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Part 3 of 7 · Supplier lead time watcher series ~5 min read

Why the average is the wrong number

An average lead time is the number every system reports and it has a property nobody states out loud: half of all orders take longer than it. Setting a reorder point against it is a decision to run out roughly half the time.

Key takeaways

  • The average is exceeded on about half of orders, by definition.
  • Use a high percentile — the 90th is a reasonable default for most goods.
  • Variance costs more than length. A consistent 12 days beats an erratic 5-to-15.
  • Report the spread next to the number, always.
  • Say the sample size. Six orders does not have a 90th percentile worth the name.

What the average guarantees

Stockout rates at four different reorder point percentilesA stacked bar chart with four bars in per cent. Two series: orders that arrived in time in green, and orders that arrived late in red. Reordering at the mean gives fifty-two per cent in time and forty-eight per cent late. At the seventy-fifth percentile, seventy-six in time and twenty-four late. At the ninetieth, ninety-one in time and nine late. At the ninety-fifth, ninety-six in time and four late. A note says the first bar is what most reorder points are set to, and it is a coin flip.050100150200~100Reorder at the mean~100Reorder at p75~100Reorder at p90~100Reorder at p95Orders that arrived in time, %Orders that arrived late, %The first bar is what most reorder points are set to. It is a coin flip.
Fig 1. Four reorder points against the same supplier’s real distribution. Moving from the mean to the ninetieth percentile costs a few days of extra stock and removes four fifths of the stockouts.

Which percentile

The ninetieth is a sensible default and the right answer depends on what running out costs. For a cheap consumable with a substitute available, the seventy-fifth is fine and carrying less stock is worth the occasional gap. For the one component that stops a production line, the ninety-fifth or higher is cheap insurance.

The useful framing when somebody has to choose is not statistical: how many times a year are you willing to run out of this, and what happens when you do? Twelve orders a year at the ninetieth percentile means running out about once a year, which is a sentence anybody can have an opinion about.

Variance costs more than length

Why an erratic fast supplier costs more than a consistent slow oneThree boxes stacked on the left. Supplier A, five to fifteen days with a mean of nine, labelled erratic. Supplier B, eleven to thirteen days with a mean of twelve, labelled consistent. And The reorder point, set at the ninetieth percentile for each, labelled what it costs. All three converge on A holds more stock, because A's ninetieth percentile is fifteen days against B's thirteen, and that leads down to The slower supplier is the cheaper one. A note says A is three days faster on average and needs two more days of stock, so spread wins.Supplier A5 to 15 days, mean 9erraticSupplier B11 to 13 days, mean 12consistentThe reorder pointset at p90 for eachwhat it costsA holds more stockp90 is 15 days,against B's 13The slower supplieris the cheaper oneA is three days faster on average and needs two more days of stock. Spread wins.
Fig 2. Two suppliers where the faster one costs more to buy from. The comparison people make is means; the comparison that matters is the high percentile.

This is the finding that changes decisions, and it is invisible in every report that shows an average. Supplier A looks better on any dashboard comparing mean lead times and is more expensive to work with, because the stock you have to hold to absorb their unpredictability costs real money and warehouse space.

The practical output is to report mean, ninetieth percentile and range together for every supplier, and to let the person doing the comparison see all three. It takes no more space than the average alone.

Reporting the spread

The compact form that works is the range with the count: “9 days typical, 15 at the 90th, range 5–15, from 22 orders”. Four pieces of information, one line, and it cannot be misread as a promise.

The count at the end is doing real work. It is the difference between a number somebody should act on and a number that describes four orders and a coincidence.

Small samples

How sample size determines which lead time number can be usedA horizontal row of five boxes. Three orders: no distribution. Eight orders: a range, not a ninetieth percentile. Twenty orders: the ninetieth percentile is meaningful. Say which, on every number. Use the worst, when the sample is small. A note says below about ten orders, the longest one you have seen is a better planning number.HOW MUCH HISTORY YOU NEED3 ordersno distribution8 ordersa range, not a p9020 ordersp90 is meaningfulSay whichon every numberUse the worstwhen n is smallBelow about ten orders, the longest one you have seen is a better planning number.
Fig 3. What each sample size supports. The last box is the practical rule for the many suppliers you order from four times a year.
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Using the observed maximum for small samples is crude and it is honest, which beats a percentile computed from six data points and presented with the same confidence as one computed from sixty.

It also degrades gracefully: as orders accumulate the number moves from the maximum to a real percentile, and it moves in the direction of holding less stock, which is the safe direction to be wrong in while you are learning.

Next: catching the slide.

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