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Susunan wates Shewhart 3-sigma dumasar kana hal di handap ieu.

Hasil kasar tina kateusaruaan Chebyshev yen, keur unggal sebaran probabilitas, probabilitas hasil leuwih gedé tinimbang simpangan baku k tina mean nu loba dipaké nyaéta 1/k2.

Hasil nu leuwih alus tina kateusaruaan Vysochanskii-Petunin, yén unggal unimodal probability distribution, probabilitas hasil leuwih gedé tinimbang simpangan baku k tina méan mean nu ilahar dipaké nyaéta 4/(9k2).

Panalungtikan empiris tina rupa-rupa probability distribution nembongkeun yén ampir 99% tina panempo aya dina jeroeun tilu simpangan baku dina mean.

Shewhart meunang kasimpulan ku nyebutkeun:

... the fact that the criterion which we happen to use has a fine ancestry in highbrow statistical theorems does not justify its use. Such justification must come from empirical evidence that it works. As the practical engineer might say, the proof of the pudding is in the eating.

Ngaliwatan percobaan mimiti nu mana watesan dumasar kana sebaran probabilitas, Shewhart nuliskeun sacara pasti:

Some of the earliest attempts to characterise a state of statistical control were inspired by the belief that there existed a special form of frequency function f and it was early argued that the normal law characterised such a state. When the normal law was found to be inadequate, then generalised functional forms were tried. Today, however, all hopes of finding a unique functional form f are blasted.

Grafik kadali dijieun keur kaperluan dirina sorangan. Deming nambahan yén taya tes hipothesa tur taya motivasi tina Neyman-Pearson lemma. Pendapatna yén gabungan alami dina populasi jeung rarancang nyokot sampel dina lolobana industri leuwih remen ngagunakeun téhnik statistik konvensional. Deming museurkeun keur nempo leuwih teleb kana sistim akibar dina prosés ...under a wide range of unknowable circumstances, future and past .... manéhna nyebutkeun yén dina sababaraha kaayaan ieu, watesan 3-sigma diperlukeun keur ... a rational and economic guide to minimum economic loss... tina dua kasalahan:

Ascribe a variation or a mistake to a special cause when in fact the cause belongs to the system (common cause). (Also known as a Type I error)

Ascribe a variation or a mistake to the system (common causes) when in fact the cause was special. (Also known as a Type II error)