IPI/BIV Aptitude Test cheat sheet

A closed control loop consists of a controller, actuator, plant/process, and sensor with feedback; the manipulated variable u(t) is derived from the error e(t) = setpoint − measured value.

PID control law: u(t) = Kp·e(t) + Ki·∫e dt + Kd·de/dt; in parallel form Ki and Kd are independent gains, in standard form the integral time Ti = Kp/Ki and derivative time Td = Kd/Kp.

Steady-state error of a proportional controller on a first-order plant is nonzero; an integral term removes offset at the cost of reduced phase margin.

A plant pole in the right half-plane makes the open-loop system unstable; stability of the closed loop is judged from the roots of 1 + G(s)H(s) = 0.

Nyquist criterion: closed-loop stability requires Z = N + P, where P is open-loop right-half-plane poles and N is the number of clockwise encirclements of −1.

Gain margin is the factor by which loop gain can rise before instability; phase margin is the additional phase lag at the gain crossover frequency before the −180° point is reached.

First-order step response reaches 63.2 % of final value at one time constant τ; settling to ±2 % takes about 4τ.

Sampling theorem: the sample rate must exceed twice the highest signal frequency; the discrete equivalent of an integrator is T·z/(z−1) under backward/forward Euler or Tustin transformation.

Case handling sequence: capture the symptom and boundary conditions, reproduce the fault, isolate cause, implement the fix, verify against the specification, and document the outcome.

Change control rule: no modification of a running plant without a documented change request, risk assessment, rollback plan, and defined acceptance test.

Root-cause analysis distinguishes symptom, immediate cause, and systemic cause; correcting only the symptom leaves the systemic cause active.

Fault isolation by bisection: split the signal chain at its midpoint, verify the signal there, and halve the remaining suspect section each iteration.

Escalation trigger: escalate when the fault exceeds the technician's authorization, affects safety functions, or when the agreed diagnosis time budget is exhausted.

Measurement validity check: verify sensor calibration, lead polarity, and range setting before interpreting an unexpected reading as a process fault.

Handover must contain current state, open actions, risks, and the last verified measurement, so the next shift can act without repeating diagnostics.

Documentation standard: record date, observer, plant state, measured values with units, instrument used, and conclusion, so the record is reproducible.

Technical installations require conformity with applicable safety regulations; the operator bears responsibility for safe operation, while the manufacturer bears product-safety responsibility.

Personal data processing requires a legal basis: consent, contract, legal obligation, vital interest, public task, or legitimate interest, with purpose limitation and data minimization.

Data subjects hold rights to access, rectification, erasure, restriction, portability, and objection; requests must be answered within the statutory deadline.

Confidentiality obligations survive termination of the employment or service relationship; disclosure requires authorization or a legal duty.

Occupational safety duties: risk assessment, instruction of personnel, provision of protective equipment, and documentation of instruction dates and content.

Liability for defective work depends on whether a contract of service (success owed) or contract for services (activity owed) exists; the distinction governs warranty and acceptance.

Incident reporting: safety-relevant events must be reported to the responsible authority within the prescribed period and recorded internally regardless of reporting duty.

Retention rules: technical records, test reports, and training evidence must be kept for the statutory period and made available to auditors on request.

PDCA cycle: plan the change with a measurable target, do it on a limited scope, check against the target, act by standardizing or reverting.

Hypothesis-driven diagnosis: state the hypothesis, predict the observable, test it, and record whether the prediction held; discard hypotheses that fail.

Measurement uncertainty: report result ± expanded uncertainty with coverage factor k and state the confidence level; a single reading without uncertainty is not a valid comparison.

Design of experiments: vary one factor at a time for screening, use factorial designs when interactions are suspected, and randomize run order to avoid drift bias.

FMEA ranks failure modes by risk priority from severity, occurrence, and detection; the highest product is addressed first.

Statistical process control: a process is in control when points lie within control limits without runs or trends; control limits are not specification limits.

Traceability: every result must be linkable to instrument, calibration status, method version, operator, and timestamp.

Peer review rule: independent verification of a critical calculation or safety-relevant setting by a second qualified person before release.

Active listening technique: paraphrase the client's statement, ask an open question, then confirm the shared understanding before proposing a solution.

Feedback rule: describe observable behavior and its effect, not the person; separate observation from interpretation.

Advisory structure: situation, options with trade-offs, recommendation with rationale, and the decision the client must make.

Informed consent for a technical recommendation requires disclosing the alternatives, the risks of each, and the consequence of doing nothing.

Escalating message format: state impact, urgency, what is already done, and what decision is required, in that order.

Non-technical audience rule: lead with the consequence for the client, then the mechanism; define each technical term at first use.

Conflict handling: separate the factual disagreement from the relationship level, and resolve the factual level with shared data first.

Written confirmation: after a verbal agreement, restate scope, deadline, responsibilities, and open points in writing to create a common record.

Integrity rule: report data as measured; adjusting, omitting, or selectively presenting results to support a desired conclusion is misconduct.

Conflict of interest must be disclosed before advising; a financial or personal interest in the recommended option disqualifies the adviser from deciding alone.

Competence boundary: accept only tasks within verified qualification; state the limit and refer to a qualified party when outside it.

Safety over schedule: when a safety requirement conflicts with a delivery date, the safety requirement prevails and the conflict is escalated, not resolved silently.

Confidentiality and data protection apply to client information even after the engagement ends, unless disclosure is legally required.

Independence of testing: the person who performed the work should not be the sole verifier of its acceptance where independence is required.

Whistleblowing threshold: a serious risk to safety, health, or law that cannot be resolved internally is reported to the designated body, with documented facts.

Audit readiness: quality records must be contemporaneous, legible, attributable, and retrievable; reconstructed records after the fact undermine credibility.