CIE cheat sheet

Therbligs are the 18 fundamental motion elements (e.g., reach, grasp, move, position, release); effective therbligs advance work, ineffective ones (search, select, hold, rest) add no value.

Principles of motion economy: use both hands simultaneously, keep motions symmetrical and in opposite directions, prefer continuous curved motions over straight-line with sharp reversals, and locate tools and materials within the normal work area.

Normal and maximum work areas: normal area is swept by the forearm pivoting at the elbow; maximum area is swept by the extended arm pivoting at the shoulder.

Two-handed process chart records left- and right-hand motions on a common time scale to expose idle hand time and balance.

Flow process chart symbols: operation (circle), transport (arrow), inspection (square), delay (D-shape), storage (triangle).

Worker-machine chart distinguishes independent worker time, machine time, and combined time to identify interference and idle capacity.

Micromotion study uses film/video and therblig analysis for short-cycle, highly repetitive work; cyclegraph and chronocyclegraph trace motion paths via light trails.

Job enlargement adds tasks at the same level (horizontal loading); job enrichment adds planning and control responsibility (vertical loading).

Standard time = Normal time × (1 + allowance fraction); Normal time = Observed time × Performance Rating (rating factor).

Number of cycles to observe: n = (z·s / (k·x̄))², where s is sample standard deviation, x̄ the sample mean, k the desired precision fraction, and z the normal deviate for the confidence level (z = 1.645 for 90%, 1.96 for 95%).

Allowance types: PFD (personal, fatigue, delay) is added to normal time; the allowance fraction is applied on top of normal time, not on observed time.

Time study element breakdown should be small enough to rate but large enough to time; break at natural divisions and separate manual from machine-controlled elements.

Predetermined time systems (MTM-1, MOST, MODAPTS) build standards from basic motion times and are valid only for the motions and conditions they cover.

Work sampling: proportion estimate p, required observations n = z²·p(1-p)/e²; accuracy is on the proportion, not on individual observations.

Continuous (cumulative) timing records running elapsed time and subtracts successive readings; snapback timing resets to zero each element.

Standard data and elemental time formulas let standards be set without direct study for families of similar parts.

Linear programming: optimum of an LP occurs at a vertex of the feasible region; the simplex method moves between basic feasible solutions improving the objective.

Duality: primal max problem's dual is a min problem; dual prices (shadow prices) give the marginal change in the objective per unit increase in a binding right-hand side.

Transportation problem: initial solutions by northwest corner, least cost, or Vogel's approximation; optimality tested by MODI/stepping-stone (u_i + v_j = c_ij for used cells).

Assignment problem is solved by the Hungarian method; it is a special transportation problem with unit supplies and demands.

EOQ = sqrt(2DS/H) for deterministic demand D, order cost S, holding cost H per unit per period.

Queueing: for M/M/1, utilization ρ = λ/μ, L = ρ/(1-ρ), Lq = ρ²/(1-ρ), W = 1/(μ-λ); stability requires λ < μ.

PERT: expected activity time te = (a + 4m + b)/6, variance = ((b-a)/6)²; critical path is the longest expected-time path with zero slack.

Decision analysis: EMV = Σ(probability × payoff); expected value of perfect information = EV with PI − EV without PI.

MRP logic: Gross requirements − scheduled receipts − projected on-hand + safety stock = net requirements; planned order release = planned order receipt offset by lead time.

MRP II extends MRP with capacity planning, shop floor control, and financial integration; ERP extends MRP II across the enterprise.

Aggregate planning strategies: chase (vary workforce/output), level (constant output with inventory/backlog), and mixed; cost trade-offs compare hiring, layoff, inventory, and stockout costs.

Inventory costs: holding (carrying) cost per unit per period, ordering/setup cost per order, and shortage cost; total cost minimum occurs where ordering cost equals holding cost under EOQ assumptions.

Safety stock for a given service level = z·σ_d·sqrt(L) when demand variability dominates and lead time is constant.

ABC classification: A items are few high-value (tight control), C items are many low-value (loose control); Pareto logic, roughly 80/20 value split.

Capacity: rated (demonstrated) capacity, required capacity from load = standard time × planned quantity; load profile compares required against available hours by work center.

Kanban/pull sizing relates to replenishment lead time and demand rate; a two-bin system reorders when the reserve bin is opened.

Systematic Layout Planning (SLP): relationship (from-to) chart, activity relationship chart, and space requirements drive block layout; closeness ratings A, E, I, O, U, X.

From-to chart counts material flow between departments; a load-distance score = Σ(flow_ij × distance_ij) is minimized for good layouts.

Flow patterns: straight line (product layout), U-shape (reduces travel and improves supervision), and L or S shapes for building constraints.

Process (job shop) layout groups similar equipment; product (flow line) layout arranges by operation sequence; cellular layout groups part families into manufacturing cells (group technology).

Assembly line balancing: cycle time = available time / required output; theoretical minimum stations = Σ task times / cycle time; balance delay = 1 − efficiency.

Material handling principles include unit load, shortest distance, gravity flow, and mechanization matched to volume; 10 material handling principles guide selection.

Conveyors suit high-volume fixed paths; industrial trucks (forklifts) suit variable paths and lower volume; AGVs and AS/RS automate repetitive moves and storage.

Warehouse layout: dedicated vs. random storage; cube utilization and slotting by popularity (ABC) reduce pick travel time.

Control chart limits use ±3 sigma of the plotted statistic; for X̄-R charts, UCL_X̄ = X̄̄ + A2·R̄, LCL_X̄ = X̄̄ − A2·R̄, UCL_R = D4·R̄, LCL_R = D3·R̄.

For p-charts: center line p̄, limits p̄ ± 3·sqrt(p̄(1−p̄)/n); for c-charts: c̄ ± 3·sqrt(c̄).

Process capability: Cp = (USL − LSL)/(6σ); Cpk = min[(USL − μ), (μ − LSL)]/(3σ); Cpk < 1 means the process is not capable of meeting specifications.

Western Electric / Nelson rules detect nonrandom patterns: one point beyond 3σ, two of three beyond 2σ, runs of points on one side, trends, and excessive variation.

Type I error (α) is producer's risk (false alarm); Type II error (β) is consumer's risk (missed shift); OC curves plot probability of acceptance vs. fraction defective.

Acceptance sampling: AQL is the acceptable quality level, LTPD the lot tolerance percent defective; operating characteristic curve relates lot quality to probability of acceptance.

Gage R&R separates repeatability (equipment) and reproducibility (appraiser) variation; measurement system variation should be small relative to tolerance and process variation.

Six Sigma DMAIC: define, measure, analyze, improve, control; process sigma level relates DPMO to z-value (e.g., 3.4 DPMO ≈ 6σ with 1.5σ shift).

Time value: F = P(1+i)^n; P = F(1+i)^−n; (1+i)^n is the compound amount factor (F/P, i, n).

Uniform series: A = P·[i(1+i)^n / ((1+i)^n − 1)] (capital recovery factor); P = A·[((1+i)^n − 1)/(i(1+i)^n)] (P/A factor).

Sinking fund factor: A = F·[i/((1+i)^n − 1)]; used to accumulate a future amount from equal periodic deposits.

Net present value: discount all cash flows to present at the MARR; accept if NPV ≥ 0. IRR is the i that makes NPV = 0; accept if IRR ≥ MARR.

Payback period ignores time value beyond the recovery point; discounted payback accounts for it but still ignores cash flows after payback.

Depreciation: straight-line = (cost − salvage)/life; MACRS uses accelerated declining-balance with mid-year convention and half-year first/last-year rules.

Replacement analysis uses EUAC (equivalent uniform annual cost); retain the defender if its EUAC is lower than the challenger's minimum EUAC.

Benefit-cost ratio for public projects: B/C = PW(benefits)/PW(costs); accept if B/C ≥ 1.0 (using conventional or modified ratio consistently).

NIOSH lifting equation: RWL = LC × HM × VM × DM × AM × FM × CM; the lifting index (LI) = load weight / RWL; LI > 1.0 indicates increased risk.

Anthropometric design: use the 5th percentile for reach and clearance, the 95th percentile for strength and clearance dimensions; design limits depend on whether the dimension is a constraint or a demand.

NIOSH multipliers: HM = 25/H (horizontal distance), VM = 1 − 0.003·|V − 75| (vertical location), with recommended limits for frequency and coupling.

Manual materials handling risk factors: load weight, horizontal distance, vertical location, asymmetry/twisting, frequency, and coupling quality.

Workstation design: elbows near 90°, wrists neutral, monitor top at or slightly below eye level, and keyboard height at seated elbow height.

Noise: 85 dBA is the common 8-hour exposure action level; noise dose doubles with every 3 dB increase (3 dB exchange rate) under OSHA.

Thermal and lighting: WBGT index combines dry-bulb, natural wet-bulb, and globe temperature; illuminance recommendations vary by task detail (e.g., general office ~300–500 lux).

Cognitive human factors: Fitts' law (movement time increases with distance and decreases with target width), Hick's law (decision time grows logarithmically with number of choices).

The seven wastes (TIMWOOD): transport, inventory, motion, waiting, overproduction, overprocessing, defects.

Value stream mapping distinguishes value-added, necessary non-value-added, and non-value-added steps; lead time = inventory / throughput (Little's law).

5S: sort, set in order, shine, standardize, sustain; it is a foundation for visual management and standardized work.

Pull systems (kanban) authorize production based on downstream consumption; push systems schedule based on forecasts.

SMED (single-minute exchange of dies) separates internal and external setup, converts internal to external, and streamlines remaining internal steps to cut changeover time.

TPM (total productive maintenance) targets overall equipment effectiveness: OEE = availability × performance × quality.

Kaizen is continuous incremental improvement; kaizen events (blitz) are focused short-duration improvement projects; PDCA (plan-do-check-act) is the underlying cycle.

Standardized work specifies takt time, work sequence, and standard in-process stock; takt time = available production time / customer demand.