The Domino Effect in Unbalanced Lines

In a sequential line, an interruption can affect other stations. A station lacking input is starved; one unable to discharge is blocked. Propagation depends on capacities, buffers, variability, transfer rules and scheduling. Variation does not always accumulate indefinitely or create unrecoverable loss.

Separate capacity and variability

Do not add serial station capacities to obtain line throughput. In a simple deterministic case with no losses and one unit per operation, the lowest-capacity resource constrains sustainable output. In practice, changeovers, failures, mix and buffers can shift the constraint.

Mean cycle time does not describe the whole distribution. Record event durations and frequencies to investigate variability; a sampled waiting percentage does not supply both.

Teaching example

Three stations have constant cycles of 50, 60 and 55 seconds per unit. Nominal capacities are 72, 60 and 65.45 units/hour. With adequate coordination and no losses, the line reference is 60 units/hour, not 197.45 or the average capacity.

If the second station stops for ten minutes without sufficient downstream inventory, the third may starve. If the buffer ahead of station two fills, station one may block. Later spare capacity might recover part of the delay; ten failure minutes do not always cause ten lost minutes at every resource or a specified output loss.

A buffer can decouple variation but adds inventory, space and flow time. Little's relation mean WIP = throughput × mean flow time needs consistent boundaries, time bases and appropriate flow conditions; it does not calculate a minimum buffer guaranteeing no stops.

Design sampling

Define machine states: production, setup, confirmed breakdown, blocking, starvation and other. Use separate person categories; waiting for an automated cycle is not automatically unnecessary inactivity. A primary state prevents double counting; causes and attributes may be stored separately.

Select instants under the plan and keep actual times. Machines sharing the same incident are correlated. Randomisation eliminates neither that dependence nor observer reactivity.

For a proportion under the simple independent model, n=ceiling[z²p₀(1−p₀)/e²]. With z=1.96, p₀=0.5 and e=0.03, plan 1,068 readings. That count does not independently identify the constraint.

Interpret results

Assume 1,000 station readings include 120 blocked states: p̂=12%. Under independence, the approximate normal 95% margin is two points, not one. This does not establish exactly 12% loss of total line capacity: connect it to line state, production and demand.

Compare blocking, starvation, queues and departures. A wide interval reflects uncertainty, not necessarily physical variability. No universal wrench-time percentage identifies an optimised line.

Test and verify

Trial a method, replenishment or buffer change and measure good output, quality, inventory and safety. Do not automatically attribute a before/after difference to the intervention. For energy per unit, measure consumption and volume: less waiting does not guarantee less energy in every system.

OEE needs availability × performance × quality, ideal cycle time and total/good units. Sampling describes states but does not replace those inputs. WorkSamp supports planning and recording without assumed automatic causal diagnosis or sensor integration.

References

Little, 1961: L=λW. NIST: proportion intervals. OEE calculation.