Operations.

Process Capability

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The question

You promise your customers something with a number in it — delivery in five days, a reply within the hour, an error rate under one per cent — so what proportion of the time do you actually hit it, measured rather than felt? If the only figure you've ever reported is the mean, the answer is that you don't know, and neither does the customer who has been quietly counting the misses.

The idea

In 1986 Bill Smith, an engineer at Motorola, made an argument that grew into Six Sigma: products needing rework on the line failed disproportionately early in the customer's hands, so the defects you catch internally forecast the ones the customer will find. Acting on that requires a way to set how much your process varies against how much variation the customer will tolerate, and the arithmetic is disarmingly simple. Put two widths side by side: the span your process ordinarily covers, which is six standard deviations of its own results, and the tolerance your customer will actually accept. Divide the second by the first and you have Cp. If Cp is 1.0 the two are the same width, your specification sits exactly three standard deviations either side of centre, and roughly 2,700 units in every million fall outside it — and that assumes perfect centring, which no process has. Plenty of industrial customers won't accept anything under 1.33. You don't need the full statistics to use any of this: count your last thirty results, count how many fell outside the line the customer will actually take, and you've got the same number in cruder form — which is more than most businesses can produce for any promise they've already signed.

The framework

01
Your control limits never mentioned the customer.
The ordinary range you learnt to plot is calculated entirely from your own results. It tells you where this process falls when nothing unusual is happening, and no customer had any say in it. That's the half that gets taught. The other half is the specification limit — the window the customer will accept, which owes nothing at all to what you're capable of. Capability is simply the distance between the two, and it can embarrass you in either direction: a process sitting comfortably inside a tolerance nobody actually cares about, or one that's beautifully stable and stably outside what the customer will take.
02
Is it off-centre, or is it simply too wide?
Cp compares the two widths and assumes you're centred. Cpk asks where the spread actually sits inside the tolerance, and the two part company the moment your process runs high or low. That distinction decides which project you run. An off-centre process with an acceptable spread is the cheap problem: shift the setting, change the default, move the promised date, and you're done inside a week. A process whose spread is simply wider than the tolerance is the expensive one — no amount of re-centring saves it, and you're into finding and removing sources of variation.
03
Take the tolerance from the customer, never from your own comfort.
The tolerance isn't the target you set in a planning meeting; it's the point at which the customer's behaviour changes — the delay at which they chase, escalate, discount or leave. That number is discoverable: ask the last ten customers where the line sat, or find where complaints and churn actually start in your own data. Businesses habitually set the tolerance from what they can already do, which guarantees a flattering answer and explains nothing. Set it from the customer and the number gets uncomfortable, which is the only version worth having.
04
Capability is a claim about tomorrow, so it needs a settled process behind it.
A capability figure computed over a stretch when the process was jumping around measures nothing you can promise — it blends ordinary variation with one-off events, and predicts neither. So settle the process first, then compute capability, then quote it. And recompute it, because a number from last year describes an operation that has since changed staff, volume and suppliers. Once you hold it the negotiation gets honest: you can say what you're able to hold, price a tighter promise properly, and stop signing service levels your process was never going to meet.

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