Lean, Six Sigma & TOC

Most operations improvement draws on three approaches. They overlap, but each starts from a different question.

Lean (from the Toyota Production System) asks: where is the waste? Anything the customer wouldn’t pay for is waste, often remembered as TIMWOOD:

• Transport (moving things unnecessarily), Inventory (more than needed), Motion (people walking and searching),
• Waiting (idle people or machines), Overproduction (making more or earlier than needed),
• Over-processing (more work than required), Defects (scrap and rework).

Its tools include just-in-time production, kanban cards that pull material only when it’s used, quick changeovers (SMED), standard work and kaizen, small continuous improvements by the people doing the work.

Six Sigma asks: where does variation cause defects? It uses data and statistics to make processes consistent, aiming at very low defect rates (the “six sigma” level is often quoted as 3.4 defects per million opportunities). Projects follow DMAIC: define, measure, analyse, improve, control.

Theory of constraints (TOC) asks: what limits the whole system? Find the bottleneck, make it work flat out, align everything else to it, then lift it.

In practice they combine well: TOC tells you where to focus, Lean removes waste there, and Six Sigma makes the improved process stable. Many companies run “Lean Six Sigma” programmes for this reason.

Value stream mapping

A value stream map follows one product from order to delivery, recording each step’s processing time, waiting time, inventory and information flow. The key ratio is process cycle efficiency: value-added time divided by total lead time.

Sizing a kanban loop

A kanban loop circulates a fixed number of containers between a supplying process and a using one; a container is refilled only after it is emptied. The number of kanbans is:

where $D$ is demand per day, $L$ the replenishment time in days, $\alpha$ a safety factor and $C$ the container size. With 400 parts a day, half a day to replenish, a 10% safety factor and containers of 50: $400 \times 0.5 \times 1.1 / 50 = 4.4$, so 5 kanbans. Fewer kanbans means less inventory and quicker exposure of problems.

Process capability

Six Sigma asks whether a process can stay within its specification limits. For a bottle that must contain 500 ml ± 6 ml (so between 494 and 506), with a process mean of 501 ml and a standard deviation of 1.5 ml:

$C_p$ says the spread would fit comfortably if the process were centred; $C_{pk}$ is lower because the mean has drifted towards the upper limit. Re-centring to 500 ml raises $C_{pk}$ to 1.33 without reducing variation at all.

DMAIC tools

• Define: project charter, SIPOC (suppliers, inputs, process, outputs, customers).
• Measure: data collection, measurement system checks, baseline capability.
• Analyse: Pareto charts, cause-and-effect (fishbone) diagrams, regression.
• Improve: designed experiments, piloting solutions.
• Control: control charts, standard work, response plans.

Origins

• Lean grew out of the Toyota Production System, developed by Taiichi Ohno and colleagues from the 1950s, and was named and popularized in the West by Womack, Jones and Roos’s study of the car industry in 1990.
• Six Sigma was developed at Motorola in the mid-1980s and spread widely through companies such as General Electric in the 1990s. The often-quoted 3.4 defects per million opportunities assumes the process mean can drift by 1.5 standard deviations over time.
• The theory of constraints came from Eliyahu Goldratt’s work, popularized by his 1984 novel The Goal.

How they go wrong

• Lean as headcount cutting: when “lean” means layoffs, people stop suggesting improvements. Toyota’s approach rests on respect for people and on improvement by those doing the work.
• Six Sigma bureaucracy: belt certifications and project counts become the goal, while savings are claimed but never reach the profit and loss account.
• Tools without thinking: copying kanban boards or 5S labels without understanding flow and problem-solving produces visual change and little else.

Lean supply chains after recent disruptions

Just-in-time supply with minimal buffers works when supply is reliable and lead times are short. Long, global supply lines with volatile lead times need deliberately placed buffers. The pandemic and the chip shortage showed the cost of applying JIT logic to distant, fragile supply. The lesson isn’t to abandon lean, but to place buffers where variability and recovery times demand them, which is itself lean thinking about the real system.

Building an improvement culture

• Go and see (gemba): managers understand problems where the work happens.
• PDCA: plan, do, check, act, repeated in small cycles.
• Standard work: the current best way, written down, as the baseline for improvement.
• Statistical process control: control charts separate common-cause variation (the system) from special causes (events to investigate), so people don’t react to noise.

Combining them

A common sequence: use the theory of constraints to choose where to work (the constraint), lean to remove waste there, and Six Sigma to reduce variation and hold the gains. Each covers gaps in the others: lean without data can miss root causes, Six Sigma without flow can optimize the wrong step, and the theory of constraints without improvement tools can find the bottleneck but not fix it.