Six Sigma is one approach for setting quality expectations for a given process or output.As pointed out in your text,the term "Six Sigma" comes from statistics: in a normal distribution,the area (probability)outside of +/- six standard deviations from the mean value is exceedingly small.You are provided the following values from a standardized normal distribution .

Question

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Note:The Z value in the above table refers to the number of sigmas to the right of center (Z = 0).The listed probabilities refer to the area to the right of the chosen Z point,as illustrated by the graph below: 11ea6e70_bd5c_f66b_8f54_6301417c4a42_TB1699_00 
Required:
(1)Given the above,what is the probability for a 1-sigma performance level? How many defects might we expect for a process that is operating at 1-sigma level?
(2)Redo #1 above,but this time for a 3-sigma level.What is the percentage increase in quality expected under a 3-sigma performance level compared to a 1-sigma level?
(3)Redo #1 above,but this time for a 4-sigma level.Also,what is the anticipated percentage improvement in quality when moving from a 3-sigma to a 4-sigma performance level?
Please see Feedback for answers.
 Feedback: (1)Area = 0.1587 x 2 = 31.74%.Thus,the defect percentage = 31.74%;equivalently,this means that the percentage of error-free outputs is 1 - 31.74% = 68.26%.In terms of number of defects,this would translate to 317 out of every 1,000 outputs would have one or more defects.
(2)When we move to a 3-sigma performance level,the area under the curve shrinks to 2 x 0.00135 = 0.27%.That is,the percentage of good output increases to 1 - 0.27% = 99.73%.In absolute terms,this means approximately 3 out of every 1,000 outputs is defective.Note that when sigma increases from 1 to 3,there is a 100-fold increase in anticipated quality!
(3)Under a 4-sigma control level,the total area in the two tails of the distribution is 2 x 0.00003169 = 0.006338%.Thus,the percentage of good (error-free output)jumps to 1 - 0.006338% = 99.993662%.In absolute terms,this implies an error of approximately 6 per 100,000 outputs,or 1 error for every 16,667 outputs.Compared to a 3-sigma performance level,this would represent a 50-fold increase in quality .One implication of the above calculations is the dramatic improvement in quality as one moves toward a six sigma implementation.

Six Sigma Is One Approach for Setting Quality Expectations for a Given