HKIE Professional Assessment - Manufacturing, Industrial & Systems Discipline cheat sheet

Machining time for a turning pass: T = L / (f × N), where L is the tool travel length in mm, f the feed in mm/rev, and N the spindle speed in rev/min.

Taylor's tool life equation: V × T^n = C. Doubling cutting speed reduces tool life by the factor 2^(1/n); typical n is 0.1-0.15 for HSS and 0.2-0.4 for carbide.

Casting: Chvorinov's rule gives solidification time t = B × (V/A)^2, where V/A is the volume-to-surface-area ratio and B is a mould constant.

Sheet metal: minimum bend radius is commonly expressed as a multiple of sheet thickness (roughly 1t for soft aluminium, 1-2t for mild steel, 2-3t for hard alloys); bend allowance = (π/180) × (R + K×t) × θ.

Welding: heat input per unit length H = (η × V × I) / v, with η the arc efficiency (about 0.8 for MMAW, 0.85 for MIG, 0.6-0.7 for TIG), V volts, I amps, v travel speed in mm/s.

Rolling force estimate: F = σ̄ × w × √(R × Δh), where σ̄ is mean flow stress, w strip width, R roll radius and Δh the draft.

Injection moulding: clamp force must exceed cavity pressure × projected area; typical cavity pressures are 300-800 bar, so a 100 cm² projected area can need 30-80 tonnes of clamp.

Process capability of a manufacturing process is judged against tolerance, not against specification alone: Cp = (USL - LSL) / (6σ) and Cpk = min[(USL - μ), (μ - LSL)] / (3σ).

Little's Law: WIP = throughput × flow time. It holds for any stable system regardless of arrival and service distributions.

Economic order quantity: EOQ = √(2DS / H), where D is annual demand, S order cost per order and H holding cost per unit per year.

Linear programming: a basic feasible solution is optimal when all reduced costs satisfy the optimality condition (c_j - z_j ≥ 0 in minimisation for non-basic variables). Sensitivity analysis reads shadow prices from the final tableau.

Assignment problem: solved by the Hungarian method in O(n³); the dual variables give the opportunity cost of forcing a non-optimal assignment.

Queueing: for M/M/1, utilisation ρ = λ/μ, average number in system L = ρ/(1-ρ), and average wait W = 1/(μ-λ). For M/M/c, use the Erlang C formula for the probability of waiting.

Work measurement: standard time = observed time × performance rating × (1 + allowance fraction). Allowances typically cover personal, fatigue and delay (PFD) elements.

Transportation and transhipment problems: the North-West Corner or Vogel's approximation gives a starting solution; the MODI method tests optimality via opportunity costs.

Learning curve: the unit time for the nth unit is T_n = T_1 × n^b, where b = log(learning rate)/log 2; an 80% curve gives b ≈ -0.322.

The V-model pairs each decomposition level (requirements, architecture, detailed design) with a verification or validation level (unit, integration, system, acceptance).

Requirements must be verifiable: each requirement needs a test method (inspection, analysis, demonstration or test) and a traceable source in the stakeholder needs baseline.

Interface management: an interface control document (ICD) fixes physical, electrical, data and protocol characteristics between two configuration items; changes require joint configuration control.

Functional analysis allocates functions to physical components; the functional flow block diagram and N² diagram expose interfaces and coupling before integration.

Verification answers 'did we build it right' against the specification; validation answers 'did we build the right thing' against the user need. Both must be planned, not discovered at the end.

Configuration management has four activities: identification, control, status accounting, and audit (functional and physical configuration audit).

Reliability block diagrams: series R = Π R_i; parallel (active redundancy) R = 1 - Π(1 - R_i). These are distinct from fault trees, which are deductive.

Integration sequence should follow risk: integrate the highest-risk or least-understood interfaces first, so failures surface early when rework is cheapest.

Control chart constants: for X̄-R charts with subgroup n, UCL = X̄ + A2 R̄ and LCL = X̄ - A2 R̄; A2 is 1.88 at n=4, 0.58 at n=10.

Western Electric rules flag: one point beyond 3σ; two of three beyond 2σ; four of five beyond 1σ; eight consecutive on one side of the centre line.

Process capability indices: Cp measures potential capability, Cpk measures actual centring. Cpk = (1 - k) × Cp, where k = |target - μ| / (tolerance/2).

Six Sigma target of Cpk = 1.5 corresponds to about 3.4 defects per million opportunities when a 1.5σ long-term shift is assumed.

PDCA and DMAIC are improvement cycles: DMAIC (Define, Measure, Analyse, Improve, Control) is the Six Sigma project structure and ends with a control plan.

FMEA: risk priority number RPN = severity × occurrence × detection, each on a 1-10 scale; action priority tables (AIAG-VDA) now supplement or replace raw RPN ranking.

Acceptance sampling: OC curve plots probability of acceptance against lot fraction defective; producer's risk α is the chance of rejecting a good lot at AQL, consumer's risk β the chance of accepting a bad lot at LTPD.

ISO 9001:2015 is built on seven quality management principles including process approach and risk-based thinking; certification is by an accredited third-party body, not by the standard itself.

Measurement uncertainty: combined standard uncertainty u_c = √Σ(c_i × u_i)², with sensitivity coefficients c_i; expanded uncertainty U = k × u_c, with k = 2 for roughly 95% coverage.

Gauge R&R: %GRR = (GRR / tolerance) × 100 is compared to 10% (acceptable), 10-30% (conditional), above 30% (unacceptable). Also compare against process variation (6σ).

Repeatability is variation of one appraiser with one gauge on one part; reproducibility is variation between appraisers or setups.

Calibration traceability requires an unbroken chain of comparisons to a national or international standard, each link with stated uncertainty.

Reliability function R(t) = exp(-λt) for constant failure rate; MTBF = 1/λ. For repairable systems availability A = MTBF / (MTBF + MTTR).

Weibull distribution: F(t) = 1 - exp[-(t/η)^β]; β < 1 indicates infant mortality, β = 1 random failures, β > 1 wear-out. Plot ln[-ln R(t)] against ln t to estimate β from slope.

Series system reliability R_s = Π R_i, so the weakest item dominates; adding redundancy at the lowest level gives the greatest reliability gain per unit cost.

Accelerated life testing uses the Arrhenius model for temperature: rate ∝ exp(-Ea/kT); the acceleration factor between two temperatures is exp[(Ea/k)(1/T_use - 1/T_stress)].

Degrees of freedom: a rigid body in space has six; a serial robot needs at least six actuated joints for arbitrary position and orientation. Fewer means restricted orientation.

Denavit-Hartenberg convention uses four parameters per link (a, α, d, θ) to build the homogeneous transform between successive frames.

Singularities occur where the Jacobian loses rank; at a wrist singularity joint rates become unbounded, so trajectories must avoid them or use damped least squares.

Safety: ISO 10218-1/-2 governs industrial robots and ISO/TS 15066 covers collaborative operation, including power and force limiting with body-region-specific thresholds.

PLC scan cycle is read inputs, execute program, update outputs; scan time adds deterministic latency, and safety functions must use certified safety PLCs to IEC 61508/ISO 13849 (PL d or e).

OEE = Availability × Performance × Quality, where availability = run time / planned production time, performance = (ideal cycle time × count) / run time.

Industry 4.0 reference architecture (RAMI 4.0) layers: asset, integration, communication, information, functional, business. OPC UA is the common interoperability standard.

Machine vision: resolution needed ≈ field of view / smallest feature, and at least 2-3 pixels across a defect are typically required for reliable detection.

MRP logic: gross requirements → net requirements = gross - on hand - scheduled receipts → planned order releases offset by lead time. It depends on a valid MPS and accurate BOM.

Safety stock under uncertainty: SS = z × σ_d × √L for demand variability only, or SS = z × √(L × σ_d² + d² × σ_L²) when both demand and lead time vary.

Reorder point ROP = average demand × lead time + safety stock. Continuous review (Q,R) versus periodic review (R,S) differ in when the order is placed, not in the underlying balance.

Bullwhip effect causes: demand forecast updating, order batching, price fluctuation, rationing and shortage gaming. Remedies include information sharing, EDLP and vendor-managed inventory.

ABC classification by annual usage value: class A typically 10-20% of items but 70-80% of value; class C the reverse. Control effort follows the class.

Incoterms 2020: EXW places minimum obligation on the seller; DDP maximum. FOB and CIF apply only to sea and inland waterway transport.

Incoterms do not transfer title and do not replace the contract of sale; they allocate costs, risks and customs duties at named places.

Capacity planning hierarchy: sales and operations planning → master production schedule → rough-cut capacity planning → capacity requirements planning (CRP).

Net present value: NPV = Σ C_t / (1 + i)^t over t = 0..n. Accept independent projects with NPV > 0; for mutually exclusive projects choose the highest positive NPV.

Internal rate of return is the discount rate making NPV zero; IRR can give multiple roots when cash flows change sign more than once, so NPV is preferred for ranking.

Capital recovery factor: A = P × [i(1+i)^n] / [(1+i)^n - 1]. Use it to convert a present sum into an equivalent annual cost for comparison of alternatives.

Depreciation: straight line = (cost - salvage)/life; declining balance = book value × rate; MACRS uses statutory class lives and half-year convention.

Critical path method: the critical path has zero total float; total float = LS - ES = LF - EF. A delay on the critical path delays project completion by the same amount.

Earned value: CPI = EV/AC, SPI = EV/PV; EAC = BAC/CPI when current cost performance is expected to continue. SPI below 1 means behind schedule.

Risk treatment options per ISO 31000: avoid, reduce (mitigate), transfer, accept. Residual risk must be documented and accepted by an accountable owner.

Monte Carlo simulation for project risk requires three-point estimates (optimistic, most likely, pessimistic) and assumed distributions; it produces a probability distribution of completion, not a single date.

Hierarchy of controls in descending effectiveness: elimination, substitution, engineering controls, administrative controls, personal protective equipment. PPE is the last line, not the first.

Noise: daily exposure action values under typical Hong Kong and UK-style regimes are 80 dB(A) for action and 85 dB(A) for mandatory hearing protection; a 3 dB increase doubles sound energy.

Hand-arm vibration: exposure action value 2.5 m/s² A(8) and limit value 5 m/s² A(8) under the EU Physical Agents (Vibration) Directive; assess with a vibration magnitude and trigger time.

COSHH-style assessment ranks risk as hazard severity × likelihood of exposure; substitute the substance or enclose the process before relying on respiratory protection.

Machine guarding: ISO 13857 gives safety distances to prevent reaching hazardous zones; ISO 13849 determines required performance level (PLr) from risk graph.

Environmental: ISO 14001:2015 requires identification of environmental aspects and compliance obligations, with objectives and a documented operational control regime.

Waste hierarchy: prevent, reuse, recycle, recover (including energy), dispose. Hong Kong's producer responsibility schemes cover plastics, waste electrical and electronic equipment and glass containers.

Energy: specific energy consumption (kWh per unit of output) is the standard metric for factory efficiency; ISO 50001 provides the energy management system framework.

HKIE membership and the professional assessment are governed by the Institution's constitution and assessment regulations; the title 'professional engineer' is not a protected title in Hong Kong, but corporate membership is the recognised benchmark.

Registration as a Registered Professional Engineer (RPE) is administered by the Engineers Registration Board under the Engineers Registration Ordinance (Cap. 409); registration requires Corporate Membership of HKIE and relevant experience.

The Factories and Industrial Undertakings Ordinance (Cap. 59) and its subsidiary regulations (including the Safety Management Regulation and the General Duties provisions) place duties on proprietors and contractors to ensure safety of employees and others.

The Occupational Safety and Health Ordinance (Cap. 509) imposes a general duty on every employer to ensure, so far as reasonably practicable, the safety and health at work of employees.

The Employees' Compensation Ordinance (Cap. 282) requires employers to hold valid employees' compensation insurance and to report accidents causing incapacity to the Labour Department within the prescribed period.

Construction sites are regulated by the Construction Sites (Safety) Regulations; factories by the Factories and Industrial Undertakings Regulations. Manufacturing premises fall under both the FIUO framework and OSHO.

The Personal Data (Privacy) Ordinance (Cap. 486) has six data protection principles; employee monitoring, CCTV and biometric timekeeping must satisfy DPP1 (lawful and fair collection) and be proportionate.

Professional ethics: declare conflicts of interest, protect confidential information, sign only work within competence, and refuse to certify work not personally verified. Whistleblowing on serious safety risk overrides employer loyalty.