For our purposes, it is a systematic description of a phenomenon that shares important and essential features of that phenomenon. Models frequently give us leverage on problems in the absence of alternative approaches.
\(6\sigma\) is a widely used tool in TQM [total quality management]. But \(6\sigma\) isn’t actually \(6\sigma\). The famous mantra that goes with it is 3.4 dipmo [defects per million opportunities]. This means that the outer limit [and it only considers one-sided/tailed] on defects is 0.0000034.
options(scipen=8)
library(radiant)
result <- prob_norm(mean = 0, stdev = 1, plb = 0.0000034)
summary(result, type = "probs")Probability calculator
Distribution: Normal
Mean : 0
St. dev : 1
Lower bound : 0.0000034
Upper bound : 1
P(X < -4.5) = 0.0000034
P(X > -4.5) = 1\(6\sigma\) is only \(4.5\).
plot(result, type = "probs") + theme_minimal()
There are two sources of variation: realizations and averages and both vary. 4.5 \(\sigma\) in the data and \(1.5\sigma\) in the average. Total is six.