Chapter 13 — Glossary

This glossary clarifies some key terms used throughout the eBook.
It will expand in future releases as new chapters and case studies are added.

🔑 Transfer Equation

• Technical definition (simulation theory, e.g., Hammersley & Handscomb, 1964; Ripley, 1987):
  A mathematical transformation that converts a random number r ∼ U(0,1) into a random variate following a target distribution.
  Example: For an exponential distribution with rate λ,
  x = - (1/λ) * log(r).

• Modeling definition (applied Monte Carlo, e.g., Hubbard, 2014):
  The system model equation that combines input variables (themselves uncertain/random) to produce an output.
  Example: Annual Savings = (MS + LS + RMS) × PL.

• In this eBook:
  We primarily use the modeling definition (Hubbard, 2014), since in GMP and pharma applications we care about how input uncertainties (assay weights, purities, dissolution times) propagate to outputs.
  Nevertheless, the technical definition underpins the generation of random variates.

🔑 Random Number

A pseudo-random value in [0,1] generated by a computer algorithm.
Used as the raw input for creating random variates.

• In this eBook:
  Random numbers are always the starting point for generating random variates used in simulations.

🔑 Random Variate

A value drawn from a specific probability distribution (Normal, Uniform, Triangular, etc.), usually obtained by transforming a random number through the appropriate transfer equation.

• In this eBook:
  Random variates are the true simulated data points (e.g., assay %, dissolution value, microbial count) that feed into the transfer equation of the system model.

🔑 p_out (Probability of OOS)

The probability that a simulated batch falls Out of Specification (OOS).
It is estimated as the proportion of simulated values lying outside the lower and/or upper specification limits (LSL, USL).

• In this eBook:
  p_out is the central risk metric in all case studies (assay, dissolution, process validation).
  It provides a direct and intuitive measure of process conformance risk.

🔑 Capability Indices (Cp, Cpk, Percentile-based)

Indices that quantify how well a process fits within its specification limits.

• Cp: measures process spread relative to specification width.
• Cpk: also accounts for centering relative to the target/mean.

• Percentile-based indices: non-parametric alternative, comparing extreme quantiles with specification limits (useful when data are non-normal or skewed).

• In this eBook:
  Cp and Cpk are reported when applicable, but emphasis is given to percentile-based indices, which are more robust in pharmaceutical contexts (e.g., dissolution, microbiology).

🔑 Bootstrap

A resampling method that estimates variability and confidence intervals by repeatedly sampling with replacement from observed data.

• In this eBook:
  Bootstrap is used to quantify the uncertainty of capability indices and tail probabilities, especially when datasets are small (e.g., 3 PPQ batches, limited stability data).

🔑 OC Curve (Operating Characteristic Curve)

A plot that shows the probability of accepting a lot as a function of its actual quality level (e.g., % defective units).
Originates from sampling theory (e.g., ISO 2859-1, ISO 3951-1).

• In this eBook:
  OC curves are discussed in relation to future case studies on sampling and acceptance plans, where Monte Carlo is used to empirically estimate acceptance probabilities under different process conditions.

📌 Note

This glossary will be progressively expanded as new chapters are added
(e.g., dissolution, microbiology, stability, advanced capability measures).