Suppose that your business is operating at the $4\mathrm{.}5-$sigma quality level. If projects have an average

improvement rate of $50\%$ annually, how many years will it take to achieve Six Sigma quality?

The $$ level$$ performance metric incorporates a $1\mathrm{.}5$ shift in the mean that is customary with Six Sigma

applications, or $$ level$=$ z $+1\mathrm{.}5.$ As stated in the text, a $4$ quality level represents about $6210$ ppm

defective:

ppm defective for $4\mathrm{.}5$ quality level $=[1(4\mathrm{.}51\mathrm{.}5)]\backslash$times $1,000,000=1350$

The objective is to achieve the $6\backslash$sigma performance level $(3\mathrm{.}4$ ppm$).$

$3\mathrm{.}4=$ ppm$(1$ rate$)=1350(10\mathrm{.}5)$

Compute the following to determine the number of years:

$=(3\mathrm{.}4/1350)$

$0\mathrm{.}5=$

$"-$level" within specification

ppm defective

$()(1\mathrm{.}5)(41\mathrm{.}5)(2\mathrm{.}5)0\mathrm{.}993790$

$(10\mathrm{.}993790)1,000,0006210$

z

$$

$$