Suppose a business is operating at the three-sigma quality level. If projects have an average improvement rate of 50% annually, how many years will it take to achieve six-sigma quality?

  • $\begingroup$ That's a homework? $\endgroup$
    – ziggystar
    Oct 24, 2013 at 13:58

1 Answer 1


What do you mean by "average improvement rate"? If you mean that the number of faulty products are halved every year, then it is simply an exponential model that you are looking for.

$3\sigma=66,807$ faults per $1,000,000$

$6\sigma = 3.4 $ faults per $1,000,000$

An exponential model of faults is then given by $f(t)=f(0)(1+r)^t$, with $r = -0.5$, which can be solved as follows: $3.4=66,807*0.5^t \leftrightarrow {3.4 \over 66,807} = 0.5^t \leftrightarrow \log({3.4 \over 66,807})=t\log(0.5) \leftrightarrow \\ {\log({3.4 \over 66,807}) \over log(0.5)} = t$

$t=-9.8859/-0.693 = 14.265$ years. Or 14 years and 97 days.

  • $\begingroup$ Then t = -2.34 ? There might be an error. :( $\endgroup$
    – Bigbang
    Oct 24, 2013 at 12:55
  • $\begingroup$ Please see the edit by Tacio above. $\endgroup$
    – abaumann
    Oct 24, 2013 at 14:26

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