurement decision if the margin were tighter. In this case, the margin is sufficient. The inspector should document the calibration status and ensure that all equipment is within its calibration interval before use.