#4000 Problem Statements
#4000 Problem Statements
#4000 List and describe the types of problem statements, and the domains they can be applied to
Problem statements are the foundation of any structured inquiry. They define the gap between "where we are" and "where we want to be." While they all share the goal of clarity, they differ in their intent—whether that is to discover new knowledge, fix a broken process, or design something entirely new.
Here are the primary types of problem statements and the domains where they are most effective:
1. Descriptive Problem Statements
These focus on describing the characteristics or behaviors of a specific phenomenon without necessarily seeking a "solution" yet. They answer the "what is happening?" question.
Focus: Mapping, documenting, and quantifying a situation.
Domains:
Market Research: Identifying the demographic makeup of a new user base.
Sociology: Documenting the impact of urban sprawl on local community centers.
Safety & Mission Assurance: Cataloging the types of software anomalies found during a specific test phase.
2. Relational (or Correlational) Problem Statements
These explore the relationship between two or more variables. They don't always claim cause-and-effect, but they seek to understand how changes in one thing might relate to another.
Focus: Investigating links, patterns, and dependencies.
Domains:
Public Health: Studying the link between air quality and respiratory issues in specific zip codes.
Finance: Analyzing the correlation between interest rate hikes and consumer spending on luxury goods.
Engineering: Evaluating how hardware temperature affects the latency of an LLM inference.
3. Causal (or Experimental) Problem Statements
These are designed to determine if one variable causes a change in another. This is the "Gold Standard" for scientific inquiry.
Focus: Establishing cause-and-effect through controlled testing.
Domains:
Pharmaceuticals: Clinical trials testing if a new drug actually lowers blood pressure.
A/B Testing (Tech): Determining if changing a button's color increases the click-through rate.
Manufacturing: Testing if a new alloy increases the structural integrity of a rocket component under heat stress.
4. Casuist Problem Statements
These are often used in ethics and law. They compare a current "case" or problem to existing precedents or rules to determine the "right" course of action.
Focus: Ethical dilemmas, legal interpretation, and moral consistency.
Domains:
Law: Determining if a new digital privacy case falls under existing Fourth Amendment protections.
Bioethics: Deciding the priority list for organ transplants based on established medical ethics.
Policy Making: Evaluating if a new tax incentive aligns with a city's 10-year sustainability goals.
5. Design (or Technical) Problem Statements
These are "How might we..." statements. They focus on innovation and optimization—creating a solution that doesn't currently exist or improving an inefficient one.
Focus: Requirements, constraints, and functional goals.
Domains:
Software Engineering: Designing a low-latency API that can handle 10,000 requests per second.
Architecture: Creating a building that is carbon-neutral while remaining within a specific budget.
Product Design: Developing a more ergonomic bicycle seat for long-distance commuters.
Summary Comparison Table
| Type | Core Question | Best For... |
| Descriptive | What is going on? | Observation & Fact-finding |
| Relational | Are these things linked? | Pattern recognition |
| Causal | Does X lead to Y? | Scientific validation |
| Casuist | How does this fit the rules? | Ethical & Legal dilemmas |
| Design | How do we build/fix this? | Engineering & Innovation |
Would you like me to help you draft a specific problem statement for a project you're currently working on, perhaps using a framework like the "5 Whys" or TRIZ?
Are there more?
Beyond the primary research and design categories, there are several more specialized types of problem statements often used in high-level engineering, systems thinking, and philosophy.
Given your background in software process engineering and systems safety, these "advanced" archetypes might resonate more with the complexities of large-scale integration and compliance.
6. Predictive Problem Statements
These focus on forecasting future states based on existing trends or hypothetical changes. They move from "what is" to "what will be."
Focus: Risk assessment, trend analysis, and "if-then" scenarios.
Domains:
Aerospace: Predicting the failure rate of a specific sensor array after 10,000 hours of radiation exposure.
Cybersecurity: Modeling how a new encryption standard will hold up against potential quantum computing attacks.
Logistics: Forecasting supply chain bottlenecks if a specific orbital launch window is missed.
7. Ontological Problem Statements
These deal with definitions, categories, and existence. They ask: "What does it mean for this thing to exist or be classified this way?"
Focus: Standards, taxonomies, and conceptual boundaries.
Domains:
Artificial Intelligence: Defining the boundary between "agentic behavior" and "pre-programmed automation."
Law: Determining if a digital asset (like a prompt or an LLM weight) should be legally classified as "property" or "information."
Systems Engineering: Establishing the criteria for what constitutes a "Critical Safety Path" in a multi-provider integration.
8. Critical (or Emancipatory) Problem Statements
Common in social sciences and management, these look at power structures and systemic biases. They seek to uncover hidden assumptions that limit a system.
Focus: Equity, accessibility, and dismantling "the way it's always been done."
Domains:
Organizational Design: Investigating how current promotion metrics inadvertently exclude remote subcontractors.
Software Design: Identifying how "standard" UI designs create barriers for users with specific neurodivergent traits.
Public Policy: Analyzing how zoning laws in farming communities affect the availability of high-speed broadband.
9. Evaluative Problem Statements
These compare a current state against a specific standard or benchmark to measure "goodness" or compliance.
Focus: Performance gaps, audits, and optimization.
Domains:
Software Process Engineering: Determining the delta between current CMMI Level 3 practices and the requirements for Level 5.
Mission Assurance: Evaluating a launch provider's documentation against NPR 7150.2 standards to identify non-compliance.
Sustainability: Assessing a facility’s energy usage against "Net Zero" targets.
10. Archetypal (Systems) Problem Statements
Derived from Systems Thinking, these identify recurring patterns (archetypes) that cause systems to fail, such as "Shifting the Burden" or "Limits to Success."
Focus: Feedback loops, delays, and structural leverage points.
Domains:
Project Management: Solving the "Fixes that Fail" cycle where patching bugs leads to more complex architectural debt later.
Resource Management: Addressing the "Tragedy of the Commons" in shared server clusters or GPU clouds.
Comparison of Advanced Problem Types
| Type | Core Question | Key Characteristic |
| Predictive | What will happen? | Focuses on probability and risk. |
| Ontological | What is this, really? | Focuses on definitions and taxonomy. |
| Critical | Who does this serve? | Focuses on bias and power structures. |
| Evaluative | How well does this work? | Focuses on benchmarks and compliance. |
| Archetypal | What is the pattern? | Focuses on system structure and loops. |
Would you like me to help you frame a Predictive or Evaluative problem statement for a specific NASA safety standard or a software hazard you’re currently analyzing?
Provide 3 examples for each of the 10 problem statement types
To give these types some weight, let’s look at 30 concrete examples. I’ve categorized these to span across your likely professional interests (NASA, software, and systems) as well as broader industrial and social contexts.
1. Descriptive Problem Statements
Aero-Engineering: "What is the specific distribution of debris sizes encountered by the ISS in the Low Earth Orbit (LEO) environment over the last five years?"
Customer Experience: "What are the most common navigational paths users take on a quantum computing educational site before they drop off?"
Infrastructure: "How do humidity levels in a coastal Texas city vary seasonally within unconditioned warehouse environments?"
2. Relational Problem Statements
Hardware Performance: "How does the increase in VRAM on an RTX 4080 correlate with the training time of a Large Language Model (LLM)?"
Team Dynamics: "To what extent does the frequency of peer reviews in a software team relate to the number of bugs found during the integration phase?"
Biology: "What is the relationship between the nutrient density of soil in Iowa cornfields and the average height of the crop?"
3. Causal Problem Statements
Material Science: "Does the application of a ceramic-based coating reduce the rate of oxidation on a specific aluminum alloy by at least 20%?"
Software Testing: "Does switching from manual unit testing to an automated AI-driven testing suite reduce the total development cycle time?"
Agriculture: "Does the introduction of a specific species of cover crop cause a measurable increase in nitrogen levels for the following year's planting?"
4. Casuist Problem Statements
AI Ethics: "Does the training of an AI on copyrighted data for 'research purposes' fall under the established 'Fair Use' doctrine?"
Corporate Policy: "Does a subcontractor’s use of a personal laptop for NASA-related tasks violate the current cybersecurity 'Access Control' protocol?"
Medical Law: "Based on the 1990 Patient Self-Determination Act, how should a hospital handle an unconscious patient without a designated proxy?"
5. Design Problem Statements
Product Engineering: "How might we design a lightweight, foldable bicycle for commuters that weighs less than 15 lbs and fits into a standard backpack?"
Software Development: "How can we create a Domain-Specific Language (DSL) that allows non-programmers to define safety requirements for hazard analysis?"
Artistic Tech: "How might we use laser-etched acrylic sheets to create a 3D 'Ghost Model' of a naval vessel that remains clear but visible under LED light?"
6. Predictive Problem Statements
Risk Management: "Given current launch cadences, what is the probability of a 'Kessler Syndrome' event occurring in LEO by the year 2040?"
Market Trends: "How will the widespread availability of consumer-grade NPUs affect the sales of high-end dedicated GPUs over the next three years?"
Climate Modeling: "What will be the projected rise in sea level for Galveston Bay if global temperatures increase by another 1.5°C?"
7. Ontological Problem Statements
Data Science: "At what point does a collection of interconnected data points transition from a 'Database' to a 'Knowledge Graph'?"
Philosophy of Mind: "What criteria must a machine learning model meet before it can be classified as possessing 'Artificial General Intelligence' (AGI)?"
Standards/Compliance: "In the context of NPR 7150.2, what specifically differentiates 'Class A' software from 'Class B' software in a multi-agent system?"
8. Critical Problem Statements
Digital Divide: "How do current subscription-based AI tools reinforce the knowledge gap between high-budget corporations and low-budget solopreneurs?"
Urban Planning: "In what ways do traditional zoning laws in small farming communities prevent the development of affordable housing for young workers?"
Workplace Culture: "How does the 'hero culture' in software engineering marginalize the contributions of process engineers and testers?"
9. Evaluative Problem Statements
Audit/Compliance: "How well does the current software hazard analysis for the Lunar Gateway mission align with the MIL-STD-882E safety standard?"
Sustainability: "To what degree does the efficiency of a specific home HVAC system in Alvin, Texas, meet the current Energy Star 6.0 requirements?"
Academic: "How effective is the current https://www.google.com/search?q=QCTutor.com curriculum at preparing students for the IBM Quantum Developer Certification?"
10. Archetypal (Systems) Problem Statements
Management: "Is the current delay in software delivery a case of 'Shifting the Burden,' where we are fixing symptoms instead of the underlying architectural flaws?"
Economy: "How can we address the 'Tragedy of the Commons' regarding the shared compute resources in a multi-departmental GPU cluster?"
Growth: "What is the 'Limit to Success' preventing our startup from scaling past its first 1,000 users despite increased marketing spend?"
Would you like me to take one of these examples and expand it into a full Problem Definition Document, including background, constraints, and success criteria?
Provide Generative-AI and Agentic-AI workflows for "solving" each of the ten types of problem statement
Solving complex problems with AI requires choosing between two distinct paradigms: Generative AI (a reactive partner that synthesizes and drafts) and Agentic AI (a proactive system that plans, acts, and iterates).
Below are specific workflows for each of the ten problem statement types.
1. Descriptive (What is happening?)
Generative AI Workflow: Use Retrieval-Augmented Generation (RAG) to ingest unstructured logs or documents. The LLM summarizes findings and creates a "State of the System" report.
Agentic AI Workflow: A Monitoring Agent continuously polls APIs or databases, detects anomalies in real-time, and triggers a Reporting Agent to update a live dashboard.
2. Relational (Are these things linked?)
Generative AI Workflow: Input two datasets (e.g., test results and environmental data). Use Chain of Thought (CoT) prompting to ask the model to "identify potential correlations and hidden dependencies."
Agentic AI Workflow: An Analyst Agent queries multiple siloed systems (e.g., Jira and GitHub), performs cross-reference lookups, and uses a Statistical Tool to calculate correlation coefficients autonomously.
3. Causal (Does X lead to Y?)
Generative AI Workflow: Provide a set of observations and ask the model to generate three testable hypotheses and a step-by-step experimental design to prove causation.
Agentic AI Workflow: A ReAct (Reason + Act) Agent executes a series of software tests, observes the failures, modifies a single variable, and repeats the process until the root cause is isolated.
4. Casuist (How does this fit the rules?)
Generative AI Workflow: Feed a specific case study and a PDF of a standard (like NPR 7150.2) into the prompt. Ask: "Based on Section 4.2, does this case constitute a violation?"
Agentic AI Workflow: A Multi-Agent Debate setup. One agent acts as "Prosecutor" (arguing a violation), another as "Defense," and a third as "Judge" to reach a consensus based on legal/regulatory precedents.
5. Design (How do we build this?)
Generative AI Workflow: Provide constraints and use SCAMPER prompts to generate 50 distinct design iterations or DSL snippets for a new system component.
Agentic AI Workflow: An Orchestrator-Worker pattern. An "Architect Agent" breaks the design into sub-tasks, delegates "Coder Agents" to write modules, and a "Validator Agent" to run them against requirements.
6. Predictive (What will happen?)
Generative AI Workflow: Use Scenario Prompting. "Given a 5% increase in hardware latency, describe the likely impact on mission-critical software timing over a 24-hour window."
Agentic AI Workflow: A Forecasting Agent feeds real-time telemetry into a simulation model, runs Monte Carlo iterations, and sends a "Risk Alert" agentic action if the probability of failure exceeds a threshold.
7. Ontological (What is this, really?)
Generative AI Workflow: Provide a list of emerging technical terms and ask the model to draft a Taxonomy or "Ontological Map" that defines the hierarchy and relationships between them.
Agentic AI Workflow: A Knowledge Graph Agent scans new literature and documentation, proposes new "nodes" and "edges" to an existing graph, and asks a human for "Verification of Definition" before committing changes.
8. Critical (Who does this serve?)
Generative AI Workflow: Paste a project proposal and ask the AI to "Identify five hidden biases or systemic risks in this plan regarding accessibility or small-business participation."
Agentic AI Workflow: An Audit Team of agents, each assigned a different persona (e.g., Safety Engineer, End User, Auditor). They perform a "Red Team" review of the problem space to surface neglected perspectives.
9. Evaluative (How well does this work?)
Generative AI Workflow: Upload a code repository or document and a Scorecard. The AI populates the scorecard with justifications based on its analysis of the text.
Agentic AI Workflow: A Continuous Compliance Loop. Agents automatically scan every new commit, compare it against safety benchmarks, and "Block" the workflow if the evaluation score drops below the "Flight Ready" threshold.
10. Archetypal (What is the pattern?)
Generative AI Workflow: Describe a recurring organizational failure. Ask the AI: "Which Systems Thinking Archetype (e.g., 'Shifting the Burden') does this match, and what are the known leverage points?"
Agentic AI Workflow: A System Dynamics Agent creates a digital twin of the process, simulates long-term feedback loops, and identifies where "delayed responses" in the workflow are causing oscillating performance.
AI Workflow Comparison Table
| Paradigm | Interaction Style | Best For... | Key Component |
| Generative | Request → Response | Drafting, Summarizing, Ideating | Prompt Engineering |
| Agentic | Goal → Iterative Action | Execution, Integration, Solving | Planning & Tool Use |
Would you like me to develop a Python script or a CrewAI configuration for one of these specific agentic workflows—perhaps the Evaluative one for compliance checking?
This video provides a solid visual overview of how agentic design patterns differ from standard generative models, helping you visualize the transition from prompts to autonomous planning.
Describe how two or more of these workflows could be run sequentially to add value
Running problem-solving workflows in sequence creates a compounded intelligence effect. By chaining these workflows, you move from raw observation to a structured solution, ensuring that the "solution" isn't just a guess but is grounded in data and compliant with standards.
Here are three high-value sequential pairings tailored to complex systems and software engineering.
1. The "Safety Compliance" Sequence
Ontological --> Evaluative --> Agentic Mitigation
This sequence is essential for ensuring that a new system meets rigorous safety standards like NPR 7150.2.
Step 1: Ontological Workflow (Generative AI)
The AI ingest a massive body of standards and your project’s technical specifications. It defines exactly which components of your code are "Class A" (Mission Critical) vs. "Class C" (Support). It creates a Knowledge Graph mapping every software requirement to a specific safety mandate.
Step 2: Evaluative Workflow (Agentic AI)
An Audit Agent takes that Ontological map and scans your codebase. It checks every "Class A" module for compliance (e.g., cyclomatic complexity, unit test coverage). It produces a "Gap Report."
Step 3: Design Workflow (Agentic AI)
A Refactoring Agent takes the Gap Report and suggests specific code changes or drafts the missing safety-critical documentation needed to close those gaps.
2. The "Innovation Pipeline" Sequence
Descriptive --> Archetypal --> Design
This sequence is ideal for a solopreneur looking to solve a recurring market or technical bottleneck using TRIZ principles.
Step 1: Descriptive Workflow (Generative AI)
You feed the AI user feedback, bug reports, and market data. It summarizes the "Current Reality," identifying that users are struggling with a specific latency issue in a quantum simulator.
Step 2: Archetypal Workflow (Generative AI)
The AI analyzes the description and identifies the "System Archetype." It might realize the problem is "Limits to Success"—where the current software architecture can't handle the data volume. It identifies the "Leverage Point" (e.g., moving from synchronous to asynchronous processing).
Step 3: Design Workflow (Agentic AI)
A Prototyping Agent applies TRIZ "Invention Principles" (like Segmentation or The Other Way Round) to generate five architectural blueprints that address the identified leverage point.
3. The "Risk & Resilience" Sequence
Relational --> Predictive --> Causal
This sequence is used for high-stakes engineering where failure is not an option, such as hardware integration in high-humidity environments.
Step 1: Relational Workflow (Agentic AI)
An Analyst Agent pulls historical data on hardware failures and correlates them with environmental sensors (temperature, humidity). It finds a strong link between 85% humidity and specific capacitor failures in Alvin, TX.
Step 2: Predictive Workflow (Generative AI)
Using weather forecasts and mission schedules, the AI predicts a 72% chance of system failure during the next high-humidity cycle in August.
Step 3: Causal Workflow (Agentic AI)
A Testing Agent triggers a controlled stress test in a lab environment (or a simulation) to prove that humidity causes the failure, rather than just being a coincidence. It confirms the root cause, allowing for a targeted hardware fix.
Value Add Summary Table
| Sequence | Primary Goal | Value Added |
| Compliance | Verification | Reduces human error in safety audits and ensures mission readiness. |
| Innovation | Problem Solving | Moves past "band-aid" fixes to address root architectural flaws. |
| Resilience | Prevention | Prevents catastrophic failures by proving risks before they occur. |
Would you like me to create a detailed prompt template for the first step of any of these sequences to get you started?
Are there more?
While the first ten types cover the majority of engineering and research scenarios, there is a final tier of Meta-Problem Statements. These deal with the "problem of the problem"—addressing how we think, how we measure, and how we compare.
Here are five additional types to round out your taxonomy:
11. Normative Problem Statements
These focus on values, ethics, and "what ought to be." Unlike descriptive statements (what is), these address a gap between current reality and a moral or ideal standard.
Focus: Ethical benchmarks, social responsibility, and value alignment.
Examples:
AI Ethics: "To what extent should an autonomous landing system prioritize the preservation of the vehicle over the preservation of secondary experimental payloads?"
Corporate Policy: "How should a low-budget solopreneur balance the use of free 'open' models versus paid 'closed' models when handling sensitive client data?"
Sociology: "What constitutes a 'fair' distribution of high-speed satellite internet for rural Iowa communities compared to urban centers?"
AI Workflows:
Generative: Use Persona-Based Prompting to simulate a "Council of Ethicists" debating the problem from different philosophical frameworks (e.g., Utilitarianism vs. Deontology).
Agentic: An Alignment Agent that reviews project goals against a set of "Value Constraints" and flags any "Normative Drift" where the solution compromises on ethics for efficiency.
12. Exploratory Problem Statements
These are used when a problem is nebulous or poorly understood. They are the "scouts" of the problem-solving world, intended to define the scope rather than find a final solution.
Focus: Scoping, definition, and identifying variables.
Examples:
Quantum Computing: "What are the primary factors preventing the stable use of topological qubits in a high-interference laboratory environment?"
Market Innovation: "What untapped opportunities exist for using laser-etched acrylic in the high-end board game component market?"
Systems Engineering: "Which specific sections of the NASA 'Moon to Mars' architecture are most likely to be impacted by shifts in commercial launch provider pricing?"
AI Workflows:
Generative: Use Recursive Brainstorming. Ask the AI to generate a list of 20 questions about a topic, then pick the 5 most "uncertain" ones and expand them into research sub-themes.
Agentic: A Web-Crawler Agent (using tools like Serper or Brave Search) that gathers the "Lay of the Land" on a new technology and builds a summary report on "What is currently unknown."
13. Methodological Problem Statements
These address the process or tools used to solve a problem. The issue isn't the goal itself, but the way we are trying to get there.
Focus: Accuracy, efficiency of tools, and validity of measurements.
Examples:
Data Science: "Is the current method of using 'synthetic data' for training safety-critical agents creating a 'Reality Gap' that invalidates our test results?"
Software Engineering: "To what degree does our reliance on manual regression testing limit our ability to achieve continuous deployment for Class A software?"
Physics: "Does our current optical setup for measuring wave interference introduce enough vibration to negate the precision of the laser-etching process?"
AI Workflows:
Generative: Use Comparison Prompting. Provide two different methodologies and ask the AI to perform a "Stress Test" analysis on the limitations of each.
Agentic: A Tool-Evaluator Agent that runs the same small task through three different scripts or models, compares the outputs for variance, and identifies which method is the most robust.
14. Comparative Problem Statements
These analyze the strengths and weaknesses of two or more distinct entities, systems, or solutions to determine the "best fit" for a specific context.
Focus: Benchmarking, trade-off analysis, and selection.
Examples:
Hardware: "How does the performance of a local RTX 3090 Ti eGPU setup compare to a cloud-based H100 instance for fine-tuning a Domain-Specific Language (DSL)?"
Compliance: "What are the significant deltas between the European Space Agency (ESA) safety standards and NASA’s NPR 7150.2 regarding software hazard analysis?"
Energy: "In the high-humidity climate of Alvin, TX, which is more cost-effective over 10 years: a traditional central AC or a high-efficiency heat pump system?"
AI Workflows:
Generative: Use Table Synthesis. Provide technical specs for A and B, and ask the AI to generate a "Pros/Cons/Risks" matrix focused on your specific constraints.
Agentic: A Benchmarking Agent that executes the same benchmark suite on two different hardware configurations and provides a side-by-side performance visualization.
15. Theoretical Problem Statements
These deal with abstract concepts and the validity of theories. They ask if our mental models actually reflect the universe.
Focus: Logic, conceptual consistency, and paradigm shifts.
Examples:
Computing Paradigms: "Does the 'Probabilistic Computing' model provide a more efficient path to AGI than the current 'Deterministic Neural Network' model?"
Linguistics: "Can a transformer-based LLM truly understand 'meaning,' or is it simply a sophisticated 'Stochastic Parrot'?"
Physics: "If the 'Many-Worlds Interpretation' of quantum mechanics is correct, what are the implications for how we define 'Information Entropy'?"
AI Workflows:
Generative: Use First-Principles Thinking. Ask the AI to "deconstruct the theory of X and identify any logical leaps or unproven assumptions."
Agentic: A Logic-Checker Agent that takes a theoretical argument, converts it into symbolic logic, and checks for fallacies or inconsistencies using a formal solver.
Sequential Workflow: From "Vague" to "Validated"
You can chain these new workflows together to move from a raw idea to a verified implementation:
Exploratory --> Comparative: First, use an Exploratory agent to find all possible ways to solve a problem (e.g., "Ways to model wave interference"). Then, use a Comparative agent to pick the best one for your specific lab setup.
Methodological --> Evaluative: First, use a Methodological workflow to design a better way to audit NASA documents. Then, run an Evaluative workflow to actually perform the audit using that new method.
Would you like me to focus on one of these—perhaps a Methodological workflow for improving your hazard analysis process—and build a detailed agentic plan for it?
From <https://gemini.google.com/app/> Google Gemini 3.0 Pro (Thinking)
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