A technical book written in public

Reliability Engineering for AI Systems

Measuring, Predicting, and Controlling Failure in LLMs and Agents

AI systems can succeed repeatedly and still contain hidden failure modes. Their behavior depends on prompts, context, model configuration, tools, retrieved information, and other operating conditions.

Reliability Engineering for AI Systems develops a practical framework for measuring failure probability, discovering where risk concentrates, evaluating whether interventions work, and operating more reliable LLM and agent systems.

Starting with repeated trials and empirical failure estimation, the book builds toward conditional and latent failure models and applies them to tools, RAG systems, autonomous agents, guardrails, failure prediction, reliability budgets, monitoring, and production assurance.

This is a living technical book. Chapter 1 is available free now. Founding Reader access will open with Chapter 2, targeted for October 1, 2026. After that, new chapters are planned approximately every three weeks as the manuscript develops.

Early-Access Edition
Reliability Engineering
for AI Systems
Measuring, Predicting, and Controlling Failure in LLMs and Agents
Current cover treatment · final artwork to followISBN 979-8-9979028-0-3

Chapter 2

Failure Probability from Repeated Trials

Target
October 1, 2026
Founding Reader — Digital
$29
Founding Reader + Print
$59

Chapter 2 is targeted for October 1, 2026. Future release dates are approximate and may shift when the technical work requires additional time.

Founding Reader — Digital: $29 includes all future chapters and the completed digital book. The price may rise as the manuscript grows; your purchase price is locked in.

Founding Reader + Print: $59 includes everything in the digital tier plus one physical copy of the completed book. Shipping and fulfillment details will be confirmed before the print edition is released.

Engineering reliability for probabilistic AI systems

Conventional software can often be tested by asking whether a fixed input produces the expected result. LLMs and agents complicate that model: the same system can produce different outcomes across repeated executions, and its failure probability can change with prompts, context, tools, retrieval, model configuration, and deployment conditions.

Reliability Engineering for AI Systems treats reliability as an empirical engineering problem: estimate the probability of failure, understand how that probability changes under operating conditions, and determine whether interventions actually reduce risk.

The book develops that reasoning progressively:

failure countP(F)P(F | X)latent failure propensity

and then applies it to tool use, retrieval-augmented generation, agents, failure propagation, guardrails, prediction, reliability budgets, monitoring, and production assurance.

What you’ll learn

Readers will learn how to:

  1. Estimate AI failure probability using repeated trials instead of relying only on single executions or aggregate benchmark scores.

  2. Quantify uncertainty and distinguish an observed failure rate from the underlying probability it is trying to estimate.

  3. Validate human and LLM-based judges before relying on them as measurement instruments.

  4. Measure how prompts, models, configurations, tools, retrieval, and operating conditions change failure risk.

  5. Analyze reliability across RAG pipelines, tool-using systems, and long-running agent trajectories.

  6. Test interventions, predict high-risk conditions, allocate reliability budgets, and monitor reliability after deployment.

Release schedule

After Chapter 2, new chapters are planned approximately every three weeks.

This is a living technical book. Release dates may shift when experiments, validation, technical review, or editing require additional time.

  1. Available

    Chapter 1

    When AI Systems Fail

    Free

  2. Next

    Chapter 2

    Failure Probability from Repeated Trials

    Target: October 1, 2026

  3. Planned

    Chapter 3

    Uncertainty in Failure Probability

    Approximately three weeks after Chapter 2

  4. Planned

    Chapter 4

    AI Judges as Measurement Systems

    Approximately three weeks after Chapter 3

  5. Planned

    Chapter 5

    Human Validation and Judge Calibration

    Approximately three weeks after Chapter 4

Table of contents

Twenty-one chapters move from measuring failure to production reliability and assurance.

Part I — Measuring Failure5 chapters
  1. When AI Systems FailAvailable

    The reliability mental model, system boundaries, failure definitions, repeated execution, and the first reliability harness.

  2. Failure Probability from Repeated TrialsNext

    Bernoulli trials, binomial experiments, empirical failure rates, and estimating failure probability.

    p_f = P(F = 1)
  3. Uncertainty in Failure ProbabilityPlanned

    Confidence intervals, zero-failure experiments, sample size, rare failures, and the difference between observed failure rate and underlying failure probability.

  4. AI Judges as Measurement SystemsPlanned

    Rubrics, structured judgments, judge stochasticity, false positives, false negatives, and how judge error affects reliability estimates.

  5. Human Validation and Judge CalibrationPlanned

    Blinded human review, confusion matrices, precision, recall, sensitivity, specificity, Cohen’s κ, disagreement analysis, bootstrap intervals, and deciding whether an automated judge is fit for use.

Part II — Conditional Reliability4 chapters
  1. Failure Probability Depends on ConditionsPlanned

    Conditional failure probability, prompt and context effects, model and decoding settings, system prompts, harness configuration, user state, and environment.

    p_f(x) = P(F = 1 | X = x)
  2. Designing Reliability ExperimentsPlanned

    Factors, controls, replication, randomization, blocking, factorial designs, ablations, frozen artifacts, and reproducibility.

  3. Mapping the Failure SurfacePlanned

    Stress testing, interaction effects, stratification, high-risk regions, adversarial conditions, and response surfaces.

  4. Latent Failure Under Repeated InferencePlanned

    Single-run versus repeated-run evaluation, hidden failures, k-of-N outcomes, repeated-use risk, and cumulative failure probability.

    P(at least one failure in N) = 1 − (1 − p)ᴺ
Part III — Reliability of AI Systems5 chapters
  1. From Model Reliability to System ReliabilityPlanned

    Foundation models, harnesses, prompts, orchestration, memory, guardrails, APIs, and the distinction between model-level and system-level failure.

  2. Tool-Using AgentsPlanned

    Wrong-tool selection, incorrect arguments, tool execution failures, misinterpretation of results, false claims of successful action, and unsafe actions.

  3. Retrieval and Multi-Stage ReliabilityPlanned

    RAG pipelines, retrieval failures, context quality, stage-wise reliability, and propagation of upstream errors.

  4. Reliability of Long-Running AgentsPlanned

    Sequential decisions, accumulating risk, per-step reliability, task completion probability, recovery, and dependence across steps.

  5. Failure Propagation and CascadesPlanned

    Correlated failures, common-cause failures, dependencies, cascading actions, redundancy, recovery, and system reliability models.

Part IV — Predicting and Controlling Failure4 chapters
  1. Predicting Failure ProbabilityPlanned

    Risk models for AI behavior, conditional failure prediction, embeddings, metadata, graph features, telemetry, and supervised models for failure prediction.

    P(F = 1 | X)
  2. Finding Rare Failures EfficientlyPlanned

    Risk-based sampling, ranking, top-k targeting, lift, failure-discovery recall, adaptive sampling, testing budgets, and stopping criteria.

  3. Reliability Requirements and BudgetsPlanned

    Acceptable failure probabilities, severity classes, probability-consequence tradeoffs, component-level budgets, safety margins, escalation, and acceptance criteria.

  4. Improving ReliabilityPlanned

    Prompt changes, model changes, decoding, routing, retrieval, verification, guardrails, redundancy, retries, human review, and experimental verification of whether an intervention actually lowers failure probability.

Part V — Production Reliability and Assurance3 chapters
  1. Reliability Changes Over TimePlanned

    Drift, changing models, prompts, tools, user populations, retrieval corpora, distribution shift, rolling estimates, change detection, and statistical process control.

  2. Reliability IncidentsPlanned

    Detection, reproduction, diagnosis, traces, logs, root-cause analysis, failure taxonomies, corrective action, and mechanistic evidence where available.

  3. Building an AI Reliability and Assurance SystemPlanned

    Continuous testing, measurement, prediction, control, monitoring, judge validation, experiment provenance, audit trails, reliability reports, and retesting.

Built around engineering problems, not abstract theory

The mathematics appears when the engineering problem requires it. Each chapter begins with a failure or reliability question, introduces the minimum statistical machinery needed to reason about it, implements the analysis, and ends with an engineering decision.

  1. Engineering problem
  2. Mental model
  3. Probability model
  4. Experiment
  5. Code
  6. Results
  7. Engineering decision

Who should read this book

AI/ML engineers

For engineers building LLM, RAG, and agent systems who need to understand reliability beyond average benchmark performance.

AI evaluation and safety practitioners

For practitioners designing evaluations, stress tests, human-validation studies, red-team exercises, and assurance programs.

Reliability, platform, and systems engineers

For engineers bringing reliability, observability, fault analysis, and operational-risk thinking to probabilistic AI systems.

Technical leaders and model-risk practitioners

For people making deployment and governance decisions who need defensible evidence about failure probability, uncertainty, controls, and residual risk.

Keita Broadwater

Keita Broadwater is an AI and machine learning researcher and engineering leader whose work focuses on reliability, evaluation, and failure analysis in AI systems. He is the author of Graph Neural Networks in Action and has held technical and leadership roles spanning machine learning, analytics, and applied AI.

Broadwater holds a PhD in mechanical engineering, where his research included reliability-oriented engineering problems, as well as an MBA. His current research explores how repeated stochastic evaluation, statistical failure modeling, and engineering controls can be used to measure and improve the reliability of large language models and AI agents.

How Founding Reader access works

  1. 1

    Read Chapter 1 free

    The opening chapter is available now and will remain free.

  2. 2

    Purchase when Chapter 2 is released

    Choose Digital or Digital + Print with a single purchase.

  3. 3

    Keep every future chapter

    Founding Readers receive later chapters without paying future price increases as the manuscript grows.

  4. 4

    Receive the completed digital book

    The purchase includes all subsequently released chapters and the completed first edition.

Frequently asked questions

Is Chapter 1 really free?

Yes. Chapter 1 is available free now and will remain free.

When does Founding Reader access open?

It opens when Chapter 2 is published, currently targeted for October 1, 2026. The date is a target and may shift if the chapter needs additional experimental, technical, or editorial work.

What do I receive?

The current paid release, every subsequently released chapter, and the completed digital book. Early purchasers will not pay later price increases.

Will the price change?

Founding Reader — Digital will open at $29, and Founding Reader + Print will open at $59. Prices may increase as the manuscript grows, while your purchase price remains locked in.

What is included in the print tier?

Founding Reader + Print includes all digital releases and one physical copy of the completed book. Shipping and fulfillment details will be confirmed before the print edition is released.

Is this the finished book?

No. This is a living technical book. Chapters, examples, organization, and wording may change as the manuscript develops.