You have the cycle times. Now what does the picture mean?

Somebody finally plotted the cycle times. There is a chart, it has a shape, and the discussion in the room is about where the average sits.

There are four things in that chart worth acting on. The average is not among them.

One: the floor

The leftmost edge, where the data stops. Not the smallest observation, but the value below which nothing ever goes.

That number is the process working perfectly. It is the sum of the actual work with no waiting anywhere, and it is the best the current design can do. If your promise to customers is close to the floor, you have promised something that requires everything to go right, and everything does not go right.

The floor is also the thing to compare against the average. A floor of two days against a mean of six says four days of every order is waiting, which is a finding you can act on. A floor of five against a mean of six says the process is nearly always running clean and the work itself is the constraint. Those two situations look identical in a mean and need completely different responses.

Two: the right tail, and where it stops

Where the long slow cases sit, and how far out they go.

The tail is where your worst customer experiences live, and it is almost always longer than anyone in the room believes. It is also the part most likely to be dismissed as unrepresentative, which is precisely backwards: the tail is what generates complaints, escalations and the reputation the process has.

Read it as a percentile rather than as a maximum. The maximum is one event and it might never recur. The ninetieth percentile is a promise you can make and keep, and the gap between the median and the ninetieth is the honest measure of how unreliable the process is.

Three: the number of humps

This is the one that most often changes what people do next, and it is invisible in any summary statistic.

Two humps is not noise and it is not a wide distribution. It is two populations that were never separated: standard and complex, new and returning, in hours and out of hours. Everything you do to the mixture will be a compromise between two things that needed different treatment.

Split them and re-plot. Very often each half is tidy, and a problem that looked like unpredictable variation turns out to be a classification that was never made.

Four: the gaps

Empty spaces in the middle of the distribution, where you would expect data and there is none.

Gaps are almost never real. They are usually a batch boundary or a schedule: nothing completes between four and six hours because the run happens at six. A gap at exactly twenty four hours, or at a multiple of a shift, is the process telling you about a policy rather than about the work.

Those are among the cheapest fixes available, because the gap is a decision rather than a capability. Somebody set the run to twice a day, and moving it is a calendar change.

What not to read into it

Do not fit a curve before you have looked. The shape decides which curve, and fitting first hides two humps completely.

Do not delete the outliers. They are the tail. The tail is the customer experience, and the rate at which the ridiculous thing happens is itself a finding.

And do not compare two histograms with different bin widths. The bin width changes the apparent shape, and two charts drawn differently are not evidence of a change. Fix the bins before comparing anything.

What to do with it

Report three numbers, not one. The floor, the median and the ninetieth percentile. Together they say what the process does at best, typically and at its unreliable worst, and none of them is the average.

Look at the shape before any arithmetic. Count the humps, find the floor, look for gaps. That is five minutes and it usually determines what the next month of work should be.

And plot it as raw points if you have fewer than about fifty. A histogram of thirty observations is mostly a picture of your bin width. Thirty dots on a line is honest and shows the same four things.