Lean flow and takt

takt timeline balancingassembly line designwork in processcycle time

Takt time, minimum stations, balance efficiency, work in process, standard time and the learning curve, in design order.

Takt Time

T_t = \frac{T_a}{D}

The pace the customer sets: available production time in a period divided by the units the customer wants in that period. One unit must leave the line every takt.

Theoretical Minimum Number of Stations

N_{\min} = \frac{\sum t_i}{C}

Fewest workstations a line could possibly need: total work content divided by the cycle time. Round the answer UP to the next whole station — the fraction cannot be staffed.

Line Balancing Efficiency

E = \frac{\sum t_i}{N\,C}

Fraction of paid station time that is actually working: total task time divided by the stations you staffed times the cycle time. What is left over is balance delay.

Little's Law (Work in Process)

\mathit{WIP} = \mathit{TH} \times \mathit{CT}

The most general law in operations: the work sitting in a system equals the rate it flows through times how long each job stays. True for any stable system, whatever the arrival pattern.

Standard Time from a Time Study

T_s = T_o\,R\,(1 + A)

Turns a stopwatch reading into an allowed time: observed time, adjusted for how fast the operator was working, then padded for rest, personal needs and unavoidable delay.

Wright's Learning Curve (Unit Time)

T_n = T_1\,n^{\,\log b / \log 2}

Time to build the nth unit when every doubling of cumulative output cuts the time to a fraction b of what it was: the aircraft-industry curve that still prices first-of-a-kind work.

How they fit together

These are meant to be read in order, because designing a line is a sequence and each answer feeds the next. Takt time comes first and it is not a productivity target. It is the customer's pace, available working time divided by units demanded, and it is the only number in lean manufacturing set outside the factory. Running faster than takt builds inventory; running slower misses the order.

Divide the total work content by takt and you get the theoretical minimum stations, which is a lower bound nobody achieves. Round it up, because a fraction of a station cannot be staffed, then measure how far reality landed from the bound with balance efficiency. What is left over is balance delay, and it is paid for every shift whether or not it shows in a report. Tasks come in indivisible lumps, so 85% to 95% is good work rather than a failure.

Little's law is the reality check on the whole design, and it is the formula that ends arguments. Measure the work in process on the floor and the throughput leaving it, and the lead time follows. If that lead time is longer than the one being quoted to customers, no amount of expediting fixes it, because the only lever is less WIP or more throughput. The last two supply the task times everything above depends on. Standard time turns a stopwatch reading into an allowed time by adjusting for pace and then padding for rest, and Wright's learning curve warns you not to measure too early: on an 80% curve the eighth unit takes barely half as long as the first, so a time study on a new job prices work that will never be that slow again.