Operations & Logistics
SMED Setup Reduction Formula: Internal-to-External Changeover & Lot Shrinking
Quantify Shigeo Shingo’s Single-Minute Exchange of Die (SMED) conversion—separating external setup from stopped-machine internal downtime to shrink economic lot sizes by SQRT(T_new / T_old) or unlock shift availability.
Two strategic dividends of SMED: extra shift capacity OR smaller low-WIP batches
Shigeo Shingo’s Toyota Production System SMED methodology attacks machine changeover time T_old (for example, 120 minutes) in two stages: first converting steps that can be staged while the press is still running into External Setup T_ext (75 minutes), and then streamlining remaining stopped-machine clamping/calibration by T_stream (15 minutes) to achieve post-SMED internal downtime T_new = 120 - 75 - 15 = 30 minutes.
Lean plants can harvest that 4x internal-setup reduction in two ways: (1) Capacity harvest—keeping N = 3 changeovers per 480-minute shift recovers 3 * 90 = 270 productive minutes and lifts net run-time availability from 25.00% to 81.25%; or (2) Agility harvest—shrinking economic batch size via square-root scaling Q_new = Q_old * SQRT(T_new / T_old) = 1,200 * SQRT(30 / 120) = 600 units (or running 4x as many product families in the exact same setup budget).
| SMED Stage (480-min Shift, 3 Changeovers) | Internal Downtime T_int | Economic Lot Q_opt | Shift Run Availability |
|---|---|---|---|
| Baseline Unseparated Setup | 120.0 min / changeover | 1,200 units | 0.2500 (120 / 480 min) |
| Stage 1+2 Post-SMED (-75 ext, -15 stream) | 30.0 min / changeover | 600 units (-50% WIP) | 0.8125 (390 / 480 min) |
| Single-Digit Kaizen (-90 ext, -22.5 stream) | 7.5 min (< 10 min SMED!) | 300 units (-75% WIP) | 0.9531 (457.5 / 480 min) |
Post-SMED Internal Downtime & Square-Root Reduced Lot Size Formula
Subtract externalized setup B3 and internal streamlining B4 from baseline downtime B2 (floored at >= 0), and scale baseline lot B5 by SQRT(T_new / B2).
=LET(t_new, MAX(0, B2 - B3 - B4), ROUND(B5 * SQRT(t_new / B2), 0))Shift Run-Time Availability Ratio Formula
Compute remaining productive shift fraction MAX(0, Shift_Min - N_chg * T_new) / Shift_Min across N_chg daily changeovers.
=LET(t_new, MAX(0, B2 - B3 - B4), ROUND(MAX(0, B7 - B6 * t_new) / B7, 4))Try the example
Use the original values or change them to test your understanding.