PE Industrial and Systems Cheat Sheet

Systems Engineering

Not published of exam
14–21 items; percentages not fixed Markov, V&V, Value & CPM Systems & Queueing Picker Verification vs Validation

Facilities Engineering and Planning

Not published of exam
Layouts, Space & Location Material Handling, OSHA & Present Cost Facility Layout & Sizing Picker Process vs Fixed-Position Layout

Operations Engineering

Not published of exam
Forecasting, EOQ & Reorder Point MRP, Scheduling, Break-Even & ABC Inventory & Operations Picker EOQ vs Reorder Point

Work Design

Not published of exam
Methods, Line Balance & Time Study Ergonomics, OSHA Noise & Safety Work Design & Ergonomics Picker Anthropometric Reach vs Clearance

Quality Engineering

Not published of exam
SPC, Capability & Acceptance Sampling DOE, FMEA, Reliability & Maintenance Quality & Reliability Picker Control Limits vs Spec Limits

Quick Facts

Items 85, including unscored pretest items
Answering Time 8.5 hours; appointment 9.5 hours
Official Domain Counts 14–21 items in each of five
Passing Standard Unpublished scaled-score standard; pass/fail results
References Provided searchable handbook; no design standards
Next Listed Administration 30 September 2027; guide page 17
NCEES Exam Fee $400; board charges may apply
Eligibility Board decides; exam passage ≠ licensure
Percentage Weights Not fixed; use published item ranges

Little's Law Boundary Rule SY

Average WIP L equals throughput lambda times flow time W
L: average system inventory λ: stable throughput rate W: total time in system

Verification vs Validation SY

Verification

Meets specified design requirements
Checks built system against blueprint
Can pass while missing user-need

Validation

Satisfies real stakeholder operational needs
Tested in intended use environment
Confirms right system was built
Spec compliance vs stakeholder need

Systems & Queueing Model Picker SY

Independent Poisson arrivals; exponential service times → Steady-state single-server, infinite-buffer model ( λ < μ; stable FCFS system )
Throughput and flow time known → Little’s Law: L = λ × W ( Stable averages; same boundary and units )
Serial stations have unequal capacities → Smallest capacity gives ideal throughput ceiling ( Variability, starvation, blocking reduce achieved output )
Translating customer needs to specs → Build QFD House of Quality ( Voice of customer )
Checking ≤ constraint unused resource → Compute LP slack variable ( Zero means binding )

QFD, LP, Queueing & Little's Law SY

Pareto Chart Ranks largest contributors to problem
QFD House of Quality Translates customer voice to specs
LP Slack Nonnegative unused capacity for ≤ constraints
M/M/1 Mean Queue Wait Wq = λ÷[μ(μ−λ)] λ < μ; infinite-buffer, single-server
Little's Law Stable matching boundary: L = λW
Serial Line Bottleneck Ideal upper bound: smallest station capacity

Markov, V&V, Value & CPM SY

Markov Property Next state depends on present
System Verification Checks conformance to specified requirements
System Validation Checks stakeholder needs in use
Value Engineering Lower cost while preserving functions
Unconstrained CPM Duration Longest precedence path sets finish
Domain Question Range 14-21 questions per NCEES domain

Layouts, Space & Location FA

Process Layout Groups similar machines; low-volume high-variety
Fixed-Position Layout Stationary product; resources move in
Storage Footprint Pallet area plus aisle clearances
Center of Gravity Weighted coordinate heuristic; not universal optimum
Required Machine Count Ceil workload ÷ effective available machine-time
Weighted Site Score Sum weight times criterion score

Material Handling, OSHA & Present Cost FA

Forklift Load Center Forward center increases overturning moment
OSHA 1910.176 Aisle Rule Safe clearance, clear, marked passageways
Present Cost Discounting Discount future costs to base-date
Life-Cycle Costing Include capex, opex, maintenance, disposal
Handling Device Selection Match load, route, layout, conditions
Unit Load Stability Check weight, size, center position

Core MRP Inputs OP

Master Schedule, Bill of Materials, Inventory Records drive MRP
MPS: end-item timing BOM: component structure Inventory: on-hand and scheduled

Facility & Inventory Model Picker OP

Low-volume high-variety routing flexibility needed → Select functional process layout ( Group similar machines )
Product too large to move → Select fixed-position layout ( Bring tools to job )
Steady demand; instantaneous replenishment; no shortages → EOQ with fixed order/holding costs ( No discounts; matching demand/holding periods )
Setting continuous-review order trigger level → Add lead-time demand and safety-stock ( Use inventory position )
Stationary demand without trend/seasonality → Use simple exponential smoothing ( Weight actual and forecast )

Forecasting, EOQ & Reorder Point OP

Simple Exponential Smoothing F_next = αA_current + (1−α)F_current
Mean Absolute Deviation Average absolute forecast error magnitude
Basic EOQ Formula √(2DS/H); matching periods
Reorder Point Lead-time demand plus safety stock
Inventory Position On-hand plus on-order minus backorders
Cross-Docking Consolidate inbound-to-outbound with minimal storage

MRP, Scheduling, Break-Even & ABC OP

Core MRP Inputs MPS, BOM, and inventory records
SPT Sequencing Rule All released; nonpreemptive single-machine completion-time minimum
Break-Even Volume Fixed cost over unit contribution-margin
Ordinary Annuity PV Discount year-end cashflows to present
Activity-Based Costing Pool cost over total driver-units
Contribution Margin Unit price minus variable cost

Time Study Sequence WO

Observed × rating = normal; standard = normal/(1−A)
NT = OT × Rating ST = NT / (1-A) A: fraction of total time

Anthropometric Reach vs Clearance WO

Reach Design

Accommodates smaller-reach users
Uses lower-percentile limb dimensions
Keeps controls within easy grasp

Clearance Design

Accommodates larger-body users
Uses upper-percentile body dimensions
Includes clothing and gear allowance
Small reaches; large fits through

Work Design & Ergonomics Picker WO

Allowance given as total-time fraction → Divide normal time by 1-minus-A ( Not multiplied by 1+A )
Sizing minimum stations or machines → Round fractional count upward ( Check precedence separately )
8-hour TWA noise hits 85 dBA → Start OSHA hearing conservation program ( 50% noise dose )
Computing OSHA DART incidence rate → Multiply cases by 200,000 hours ( Divide by employee-hours )

Methods, Line Balance & Time Study WO

Man-Machine Chart Shows concurrent work and idle-time
Theoretical Min Stations Ceiling of work-content over cycle-time
Normal Time Observed time times performance rating
Standard Time NT÷(1−A) A: allowance fraction of total time
Cumulative-Average Learning Doubling output multiplies average by r
Work-Sampling Plan n n = ceil[z²p(1−p)/e²]; independent samples

OSHA DART 200,000 Constant WO

100 workers times 40 hours times 50 weeks equals 200,000
100 FTE workers 2,000 hours per worker-year Count cases, not lost days

Ergonomics, OSHA Noise & Safety WO

NIOSH Lifting Index Load/RWL; applicable two-handed lifting tasks
Anthropometric Reach Rule Design reach for small-stature users
Anthropometric Clearance Rule Design clearance for large-stature users
OSHA 1910.95 Action Level 85 dBA 8-hour TWA, 50% dose
DART Incidence Rate DART cases × 200,000 ÷ employee-hours
Keyed Connector Poka-Yoke Physical design prevents wrong orientation

Control Limits vs Specification Limits QU

Control Limits

Calculated from process data
Detect statistical special-cause signals
Represent voice of the process

Specification Limits

Set by engineering or customer
Define acceptable unit conformance
Not estimated from process subgroup sigma
Stability signal vs product tolerance

Quality & Reliability Picker QU

Stable approximately normal, two-sided process capability → Cpk includes mean location and spread ( Signed distance; negative outside specification limits )
Monitoring fraction nonconforming across subgroups → Use binomial 3-sigma p-chart ( Independent Bernoulli items; n-specific limits )
Constant failure rate lambda given → R(t) = exp(−λt) ( Memoryless hazard rate )
Degradation sensor indicator is available → Use condition-based predictive maintenance ( Instead of fixed calendar )

SPC, Capability & Acceptance Sampling QU

Control vs Spec Limits Process voice vs customer requirements
p-Chart 3-Sigma UCL p̄ + 3√[p̄(1−p̄)/n] Upper bound: 1
Process Capability Cp (USL−LSL)÷(6σ) Stable, approximately normal process
Two-Sided Capability Cpk min[USL−mean, mean−LSL]/(3σ); signed distances
Producer Risk Alpha Rejecting good lot at AQL
Consumer Risk Beta Accepting poor lot at LTPD

Cp vs Cpk Capability QU

Cp Index

Equals USL-minus-LSL over 6-sigma
Measures centered potential capability
Ignores process mean location

Cpk Index

Uses smaller signed specification distance
Penalizes off-center process mean
Equals Cp only when centered
Stable-process spread vs centering effect

DOE, FMEA, Reliability & Maintenance QU

Factorial Interaction Factor effect depends on another
ISO 9001 Scope Quality management system process requirements
Proactive FMEA Goal Anticipate failure modes, causes, effects
Exponential Reliability Surviving interval under constant hazard
Predictive Maintenance Triggered by measured condition degradation
Evidence-Based Root Cause Verify causal links with data

Producer's Risk α vs Consumer's Risk β QU

Producer's Risk (α)

Type I sampling error
Rejecting good lot at AQL
Hurts compliant supplier

Consumer's Risk (β)

Type II sampling error
Accepting bad lot at LTPD
Passes poor quality to buyer
Reject AQL vs accept LTPD

Predictive vs Preventive Maintenance QU

Predictive Maintenance

Driven by measured equipment condition
Tracks vibration, heat, or wear
Intervenes before detected degradation fails

Preventive Maintenance

Driven by calendar or run-hours
Fixed schedule regardless of condition
Suited for predictable wear-out
Condition sensor vs fixed clock

Common Traps

MAD vs Signed Mean Forecast Error

MAD: average absolute error magnitude ≠ Signed mean error: cancellation exposes bias

Reorder Point vs Order Quantity

ROP: when inventory position triggers replenishment ≠ EOQ: how much each order contains

Two Different Allowance Denominators

Fraction of standard time: NT/(1−A) ≠ Normal-time allowance: NT×(1+A)

DART Cases vs Lost Workdays

DART numerator: qualifying injury/illness cases ≠ Lost-day total: duration, not case count

OSHA Noise Action vs Permissible Exposure

85 dBA eight-hour TWA: conservation action ≠ 90 dBA eight-hour exposure: permissible limit

Active Specification vs Research Survey

Linked specification: effective October 2020 ≠ 2026 PAKS survey: future-update research

Last Minute

1. 85 items; 8.5 h answering time
2. Five domains: 14–21 items each
3. Wrong answers: no deduction
4. Alternative items: no partial credit
5. Provided handbook; no design standards
6. M/M/1 Wq: λ÷(μ²−μλ)
7. M/M/1 stable: λ<μ
8. Stable Little’s Law: L = λW
9. EOQ: √[2DS/H]; matching periods
10. ROP: lead-time demand plus safety stock
11. Total-time allowance: ST = NT/(1−A)
12. Two-handed lifting: LI = load÷RWL
13. Noise conservation: 85 dBA, eight-hour TWA
14. Cpk: minimum signed distance ÷ 3σ

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