DPEE cheat sheet

Ohm's law: V = I·R; power P = V·I = I²R = V²/R. For three-phase balanced loads, P = √3·V_L·I_L·cos φ.

Stress σ = F/A; axial strain ε = ΔL/L; Hooke's law σ = E·ε holds only in the linear-elastic region below yield.

Thermal expansion: ΔL = α·L·ΔT. Restrained expansion stress σ = E·α·ΔT (fully constrained member).

First law for a control volume at steady state: Q̇ − Ẇ = ṁ·[(h₂ − h₁) + ½(v₂² − v₁²) + g(z₂ − z₁)].

Bernoulli (ideal, incompressible, steady): p₁/γ + v₁²/2g + z₁ = p₂/γ + v₂²/2g + h_loss.

Reynolds number Re = ρvD/μ = vD/ν; laminar pipe flow below ~2,300, transitional to ~4,000, turbulent above.

Beam bending: σ = M·y/I and deflection scales with 1/EI; second moment I = b·h³/12 for a rectangle about its centroid.

Heat transfer modes: conduction q = kA·ΔT/L; convection q = hA·ΔT; radiation q = εσA(T_s⁴ − T_surr⁴) with σ = 5.67×10⁻⁸ W/(m²·K⁴).

Material selection driver: specific stiffness E/ρ and specific strength σ_y/ρ; compare Ashby indices rather than absolute values.

Design factor (safety factor) n = failure strength / allowable stress; required n rises with uncertainty, consequence of failure, and non-ductile behavior.

Von Mises equivalent stress for plane stress: σ_vm = √(σx² − σx·σy + σy² + 3τxy²); compare to yield strength.

Fatigue: alternating and mean stresses σ_a = (σ_max − σ_min)/2, σ_m = (σ_max + σ_min)/2; mean stress reduces allowable amplitude (Goodman line).

Stress concentration factor K_t multiplies nominal stress at a geometric discontinuity; fatigue notch factor K_f ≤ K_t.

Tolerance stack-up: worst-case = sum of tolerances; statistical (RSS) = √(Σt_i²) assuming independent, centered distributions.

Buckling: Euler critical load P_cr = π²EI/(K·L)²; K = 1 pinned-pinned, 0.5 fixed-fixed, 0.7 fixed-pinned, 2 fixed-free.

Design verification hierarchy: analysis, then component test, then system test; the verification method must match the requirement's criticality.

Failure modes and effects analysis (FMEA) risk priority number RPN = Severity × Occurrence × Detection; rank mitigations by RPN.

Time value: F = P(1+i)^n; P = F/(1+i)^n; annuity A = P·[i(1+i)^n]/[(1+i)^n − 1].

Net present value: accept independent projects with NPV > 0 at the hurdle rate; among mutually exclusive options choose highest NPV.

Internal rate of return is the i where NPV = 0; IRR ranking can mislead when project scale or timing differs - use incremental analysis.

Payback period ignores cash flows after payback and the time value of money unless discounted; use as a screening, not a decision, metric.

Straight-line depreciation D = (cost − salvage)/life; MACRS uses declining-balance with a mid-year convention and a recovery period set by asset class.

Critical path method: float (slack) = LS − ES = LF − EF; the critical path has zero total float and sets project duration.

Earned value: CV = EV − AC; SV = EV − PV; CPI = EV/AC; SPI = EV/PV; EAC ≈ BAC/CPI when the current cost trend persists.

Risk response categories: avoid, mitigate, transfer, accept (threats); exploit, enhance, share, accept (opportunities).

Order of precedence for a licensed engineer: public health, safety, and welfare first; then client/employer; then the profession; then oneself.

Seal and signature certify competence and responsibility for the work; sealing work outside one's competence is a violation even if technically correct.

Conflict of interest exists when a secondary interest could improperly influence professional judgment; disclose in writing and recuse where required.

Confidentiality: client information is confidential except where disclosure is required by law, safety, or legal process.

Bribery and facilitation payments: gifts or payments intended to influence decisions are prohibited; nominal hospitality must be transparent and within policy.

Sustainable development framing: meet present needs without compromising future generations' ability to meet theirs (Brundtland definition).

Regulatory hierarchy: statute → regulation → standard/code → guidance; a standard incorporated by reference in a regulation becomes enforceable.

Whistleblowing escalation: report internally first unless imminent danger or the internal channel is ineffective; document contemporaneously.

Hierarchy of controls, most to least effective: elimination, substitution, engineering controls, administrative controls, PPE.

Hazard vs risk: a hazard is a source of harm; risk combines likelihood and severity of harm from that hazard.

Risk score = likelihood × severity; ALARP means reducing risk until further reduction is grossly disproportionate to the benefit.

Permit-to-work systems govern hot work, confined space entry, lockout/tagout, and excavation; each requires hazard-specific controls and authorization.

Confined space: test atmosphere before and during entry; oxygen-deficient below 19.5% O₂, oxygen-enriched above 23.5%.

Lockout/tagout isolates hazardous energy (electrical, mechanical, pneumatic, hydraulic, thermal, gravitational, stored); verify zero energy state.

Hierarchy of waste management: prevent, reduce, reuse, recycle, recover energy, dispose.

Environmental aspects and impacts: an aspect is an activity or product that interacts with the environment; an impact is the resulting change.

PDCA: Plan (define and analyze), Do (pilot), Check (measure results), Act (standardize or adjust).

DMAIC: Define, Measure, Analyze, Improve, Control - the Six Sigma improvement cycle for existing processes.

Statistical process control: control limits at μ ± 3σ describe the process's natural variation, not specification limits.

Cp = (USL − LSL)/(6σ); Cpk = min[(USL − μ), (μ − LSL)]/(3σ); Cpk < 1 means the process mean is too close to a limit.

Process capability requires a stable, in-control process; capability indices are meaningless while special-cause variation is present.

Seven basic quality tools: check sheet, histogram, Pareto chart, cause-and-effect (fishbone) diagram, scatter diagram, control chart, flowchart.

Pareto principle: roughly 80% of effects come from 20% of causes; prioritize the vital few.

Cost of quality: prevention + appraisal (cost of good quality) vs internal + external failure (cost of poor quality); failure costs usually dominate.

Tuckman stages: forming, storming, norming, performing, adjourning; conflict peaks in storming and is resolved by clarifying roles and goals.

RACI assigns exactly one Accountable per task; Responsible does the work, Consulted gives input, Informed is notified.

Active listening: paraphrase the content, reflect the feeling, then ask an open question before responding.

Situational leadership matches style to follower readiness: directing (low competence/high commitment), coaching, supporting, delegating.

Feedback model: describe observed behavior, state its impact, request or propose a specific change - avoid judgments about character.

Technical writing for decisions: lead with the recommendation, then evidence, then assumptions and risks; keep one idea per paragraph.

Conflict modes (Thomas-Kilmann): competing, collaborating, compromising, avoiding, accommodating; collaborating needs time and trust.

Stakeholder communication plan: audience, message, channel, frequency, owner, and escalation path for each stakeholder group.

Digital twin: a synchronized virtual model of a physical asset, fed by sensor data, used for simulation, prediction, and optimization.

Sensor data pipeline: sense → condition/convert → transmit → store → analyze → act; sample above 2× the highest frequency of interest (Nyquist).

Model-based definition (MBD) and digital thread link design, manufacturing, and service data to a single authoritative model.

BIM/digital delivery maturity levels: 0 (paper), 1 (2D/3D CAD), 2 (federated models with separate discipline files), 3 (integrated shared model).

Machine learning types: supervised (labeled data), unsupervised (structure discovery), reinforcement (reward-driven sequential decisions).

Data governance: ownership, stewardship, quality, lineage, and access control must be defined before analytics results are trusted.

Cybersecurity for OT/ICS: segment IT and OT networks, apply least privilege, patch on a validated schedule, and monitor for anomalous control traffic.

Edge computing reduces latency and bandwidth by processing near the sensor; cloud suits aggregation, long-term storage, and cross-site analytics.

Additive manufacturing: design for the process - support structures, anisotropy of layer orientation, and post-processing affect mechanical properties.