crossrun

crossrun computes the joint distribution of the number of crossings and the longest run in sequences of independent Bernoulli observations to support statistical process control analyses.

Key Features:

• Joint Distribution Calculation: Computes the joint distribution of the number of crossings and the longest run for sequences of independent Bernoulli observations.
• Bernoulli-sequence Analysis: Operates explicitly on sequences of independent Bernoulli trials as the input data model.
• Metric Definitions: Distinguishes crossings (points where a sequence crosses a specified threshold) and runs (consecutive occurrences, with focus on the longest run) in its calculations.

Scientific Applications:

• Statistical Process Control: Supports investigation and refinement of SPC rules to distinguish signal from noise based on the joint distribution of crossings and runs.
• Manufacturing and Quality Assurance: Enables detection of genuine signals amid noise in manufacturing and quality-assurance processes that rely on SPC monitoring.

Methodology:

Analyzes sequences of independent Bernoulli trials to determine the joint distribution of the number of crossings (threshold crossings) and the longest run (consecutive occurrences of a particular outcome).