Industrial & Systems Engineering StudioLean · Six Sigma · OEE · Operations Research · Inventory & Supply Chain · FE/PE Prep

Compute Overall Equipment Effectiveness from planned production time, downtime, ideal cycle time, and good vs total units. Breaks the result into Availability × Performance × Quality, color-codes each factor, and benchmarks against the world-class 85% target and the six big losses.

Find the pace of production needed to meet customer demand. Enter available time, planned stops, and demand to get takt time in sec/unit and min/unit, then compare actual cycle time to see whether the line keeps up and how many workstations are required.

Relate work-in-process, throughput, and lead time with L = λ × W. Solve for any of the three variables given the other two, with clear unit handling — the backbone of queuing, lean flow, and the Theory of Constraints.

Economic Order Quantity that minimizes total inventory cost. Enter annual demand, ordering cost, and holding cost to get EOQ, orders per year, time between orders, total annual cost, and the reorder point from lead time.

Balance an assembly line across workstations. Enter task times and a target cycle time (or daily output) to get the theoretical minimum number of stations, line efficiency, balance delay, and bottleneck flags.

Assess whether a process can meet specification. Enter spec limits, mean, and standard deviation to get Cp, Cpk, Pp, Ppk, an estimated sigma level and ppm out of spec, with color-coded capability indices.

Build a value stream map: chain process boxes with cycle time, changeover, uptime, and operators, set inventory buffers between them, and get takt time, total lead time, value-added time, and process cycle efficiency — with a live VSM diagram and timeline ladder.

Single- and multi-server queue analysis. Enter arrival and service rates and the number of servers to get utilization, average queue length and number in system, and waiting times — with an instability warning when ρ ≥ 1.

Build a project network of activities with durations (or three-point PERT estimates) and predecessors. Forward/backward pass computes ES/EF/LS/LF and slack, identifies the critical path and project duration, and gives PERT variance.

Component and system reliability. Compute R(t)=e^(−λt), MTBF, and availability from MTTR, then combine components in series or parallel for system reliability.

Inherent availability, expected annual downtime, failure rate, and reliability R(t) from MTBF and MTTR — with an N-parallel redundancy mode comparing system-level availability against a single unit.

Convert between defects per million opportunities, sigma level (with the 1.5σ shift), and yield. Enter defects, units, and opportunities, or go backward from a target sigma level, with a reference table.

Build X̄-R or p-charts from your subgroup data. Computes the center line and control limits with the standard SPC constants, flags out-of-control points, and plots the chart.

Size safety stock and the reorder point from demand and lead-time variability and a target service level. Converts service level to a Z-value and accounts for demand and lead-time standard deviation.

Wright's learning curve: enter the first-unit time and learning rate to get the time for any unit, the cumulative total, and cumulative average — for estimating production runs and labor as workers gain experience.

Convert an observed cycle time to normal and standard time using performance rating and allowances, and get standard output per shift — the core of time study and work measurement.

Forecast a demand series with moving average, weighted moving average, or exponential smoothing, and measure accuracy with MAD, MSE, MAPE, and bias.

Ergonomic manual-lifting assessment. Compute the Recommended Weight Limit (RWL) from the horizontal, vertical, distance, asymmetry, frequency, and coupling multipliers, plus the Lifting Index (LI).

Least-squares regression on your (x, y) data: slope, intercept, correlation r, and R², with prediction and a scatter-plus-fitted-line plot.

Economic Production Quantity with gradual replenishment, plus an EOQ-with-quantity-discounts mode. Get the optimal run size, maximum inventory, number of runs, and total annual cost.

Sequence n jobs on two machines to minimize makespan using Johnson's rule. Get the optimal order, the makespan, and a Gantt-style timeline with idle time.

Why a perfectly repeatable measurement can still be completely wrong. Four-quadrant scatter comparison plus a real calibration-drift example: a pressure gauge that's precise but reads 5% high.

Three different answers to "how reliable is it?" Why a high MTBF doesn't guarantee high uptime without also knowing MTTR — illustrated with an up/down timeline and two systems with identical MTBF but very different repair times.

Three different clocks running on your line. Why a station with excellent cycle time everywhere can still leave you with a terrible lead time — illustrated with a bottleneck bar chart against the takt line and a value-stream timeline dominated by queue waits.

"Did we build it right?" vs. "did we build the right thing?" Why a product can pass every verification test against its own spec and still fail validation against the real customer need — illustrated with a spec-vs-product-vs-real-need diagram and a concrete IP54-enclosure failure case.

Bottom-up vs. top-down reliability thinking. Why FMEA's one-component-at-a-time sweep can miss failure combinations that Fault Tree Analysis's AND/OR logic gates are built to reveal — and why safety-critical systems use both together.

Why a process can post an excellent Cp and still be quietly manufacturing defects. Illustrated with an identical tight distribution shown first well-centered, then shifted off-target — Cp stays flat while Cpk collapses.

Why Kanban cards let downstream demand control the line, not a forecast. Illustrated with a push system piling up work-in-process against a stalled downstream station, against a pull system whose WIP is hard-capped by the number of Kanban cards in circulation.

Why maintaining on a fixed schedule isn't the same as maintaining based on actual condition. Illustrated with a preventive timeline that can waste remaining life or miss an early failure, against a predictive trend line triggered by a real measured threshold crossing.

Why a machine can run 100% of its scheduled time and still post a terrible OEE. Illustrated with an 8-hour shift cascaded through three multiplied losses, and two machines that land on the same 60% OEE for opposite reasons — one a downtime problem, one a quality problem.

Why a station can have perfectly clear, detailed work instructions for every task and still have zero Standard Work. Illustrated with a triangle diagram — takt time, work sequence, and standard WIP — with work instructions plugged in as supporting detail, not a fourth peer.

Both stop defects — but at different points in time. Illustrated with an asymmetric locating fixture that makes a wrong-orientation part impossible to seat (poka-yoke), against an andon-triggered auto-stop that catches an abnormality immediately after it occurs (jidoka).

Why EPQ always recommends a bigger lot size than EOQ for the exact same demand. Illustrated with two inventory sawtooth charts — an instant spike-and-decline for a purchased lot against a gradual ramp-and-decline for a manufactured lot, where demand eats into the batch while it's still being produced.

A 12-section interactive reference covering lean and the 8 wastes, Six Sigma DMAIC, OEE, takt/cycle time and line balancing, Little’s Law and the Theory of Constraints, SPC and process capability, inventory (EOQ/EPQ/ROP/safety stock), queuing theory, CPM/PERT, forecasting, and a master formula quick-reference. First 3 free to preview.