Sigma Level (σ) is a representation
of the process capability in terms of opportunities and defects. It
refers to number of defects per million opportunities (DPMO).
Higher the sigma level, lower the number of defects
1σ = 691,462 DPMO
2σ = 308,538 DPMO
3σ = 66,807 DPMO
4σ = 6,210 DPMO
5σ = 233 DPMO
6σ = 3.4 DPMO
An exponential model of faults is then given by f(t)=f(0)(1+r)t , where t is time and r is fault rate
To achieve 3.4 DPMO from 66,807 DPMO with improvement rate 30%, we need find t years,
Here,
f(t) =3.4
f(0)= 66807
r = -0.30
By solving equation we get,
3.4 = 66807(1 - 0.30)t
0.7t
= 5.0893 * 10-05
taking log on both side we get
t
log(0.7) = log(5.0893) - 5 log(10)
t*
(-0.1549) = 0.7067 - 5
t
= -4.2933 / -0.1549
t = 27.71659 years
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