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Uncertainty: Overview

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In analytical chemistry, we often perform repetitive measurements to detect and minimize inaccuracies caused by both determinate and indeterminate errors. Despite the cares we take, the presence of random errors means that repeated measurements almost never have exactly the same magnitude. The collective difference between these measurements - observed values - and the estimated or expected value is called uncertainty. Uncertainty is conventionally written after the estimated or expected value.

Uncertainty: Confidence Intervals

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The confidence interval is the range of values around the mean that contains the true mean. It is expressed as a probability percentage. The interpretation of a 95% confidence interval, for instance, is that the statistician is 95% confident that the true mean falls within the interval. The upper and lower limits of this range are known as confidence limits. The confidence limits for the true mean are estimated from the sample's mean, the standard deviation, and the statistical factor...

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Propagation of Uncertainty from Random Error

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An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...

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The atomic mass of an element varies due to the relative ratio of its isotopes. A sample's relative proportion of oxygen isotopes influences its average atomic mass. For instance, if we were to measure the atomic mass of oxygen from a sample, the mass would be a weighted average of the isotopic masses of oxygen in that sample. Since a single sample is not likely to perfectly reflect the true atomic mass of oxygen for all the molecules of oxygen on Earth, the mass we obtain from this...

The Uncertainty Principle

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Werner Heisenberg considered the limits of how accurately one can measure properties of an electron or other microscopic particles. He determined that there is a fundamental limit to how accurately one can measure both a particle’s position and its momentum simultaneously. The more accurate the measurement of the momentum of a particle is known, the less accurate the position at that time is known and vice versa. This is what is now called the Heisenberg uncertainty principle. He...

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Rendezvous Under Temporal Uncertainty.

Colleen E Patton¹, Christopher D Wickens¹, Kayla M Noble¹

¹Colorado State University, Fort Collins, CO, USA.

|July 8, 2021

Summary

This summary is machine-generated.

Controlling a ship to meet another vessel is challenging, with a tendency to arrive late. Unpredictable movement delays significantly impact rendezvous success, especially when infrequent but prolonged.

Keywords:

attentional processes cognitive biases decision-making planning fallacy ship navigation

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Area of Science:

Human-computer interaction
Maritime simulation
Cognitive psychology

Background:

Cognitive aspects of rendezvous are under-researched.
Planning fallacy and time-to-contact biases suggest a tendency for late arrivals.
Understanding ship rendezvous performance is crucial for navigation safety.

Purpose of the Study:

Investigate performance limitations in ship rendezvous control.
Examine the impact of movement uncertainty on rendezvous success.
Analyze different control strategies for ship rendezvous.

Main Methods:

Three experiments using a simplified ship simulation.
Participants controlled ship speed and/or heading.
Scenarios involved varying starting geometries and unpredictable movement delays.

Main Results:

Rendezvous success was difficult, with a common tendency for late arrivals.
Infrequent, longer delays disrupted performance more than frequent, shorter delays.
Participants did not delay action due to potential delays; dual-axis control was preferred.

Conclusions:

Ship rendezvous is prone to late arrivals, influenced by approach angles and relative speed.
Uncertainty from unpredictable delays significantly affects rendezvous performance.
Control strategy selection, particularly dual-axis control, is key to improving rendezvous outcomes.