instrumentation error

An error is a deviation from the expected result.
Human Error: Often due to improper use of equipment, leading to incorrect readings.
Example of Human Error: Not following the correct procedure to measure something, resulting in inaccurate results.

Example 1: Measuring with a Ruler
- Professor Messer incorrectly measures a piece of wood.
- Common mistakes:
  1. Measuring from the wrong end (100 mm instead of 0 mm).
  2. Incorrect reported length (95.4 mm).
  3. Using wrong units (should be centimeters instead of millimeters).
  4. Wobbling while measuring handheld objects affects accuracy.
  5. Distance between the object and the ruler introduces error.
  6. The object's end is not aligned with the ruler.
  7. Parallax error: observer's eye is not perfectly aligned with the measurement.
  8. Viewing from the wrong side of the ruler creates a distorted reading.

Example 2: Best Eye Position to Avoid Errors
- Ideal eye position ensures accurate reading of measurements.
- Gaps can introduce errors; aim for minimal gap.

Anomalous readings are odd, inconsistent measurements.
Best identified through graphing data to spot outliers.
- Graph Example: Identify which data point is likely anomalous, indicating the need for remeasurement.

Gross Errors:
- Caused by human mistakes; often unquantifiable.
- Minimization through careful reading and recording.
Systematic Errors:
- Caused by instrument flaws or environmental effects.
- Types:
  - Instrumental Errors: Arise from measuring instrument design flaws.
  - Environmental Errors: Result from changes in surrounding conditions like temperature or pressure.
  - Observational Errors: Include parallax errors caused by improper viewing angles.
Random Errors:
- Caused by unpredictable variations in measurement.
- Can be reduced by averaging multiple readings.

Characteristics: Systematic errors consistently skew results in one direction (either positive or negative), introducing bias into measurements.
Example: Using a miscalibrated ruler yields inaccuracies across all measurements.

A specific type of systematic error.
Solutions for Zero Error in Instruments:
- Regular calibration to ensure accurate measurements.
- Adjust mechanisms if zero error is identified.

Each instance of random errors varies across measurements and can be caused by external factors.
Increased measurement frequency and averaging reduce these errors.

When measurement results deviate from the true value by a consistent amount.
Example: A scale consistently reading 0.2 cm too high leads to systematic discrepancies.

Given true value = 122 mm and expected value = 120 mm.
- Absolute error = 122 mm - 120 mm = 2 mm.
- Relative error =

[ \frac{2}{120} = 0.017 ]

The reported acceptable error ranges:
- 5-10% for consumer purposes.
- 1% for engineering purposes.
- 0.1% for scientific applications.

Reports the nominal value with a tolerance (±N). For example, a nominal value of 120 mm ±1 mm indicates a range between 119 mm and 121 mm.

Accuracy: Closeness of a measurement to the true value.
Resolution: Smallest observable change in a variable by an instrument.
Precision: Consistency across multiple measurements.
Sensitivity: Instrument's response ratio to change.
Expected value — the design value or the most probable value
that expect to obtain.
Error - the deviation of the true value from the desired value.

Human errors often result from poor technique which can lead to parallax errors.
Anomalous results can be graphed for identification.
Random errors may be averaged to reduce their impact, whereas systematic errors lead to consistent inaccuracies.