Coupled stages multiply their losses, and buffers sized to protect the constraint win them back
Two coupled stages at 80% availability run at 64%. Decoupling them recovers 25% more throughput, and 56% on three stages.
With no buffer between stages, availability is the product of every stage
On a line where stages run in series with no buffer, system availability is each stage’s availability multiplied together. So coupling losses compound quickly as you add stages.
- Two stages at 80% availability: 0.80 × 0.80 = 64%. Decoupled, the line runs at 80%, a gain of 25%.
- Three stages at 80% availability: 0.80³ = 51.2%. Decoupled, the line runs at 80%, a gain of 56%.
System Availability (coupled) = A₁ × A₂ × … × Aₙ
Hikers in single file show how it works
Picture a group of hikers walking in single file, each keeping pace with the person ahead. The slowest hiker sets the pace for the whole group.
When a faster hiker stumbles, the group barely notices, because that hiker catches up. When the slowest hiker stops, the group loses that time for good. The slowest hiker was already walking at the group’s top pace.
The gap between hikers is the buffer. It must be big enough that a faster hiker’s stumble never reaches the slowest one. If it does, the whole group covers less ground.
Worked example from food manufacturing. Mixing runs at 75% availability, forming at 82% and packaging at 78%.
Coupled, the line runs at 0.75 × 0.82 × 0.78 = 48.0%. Decoupled, with forming as the constraint, it runs at 82%. That is a gain of 71%.
The constraint should only stop for its own reasons
Core principle: the system constraint should only stop for reasons it would have stopped for anyway. Another stage should never force it to stop.
The target: at least 95% of constraint stops are its own, and no more than 5% come from other stages.
Upstream buffers stay full and downstream buffers stay empty
Each buffer protects the constraint in one direction. The upstream buffer stops it starving, and the downstream buffer stops it being blocked.
Upstream buffer, before the constraint
Target: full. Run upstream at full speed while the buffer is below target. Match the constraint’s speed once the buffer is full.
Downstream buffer, after the constraint
Target: empty. Run downstream at full speed while the buffer holds stock. Match the constraint’s speed once the buffer is empty.
A buffer needs room for stops and for speed differences
Buffer size has two parts. You need both to decouple the stages fully.
Part 1: availability protection
Availability buffer = 95th percentile upstream stop duration × downstream speed
Use the downstream speed, not its effective throughput. While upstream is down, the downstream stage keeps consuming at its full rated speed.
Size the buffer to cover 95% of disruptions. A smaller buffer only partly decouples the stages.
- Mixing Upstream 100 units/hr
- Upstream buffer Target: full 30 units
- Forming The constraint 80 units/hr
- Downstream buffer Target: empty 15 units
- Packing Downstream 90 units/hr
- Normal running. All three stages run at rated speed. The upstream buffer fills by 20 units an hour and the downstream buffer drains by 10.
- Buffers at target. The upstream buffer is full, so mixing slows to 80 to match forming. The downstream buffer is empty, so packing is capped at forming’s 80.
- Upstream stops. Mixing stops. Forming keeps running at 80 units an hour by drawing on the upstream buffer. Packing stays capped at 80.
- Recovery. Mixing restarts at 100 units an hour. The extra 20 units an hour refill the upstream buffer. Packing stays at 80.
- Downstream stops. Packing stops. Forming keeps running, and its output fills the downstream buffer. Mixing runs at 80 because the upstream buffer is full.
- Recovery. Packing restarts at 90 units an hour. The extra 10 units an hour empty the downstream buffer. Then every stage matches forming at 80 again.
Forming, the constraint, never stops in any of the six steps.
Part 2: speed differential
Speed differential buffer = |upstream speed − downstream speed| × campaign duration
If upstream is faster, the buffer builds up and downstream must empty it in time. If downstream is faster, the buffer runs down and downstream must slow down or run in campaigns.
Total buffer
Conservative = Part 1 + Part 2
Practical = the larger of Part 1 and Part 2
Worked example: an 80-unit buffer
| Upstream mixing | 100 units/hr, 75% availability |
|---|---|
| Downstream forming (the constraint) | 80 units/hr, 90% availability |
| Speed ratio | 100 ÷ 80 = 1.25, so upstream is 25% faster |
| 95th percentile upstream stop | 30 minutes |
| Availability buffer | 30 minutes × 80 units/hr = 40 units |
| Speed buffer, 2-hour campaign | (100 − 80) × 2 = 40 units |
| Total, conservative | 40 + 40 = 80 units |
The same decoupling can be worth 10 to 100 times more on a production-constrained site
The value of a decoupling improvement depends on whether you could sell more if you made more.
Production-constrained
A manufacturer with £30m revenue runs a three-stage line, coupled at 48% system availability.
Decoupling it to 82%, the constraint’s availability, gives 71% more throughput.
The buffers cost about £150k of capital plus £80k a year to hold. Payback: 2.6 days.
Sales-constrained
The same throughput gain becomes a 20 to 36% cut in operating time.
Its value is the labour hours saved × the fully loaded labour cost.
It also lets you run in campaigns and frees labour trapped between stages.
Getting the constraint right is not optional. The same improvement can be worth 10 to 100 times more when you can sell everything you make.
A process control analysis runs in six stages
- Map the process and set a baseline. Map every stage, measure current throughput and find the buffers that exist today.
- Analyse throughput. Work out each stage’s effective throughput: speed × availability. The constraint is the stage with the lowest.
- Assess coupling. Classify each link between stages by how much protection its buffer gives. Fully coupled is below the 50th percentile, partially decoupled the 50th to 95th, fully decoupled the 95th or above.
- Quantify the opportunity. Throughput gain = (1 ÷ the product of Aᵢ for the non-constraint stages − 1) × 100%.
- Size the buffers. Upstream: the 95th percentile stop duration × constraint speed. Downstream: set by the speed differential and the campaign duration.
- Validate. Decoupling Effectiveness = measured system availability ÷ constraint availability. The target is 0.95 or more.
Ten terms explain the methodology
| Term | Definition |
|---|---|
| System availability | The share of planned time in which a system, or a stage, can produce. On a coupled line it is the product of each stage’s availability. |
| Constraint | The stage with the lowest effective throughput (speed × availability). It sets the pace for the whole system. |
| Buffer | Stock held between stages to absorb stops and speed differences, so one stage’s stop does not spread to another. |
| Coupling | How much stages depend on each other in real time. Fully coupled stages have no buffer, so any stop spreads at once. |
| Decoupling | Putting a buffer between stages so each can run on its own for a while. Full decoupling covers 95% or more of disruptions. |
| Effective throughput | A stage’s actual output rate, allowing for both its rated speed and its availability: speed × availability. |
| Bottleneck Speed (BNS) | The maximum rated speed of the constraint stage. The reference for potential output and for how fast a buffer is used. |
| Overall Equipment Effectiveness (OEE) | Potential Time ÷ Planned Production Time, which equals Good Output ÷ Potential Output. Our additive equivalent of textbook A × P × Q, without double-counting speed losses on waste. The derivation is on best practice for calculating efficiency. |
| Campaign duration | The planned run time between changeovers or planned stops. It sets the speed differential part of the buffer. |
| Decoupling Effectiveness | Measured system availability ÷ constraint availability. A value of 0.95 or more means the decoupling works. |