Values of Area under Normal Curve

abhishreshthaa

New member
Values of Area under Normal Curve
Sigma Percentage data Parts per levels with in curve million


Before Six-Sigma methodology came in vogue, 3 sigma tolerance levels (for any process) used to be the benchmark for quality measurements. But Motorola engineers argued that a process could shift 1.5 sigma in regular course, as shown in the figure below.

Now, to keep the data points within earlier permissible area, with mean shifting by 1.5 sigma, the sigma level has to be half. Thus, to accommodate 1.5-sigma shift, they proposed that the tolerance has to be +/- 6 sigma. In six-sigma methodology 99.9996599% (or more) of process data lies within +/- six sigma from the mean, thus having only 3.4 defects per million opportunities (DPMO). Now, 99.9996599% value is actually for 4.5 sigma level in Normal curve, but keeping in view the 1.5 sigma process shift, the process sigma level is actually six.
 
Values of Area under Normal Curve
Sigma Percentage data Parts per levels with in curve million


Before Six-Sigma methodology came in vogue, 3 sigma tolerance levels (for any process) used to be the benchmark for quality measurements. But Motorola engineers argued that a process could shift 1.5 sigma in regular course, as shown in the figure below.

Now, to keep the data points within earlier permissible area, with mean shifting by 1.5 sigma, the sigma level has to be half. Thus, to accommodate 1.5-sigma shift, they proposed that the tolerance has to be +/- 6 sigma. In six-sigma methodology 99.9996599% (or more) of process data lies within +/- six sigma from the mean, thus having only 3.4 defects per million opportunities (DPMO). Now, 99.9996599% value is actually for 4.5 sigma level in Normal curve, but keeping in view the 1.5 sigma process shift, the process sigma level is actually six.

Hey abhi, very nice work! I really liked your work and also want to thank to you for sharing this information here. BTW, i have also some important information regarding the mentioned topic and would like to share it with you.
 

Attachments

  • Values of Area under Normal Curve.pdf
    146.2 KB · Views: 0
Top