Unit 2: Problem identification and formulation

Problem formulation is the stage of research where a vague area of interest is narrowed into a precise, investigable statement. It converts curiosity into a testable proposition and determines the entire downstream design.

• Governing principle: A good problem is researchable (data can be gathered), significant (fills a real gap), and feasible (bounded by time, cost, and access).
• Sequence assumed: broad topic → literature survey → gap → research question → problem statement → hypothesis → plan (timeline).
• FINER criteria: a well-formed problem is Feasible, Interesting, Novel, Ethical, and Relevant.
• Convention: the problem is described in the present tense as a deficiency in existing knowledge or practice, never as a proposed solution.

II. The Research Question

From topic to a single answerable query.

A. Definition and function

A research question is the specific interrogative sentence the study sets out to answer.

• Role: it operationalises the topic — "battery degradation" becomes "How does charge rate affect the cycle life of Li-ion 18650 cells at 25 °C?"
• Scope control: it fixes the population, variable(s), and context, thereby bounding data collection.
• Types:
  • Descriptive: what is happening (e.g., prevalence of a fault).
  • Relational/correlational: whether two variables move together.
  • Causal: whether X produces a change in Y.

B. Criteria for a strong question — SMART/FINER

A question earns its place when it is measurable and bounded.

• Specific: names one phenomenon, not several.
• Measurable: admits a quantifiable or codable answer.
• Achievable: answerable with available instruments and sample.
• Relevant: tied to a documented gap.
• Time-bound: answerable within the project window.

III. Literature Survey and Research Gap Identification

Mapping what is known to expose what is not.

A. Purpose and principle

The survey systematically reviews prior work to locate the frontier of knowledge and justify a new study.

• Function: avoids duplication, supplies methods and instruments, and establishes theoretical grounding.
• Types of review:
  • Narrative: thematic overview of a field.
  • Systematic: protocol-driven, reproducible search with inclusion/exclusion criteria.
  • Meta-analysis: statistical pooling of quantitative results across studies.

B. Literature survey

The survey proceeds from broad to specific and is organised thematically, not source-by-source.

• Steps: define keywords → search databases → screen abstracts → read full texts → extract and tabulate findings.
• Synthesis matrix: a table with rows = papers and columns = author/year, method, sample, findings, limitations — this reveals patterns and contradictions.
• Citation chaining: backward (references of a paper) and forward (papers citing it) to trace a topic's lineage.

C. Research gap identification

A research gap is an unanswered question or unexamined area the literature reveals.

• Common gap types:
  • Knowledge gap: a relationship never studied.
  • Methodological gap: prior work used weak or narrow methods.
  • Population/context gap: results untested in a new setting (e.g., a model validated in the West, untested locally).
  • Contradictory-evidence gap: studies disagree and need reconciliation.
• Signal phrases to hunt for: "further research is needed", "little is known about", "future work should" in Discussion sections.

IV. Problem Identification

Recognising the deficiency worth solving.

A. Definition

Problem identification is the act of pinpointing a specific difficulty, discrepancy, or unmet need that research can address.

• Trigger sources: observed anomalies, technological change, stakeholder complaints, policy shifts, and the literature gap itself.
• Discrepancy model: a problem exists where there is a gap between the current state and the desired state (e.g., current solar panel efficiency 18 % vs. desired 25 %).

B. Techniques and screening

The identified problem must be validated before commitment.

• Root-cause tools: the 5 Whys and the Ishikawa (fishbone) diagram separate symptoms from causes.
• Screening questions: Is it real? Is it new? Is it mine to solve within constraints?
• Feasibility check: measure against time, funding, equipment, ethics clearance, and data access.

V. Constructing the Problem Statement as per Industrial and Societal Needs

Writing the deficiency down with justification.

A. Anatomy of a problem statement

A problem statement is a concise paragraph that names the problem, its context, its consequences, and the proposed remedy scope.

• Four moves:
  • Ideal/context: what should be happening.
  • Reality: the current shortfall, with evidence.
  • Consequence: the cost of leaving it unsolved.
  • Proposal: what the study will investigate.
• Example core: "Municipal water networks lose an estimated 30 % of supply to undetected leaks; existing acoustic sensors miss slow leaks, causing shortages — this study develops a pressure-transient detection method."

B. Industrial and societal needs

The two demand drivers are contrasted because they shape the problem's framing differently.

1. Industrial need: driven by profitability, efficiency, reliability, and compliance.
   • Anchor: reduce machine downtime, cut defect rate, meet an ISO/BIS standard, lower unit cost.
   • Metric-led: stated in throughput, yield, or cost per unit.
2. Societal need: driven by welfare, safety, equity, and sustainability.
   • Anchor: clean water access, affordable healthcare diagnostics, pollution reduction, aligned with UN Sustainable Development Goals.
   • Impact-led: stated in beneficiaries reached, emissions cut, or risk lowered.

• Alignment: the strongest statements serve both — e.g., an energy-efficient motor cuts a firm's cost and national emissions.

VI. Use of Databases, Search Engines and Research Gateways

Tools that supply and refine the literature.

A. Databases

Curated repositories index peer-reviewed and indexed literature with rich metadata.

• Examples: Scopus and Web of Science (citation databases), IEEE Xplore, PubMed, ScienceDirect, ACM Digital Library.
• Advantage: controlled quality, citation counts, and impact metrics (h-index, impact factor).

B. Search engines

General and scholarly engines cast a wide net across sources.

• Google Scholar: free, broad coverage, "cited by" and "related articles" links.
• Boolean operators: refine results precisely.

("machine learning" OR "deep learning") AND "leak detection"
AND NOT "gas pipeline"

• Field filters: intitle:, quotation marks for exact phrases, and date-range limits sharpen recall vs. precision.

C. Research gateways

Gateways aggregate access, profiles, and full texts.

• Examples: ResearchGate and Academia.edu (author networks, PDF requests), DOAJ (open-access journals), Shodhganga (Indian theses), CORE.
• Persistent identifiers: the DOI uniquely locates a paper; ORCID disambiguates authors.

VII. Framing of Timeline / Gantt Chart

Scheduling the research within its window.

A. Purpose and principle

A timeline breaks the project into tasks with start and end dates to manage feasibility.

• Work breakdown: decompose into phases — review, design, data collection, analysis, writing.
• Milestones: dated checkpoints (e.g., "proposal approved", "data complete").
• Dependencies: analysis cannot start before data collection ends (finish-to-start link).

B. Gantt chart construction

A Gantt chart is a horizontal bar chart plotting tasks (rows) against time (columns).

• Elements: each bar's length = task duration; overlap shows parallel tasks; a vertical marker shows "today".
• Example (project weeks):

Task                Wk1 Wk2 Wk3 Wk4 Wk5 Wk6
Literature review   ███ ███ ██
Problem formulation      ██  ██
Data collection              ███ ███
Analysis                          ██ ██
Report writing                       ██ ███

• Critical path: the longest dependent chain; a slip here delays the whole project.

VIII. Hypothesis — Null and Alternate

Turning the question into a testable statement.

A. Definition and criteria

A hypothesis is a tentative, testable statement predicting the relationship between variables.

• Requirements: it must be falsifiable, state variables clearly, and be derived from theory or the gap.
• Variables: the independent variable is manipulated; the dependent variable is measured.

B. Null and Alternate hypotheses

The two are stated as a complementary pair, one asserting no effect and one asserting an effect.

1. Null hypothesis (H₀): states there is no effect, difference, or relationship — the default assumed true until evidence rejects it.
   • Form: H₀: μ₁ = μ₂ (two population means are equal).
2. Alternate hypothesis (H₁ or Hₐ): states there is an effect; accepted only if H₀ is rejected.
   • Directional (one-tailed): H₁: μ₁ > μ₂.
   • Non-directional (two-tailed): H₁: μ₁ ≠ μ₂.

• Decision rule: compare the p-value to significance level α (commonly 0.05); if p ≤ α, reject H₀.
• Errors:
  • Type I (α): rejecting a true H₀ — a false positive.
  • Type II (β): failing to reject a false H₀ — a false negative; power = 1 − β.

C. Worked example

A firm claims a new coating raises mean tool life above the current 100 hours.

H₀: μ = 100   (coating makes no difference)
H₁: μ > 100   (coating increases life)
Sample: n = 36, x̄ = 104 h, s = 9 h, α = 0.05
z = (x̄ − μ) / (s / √n) = (104 − 100) / (9 / 6) = 4 / 1.5 = 2.67

• Interpretation: z = 2.67 exceeds the one-tailed critical value 1.645, so p < 0.05 — reject H₀ and conclude the coating significantly extends tool life.