Appendix A — Glossary

Definitions of technical terms used throughout the book. Each entry notes the chapter where the term is first introduced or most fully explained.

A.1 Probability & Distributions

Confidence interval A range of values that, under repeated sampling, would contain the true parameter a stated percentage of the time (e.g., 95%). In the context of the Second Moment Method, a 95% CI is $\mu \pm 1.96\sigma$. See Chapter 3.

Distribution, normal A symmetric bell-shaped probability distribution fully described by its mean $\mu$ and standard deviation $\sigma$. The default assumption for task durations when uncertainty is roughly symmetric around the estimate. See Chapter 2.

Distribution, triangular A distribution defined by a minimum $a$, most likely (mode) $b$, and maximum $c$. Used when subject-matter experts can provide three-point estimates. Asymmetric when $b \neq (a+c)/2$. See Chapter 2.

Distribution, uniform A distribution where all values in the interval $[\text{min}, \text{max}]$ are equally likely. Used for tasks where there is no strong reason to prefer any duration over another within a range. See Chapter 2.

Expected value (mean) The probability-weighted average of all possible outcomes of a random variable. For a project total, it equals the sum of the individual task means. Denoted $\mu$ or $E[X]$. See Chapter 3.

P50 / P80 / P95 The 50th, 80th, and 95th percentiles of a distribution. P50 is the median, with half of outcomes falling below it. P80 and P95 are common targets for schedule and cost contingency. See Chapter 2.

Percentile The value below which a given percentage of outcomes fall. The $p$-th percentile is the value $x$ such that $P(X \leq x) = p$. See Chapter 2.

Standard deviation The square root of variance; has the same units as the original variable. A measure of spread: roughly two-thirds of normally distributed outcomes fall within one standard deviation of the mean. Denoted $\sigma$. See Chapter 3.

Variance The expected squared deviation from the mean: $\sigma^2 = E[(X - \mu)^2]$. The key quantity in both the Second Moment Method and sensitivity analysis because variances add (for independent tasks). Denoted $\sigma^2$. See Chapter 3.

A.2 Monte Carlo Simulation & Sensitivity

Contingency reserve The additional budget or schedule allocated above the base estimate to cover uncertainty. Commonly set as the difference between a high percentile (P80 or P95) and the base estimate (P50). See Chapter 2.

Monte Carlo simulation (MCS) A method that estimates the distribution of a model output by drawing thousands of random samples from the input distributions and recording each result. Named after the Casino de Monte Carlo. See Chapter 2.

Sensitivity index A dimensionless number that quantifies how much a given task’s variance contributes to total project variance, accounting for correlations with other tasks. Independent tasks all have index = 1; index > 1 indicates amplification through positive correlation. See Chapter 4.

Tornado chart A horizontal bar chart where tasks are sorted from highest to lowest sensitivity index (or variance contribution), producing a shape that narrows like a tornado. The standard deliverable for communicating sensitivity results to stakeholders. See Chapter 4.

Variance decomposition The process of partitioning total project variance into contributions from individual tasks. The foundation of sensitivity analysis. See Chapter 4 and Appendix B.

A.3 Second Moment Method

Central Limit Theorem (CLT) A statistical result stating that the sum of many independent random variables tends toward a normal distribution, regardless of the shape of the individual distributions, as the number of terms grows. The theoretical justification for treating total project duration as approximately normal. See Chapter 3 and Appendix B.

Second moment The second moment of a probability distribution is its mean squared plus its variance: $E[X^2] = \mu^2 + \sigma^2$. The “Second Moment Method” is named for its use of the first two moments (mean and variance) to characterise uncertainty. See Chapter 3.

Second Moment Method (SMM) An analytical technique that computes total project mean and variance from individual task means, variances, and pairwise correlations, without simulation. Fast, but assumes that the normal approximation for the total is adequate. See Chapter 3.

A.4 Earned Value Management

Actual Cost (AC) The total cost actually incurred for work performed up to the reporting period. Also called Actual Cost of Work Performed (ACWP). See Chapter 5.

Budget at Completion (BAC) The total planned budget for the project. The sum of all planned costs. See Chapter 5.

Cost Performance Index (CPI) The ratio of Earned Value to Actual Cost: $\text{CPI} = EV / AC$. A CPI below 1.0 means the project is over budget for the work accomplished. See Chapter 5.

Cost Variance (CV) The difference between Earned Value and Actual Cost: $CV = EV - AC$. Negative means over budget. See Chapter 5.

Earned Value (EV) The budgeted value of work actually completed: $EV = \text{BAC} \times \% \text{complete}$. Also called Budgeted Cost of Work Performed (BCWP). See Chapter 5.

Estimate at Completion (EAC) The forecast of total project cost at completion, computed from current performance. Three common methods: typical ($EAC = AC + (BAC - EV) / CPI$), atypical ($EAC = AC + BAC - EV$), and combined. See Chapter 5.

Estimate to Complete (ETC) The expected cost to finish the remaining work: $ETC = EAC - AC$. See Chapter 5.

Planned Value (PV) The budgeted cost for work scheduled to be done by the reporting period: $PV = \text{BAC} \times \% \text{planned}$. Also called Budgeted Cost of Work Scheduled (BCWS). See Chapter 5.

Schedule Performance Index (SPI) The ratio of Earned Value to Planned Value: $\text{SPI} = EV / PV$. An SPI below 1.0 means the project is behind schedule. See Chapter 5.

Schedule Variance (SV) The difference between Earned Value and Planned Value: $SV = EV - PV$. Negative means behind schedule. See Chapter 5.

To-Complete Performance Index (TCPI) The cost efficiency required on remaining work to meet the Budget at Completion: $\text{TCPI} = (BAC - EV) / (BAC - AC)$. A TCPI above 1.0 means the team must perform better than it has been. See Chapter 5.

Variance at Completion (VAC) The difference between the original budget and the current forecast: $VAC = BAC - EAC$. Negative means the project is forecast to overrun. See Chapter 5.

A.5 Bayesian Inference

Bayes’ theorem The rule for updating probabilities given evidence: $P(H|E) = P(E|H) \cdot P(H) / P(E)$. The foundation of all Bayesian risk updating in this book. See Chapter 6 and Appendix B.

Conditional probability The probability of an event given that another event is known to have occurred: $P(A|B) = P(A \cap B) / P(B)$. See Chapter 6.

Likelihood The probability of observing the evidence given a hypothesis: $P(E|H)$. In project risk terms, the probability that a root cause would be observable if the risk event occurred (or did not occur). See Chapter 6.

Posterior probability The updated probability of a hypothesis after observing new evidence: $P(H|E)$. The output of Bayesian updating. Computed by risk_post_prob(). See Chapter 6.

Prior probability The probability of a hypothesis before observing new evidence, based on historical data or expert judgment. Computed from root-cause probabilities by risk_prob(). See Chapter 6.

Root cause An underlying condition or event that can trigger a risk event. Multiple root causes can independently contribute to the same risk. In PRA, root causes are modelled as independent with known probabilities. See Chapter 6.

A.6 Learning Curves

Gompertz model A sigmoidal growth model with an asymmetric S-shape: slow initial growth, rapid acceleration, then deceleration. The inflection point occurs at roughly 37% of the ceiling. Useful when early adoption is very slow. See Chapter 7.

Logistic model A symmetric sigmoidal growth model: $y = K / (1 + e^{-r(t - t_0)})$. Growth accelerates from 0 to $K/2$ then decelerates symmetrically toward the ceiling $K$. See Chapter 7.

Pearl model Functionally identical to the logistic model, a symmetric S-curve with the same formula. Named after Raymond Pearl who applied it to population growth. See Chapter 7.

Residual standard error (RSE) The standard deviation of the residuals (observed minus fitted values) in a regression model. Lower RSE indicates a better fit. Used to compare logistic, Gompertz, and Pearl model fits. See Chapter 7.

Sigmoidal curve An S-shaped curve that models bounded growth: starts near zero, accelerates, then levels off at a ceiling. All three learning curve models in this book (Logistic, Pearl, Gompertz) are sigmoidal. See Chapter 7.

A.7 Structural Methods

Bayesian network A directed acyclic graph (DAG) in which nodes represent random variables and edges represent conditional dependencies. Used in PRA to model how risk events propagate through resources and tasks to project cost. See Chapter 9.

DAG (Directed Acyclic Graph) A graph of nodes and directed edges with no cycles; you cannot return to a starting node by following edges in their directed direction. The required structure for Bayesian networks. See Chapter 9.

Design Structure Matrix (DSM) A square matrix that encodes task-to-task dependencies. In PRA, DSMs are derived from shared resource and risk structures, making hidden coupling between tasks visible and quantifiable. See Chapter 8.

Grandparent DSM A tasks-by-tasks matrix derived from the chain Risk → Resource → Task. Off-diagonal entries count the number of risks shared between each pair of tasks via the intermediate resource layer. Computed by grandparent_dsm(). See Chapter 8.

Parent DSM A tasks-by-tasks matrix derived directly from the Resource-Task matrix. Off-diagonal entry $P[j,k]$ counts the number of resources shared by tasks $j$ and $k$. Computed by parent_dsm(). See Chapter 8.

Resource-Task matrix (S) A binary matrix with resources as rows and tasks as columns. Entry $S[i,j] = 1$ means resource $i$ is used by task $j$. The primary input to parent_dsm(). See Chapter 8.

Risk-Resource matrix (R) A binary matrix with risks as rows and resources as columns. Entry $R[i,j] = 1$ means risk $i$ affects resource $j$. Used together with S in grandparent_dsm(). See Chapter 8.

A.8 Agentic Framework

MCP (Model Context Protocol) An open protocol that allows AI clients (such as Claude Desktop or Claude Code) to call external tools, including PRA functions, directly from a conversation. See Chapter 11.

RAG (Retrieval-Augmented Generation) A technique that augments an LLM’s response by first retrieving relevant documents from a knowledge base. In PRA, RAG grounds conceptual answers in the built-in methods documentation, reducing hallucination. See Chapter 11.

Slash command A deterministic command prefix (e.g., /mcs, /evm) that bypasses the LLM and executes a PRA function directly. Guarantees reproducible results regardless of model. See Chapter 11.

Tool call An LLM action where the model selects and invokes an external function (tool) to answer a user query. In PRA, tool calls route numerical queries to the appropriate analysis function. See Chapter 11.

# Glossary {#sec-glossary} Definitions of technical terms used throughout the book. Each entry notes the chapter where the term is first introduced or most fully explained. --- ## Probability & Distributions **Confidence interval** A range of values that, under repeated sampling, would contain the true parameter a stated percentage of the time (e.g., 95%). In the context of the Second Moment Method, a 95% CI is $\mu \pm 1.96\sigma$. See @sec-smm. **Distribution, normal** A symmetric bell-shaped probability distribution fully described by its mean $\mu$ and standard deviation $\sigma$. The default assumption for task durations when uncertainty is roughly symmetric around the estimate. See @sec-mcs. **Distribution, triangular** A distribution defined by a minimum $a$, most likely (mode) $b$, and maximum $c$. Used when subject-matter experts can provide three-point estimates. Asymmetric when $b \neq (a+c)/2$. See @sec-mcs. **Distribution, uniform** A distribution where all values in the interval $[\text{min}, \text{max}]$ are equally likely. Used for tasks where there is no strong reason to prefer any duration over another within a range. See @sec-mcs. **Expected value (mean)** The probability-weighted average of all possible outcomes of a random variable. For a project total, it equals the sum of the individual task means. Denoted $\mu$ or $E[X]$. See @sec-smm. **P50 / P80 / P95** The 50th, 80th, and 95th percentiles of a distribution. P50 is the median, with half of outcomes falling below it. P80 and P95 are common targets for schedule and cost contingency. See @sec-mcs. **Percentile** The value below which a given percentage of outcomes fall. The $p$-th percentile is the value $x$ such that $P(X \leq x) = p$. See @sec-mcs. **Standard deviation** The square root of variance; has the same units as the original variable. A measure of spread: roughly two-thirds of normally distributed outcomes fall within one standard deviation of the mean. Denoted $\sigma$. See @sec-smm. **Variance** The expected squared deviation from the mean: $\sigma^2 = E[(X - \mu)^2]$. The key quantity in both the Second Moment Method and sensitivity analysis because variances add (for independent tasks). Denoted $\sigma^2$. See @sec-smm. --- ## Monte Carlo Simulation & Sensitivity **Contingency reserve** The additional budget or schedule allocated above the base estimate to cover uncertainty. Commonly set as the difference between a high percentile (P80 or P95) and the base estimate (P50). See @sec-mcs. **Monte Carlo simulation (MCS)** A method that estimates the distribution of a model output by drawing thousands of random samples from the input distributions and recording each result. Named after the Casino de Monte Carlo. See @sec-mcs. **Sensitivity index** A dimensionless number that quantifies how much a given task's variance contributes to total project variance, accounting for correlations with other tasks. Independent tasks all have index = 1; index > 1 indicates amplification through positive correlation. See @sec-sensitivity. **Tornado chart** A horizontal bar chart where tasks are sorted from highest to lowest sensitivity index (or variance contribution), producing a shape that narrows like a tornado. The standard deliverable for communicating sensitivity results to stakeholders. See @sec-sensitivity. **Variance decomposition** The process of partitioning total project variance into contributions from individual tasks. The foundation of sensitivity analysis. See @sec-sensitivity and @sec-math. --- ## Second Moment Method **Central Limit Theorem (CLT)** A statistical result stating that the sum of many independent random variables tends toward a normal distribution, regardless of the shape of the individual distributions, as the number of terms grows. The theoretical justification for treating total project duration as approximately normal. See @sec-smm and @sec-math. **Second moment** The second moment of a probability distribution is its mean squared plus its variance: $E[X^2] = \mu^2 + \sigma^2$. The "Second Moment Method" is named for its use of the first two moments (mean and variance) to characterise uncertainty. See @sec-smm. **Second Moment Method (SMM)** An analytical technique that computes total project mean and variance from individual task means, variances, and pairwise correlations, without simulation. Fast, but assumes that the normal approximation for the total is adequate. See @sec-smm. --- ## Earned Value Management **Actual Cost (AC)** The total cost actually incurred for work performed up to the reporting period. Also called Actual Cost of Work Performed (ACWP). See @sec-evm. **Budget at Completion (BAC)** The total planned budget for the project. The sum of all planned costs. See @sec-evm. **Cost Performance Index (CPI)** The ratio of Earned Value to Actual Cost: $\text{CPI} = EV / AC$. A CPI below 1.0 means the project is over budget for the work accomplished. See @sec-evm. **Cost Variance (CV)** The difference between Earned Value and Actual Cost: $CV = EV - AC$. Negative means over budget. See @sec-evm. **Earned Value (EV)** The budgeted value of work actually completed: $EV = \text{BAC} \times \% \text{complete}$. Also called Budgeted Cost of Work Performed (BCWP). See @sec-evm. **Estimate at Completion (EAC)** The forecast of total project cost at completion, computed from current performance. Three common methods: typical ($EAC = AC + (BAC - EV) / CPI$), atypical ($EAC = AC + BAC - EV$), and combined. See @sec-evm. **Estimate to Complete (ETC)** The expected cost to finish the remaining work: $ETC = EAC - AC$. See @sec-evm. **Planned Value (PV)** The budgeted cost for work scheduled to be done by the reporting period: $PV = \text{BAC} \times \% \text{planned}$. Also called Budgeted Cost of Work Scheduled (BCWS). See @sec-evm. **Schedule Performance Index (SPI)** The ratio of Earned Value to Planned Value: $\text{SPI} = EV / PV$. An SPI below 1.0 means the project is behind schedule. See @sec-evm. **Schedule Variance (SV)** The difference between Earned Value and Planned Value: $SV = EV - PV$. Negative means behind schedule. See @sec-evm. **To-Complete Performance Index (TCPI)** The cost efficiency required on remaining work to meet the Budget at Completion: $\text{TCPI} = (BAC - EV) / (BAC - AC)$. A TCPI above 1.0 means the team must perform better than it has been. See @sec-evm. **Variance at Completion (VAC)** The difference between the original budget and the current forecast: $VAC = BAC - EAC$. Negative means the project is forecast to overrun. See @sec-evm. --- ## Bayesian Inference **Bayes' theorem** The rule for updating probabilities given evidence: $P(H|E) = P(E|H) \cdot P(H) / P(E)$. The foundation of all Bayesian risk updating in this book. See @sec-bayes and @sec-math. **Conditional probability** The probability of an event given that another event is known to have occurred: $P(A|B) = P(A \cap B) / P(B)$. See @sec-bayes. **Likelihood** The probability of observing the evidence given a hypothesis: $P(E|H)$. In project risk terms, the probability that a root cause would be observable if the risk event occurred (or did not occur). See @sec-bayes. **Posterior probability** The updated probability of a hypothesis after observing new evidence: $P(H|E)$. The output of Bayesian updating. Computed by `risk_post_prob()`. See @sec-bayes. **Prior probability** The probability of a hypothesis before observing new evidence, based on historical data or expert judgment. Computed from root-cause probabilities by `risk_prob()`. See @sec-bayes. **Root cause** An underlying condition or event that can trigger a risk event. Multiple root causes can independently contribute to the same risk. In `PRA`, root causes are modelled as independent with known probabilities. See @sec-bayes. --- ## Learning Curves **Gompertz model** A sigmoidal growth model with an asymmetric S-shape: slow initial growth, rapid acceleration, then deceleration. The inflection point occurs at roughly 37% of the ceiling. Useful when early adoption is very slow. See @sec-sigmoidal. **Logistic model** A symmetric sigmoidal growth model: $y = K / (1 + e^{-r(t - t_0)})$. Growth accelerates from 0 to $K/2$ then decelerates symmetrically toward the ceiling $K$. See @sec-sigmoidal. **Pearl model** Functionally identical to the logistic model, a symmetric S-curve with the same formula. Named after Raymond Pearl who applied it to population growth. See @sec-sigmoidal. **Residual standard error (RSE)** The standard deviation of the residuals (observed minus fitted values) in a regression model. Lower RSE indicates a better fit. Used to compare logistic, Gompertz, and Pearl model fits. See @sec-sigmoidal. **Sigmoidal curve** An S-shaped curve that models bounded growth: starts near zero, accelerates, then levels off at a ceiling. All three learning curve models in this book (Logistic, Pearl, Gompertz) are sigmoidal. See @sec-sigmoidal. --- ## Structural Methods **Bayesian network** A directed acyclic graph (DAG) in which nodes represent random variables and edges represent conditional dependencies. Used in `PRA` to model how risk events propagate through resources and tasks to project cost. See @sec-network. **DAG (Directed Acyclic Graph)** A graph of nodes and directed edges with no cycles; you cannot return to a starting node by following edges in their directed direction. The required structure for Bayesian networks. See @sec-network. **Design Structure Matrix (DSM)** A square matrix that encodes task-to-task dependencies. In `PRA`, DSMs are derived from shared resource and risk structures, making hidden coupling between tasks visible and quantifiable. See @sec-dsm. **Grandparent DSM** A tasks-by-tasks matrix derived from the chain Risk → Resource → Task. Off-diagonal entries count the number of risks shared between each pair of tasks via the intermediate resource layer. Computed by `grandparent_dsm()`. See @sec-dsm. **Parent DSM** A tasks-by-tasks matrix derived directly from the Resource-Task matrix. Off-diagonal entry $P[j,k]$ counts the number of resources shared by tasks $j$ and $k$. Computed by `parent_dsm()`. See @sec-dsm. **Resource-Task matrix (S)** A binary matrix with resources as rows and tasks as columns. Entry $S[i,j] = 1$ means resource $i$ is used by task $j$. The primary input to `parent_dsm()`. See @sec-dsm. **Risk-Resource matrix (R)** A binary matrix with risks as rows and resources as columns. Entry $R[i,j] = 1$ means risk $i$ affects resource $j$. Used together with **S** in `grandparent_dsm()`. See @sec-dsm. --- ## Agentic Framework **MCP (Model Context Protocol)** An open protocol that allows AI clients (such as Claude Desktop or Claude Code) to call external tools, including `PRA` functions, directly from a conversation. See @sec-agent. **RAG (Retrieval-Augmented Generation)** A technique that augments an LLM's response by first retrieving relevant documents from a knowledge base. In `PRA`, RAG grounds conceptual answers in the built-in methods documentation, reducing hallucination. See @sec-agent. **Slash command** A deterministic command prefix (e.g., `/mcs`, `/evm`) that bypasses the LLM and executes a `PRA` function directly. Guarantees reproducible results regardless of model. See @sec-agent. **Tool call** An LLM action where the model selects and invokes an external function (tool) to answer a user query. In `PRA`, tool calls route numerical queries to the appropriate analysis function. See @sec-agent.