Question

Chapter2 Question: 9.) Suppose that your business is operating at the 3 sigma quality level. If projects have an average improvement rate of 30% annually, how many years will it take to achieve 6 sigma quality?

Answer 1

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,

^{$\fn_cm \Rightarrow$} 3.4 = 66807(1 - 0.30)^t

^{$\fn_cm \Rightarrow$}0.7^t = 5.0893 * 10^-05

taking log on both side we get

^{$\fn_cm \Rightarrow$}t log(0.7) = log(5.0893) - 5 log(10)

^{$\fn_cm \Rightarrow$}t* (-0.1549) = 0.7067 - 5

^{$\fn_cm \Rightarrow$}t = -4.2933 / -0.1549

^{$\fn_cm \Rightarrow$} t = 27.71659 years