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A “4.5 Sigma” level process is normally distributed, and its mean is centered at the specification...

A “4.5 Sigma” level process is normally distributed, and its mean is centered at the specification target. The lower and upper specifications are mapped to +/- 4.5 standard deviations from the mean. If the process mean shifts up by 1.5 standard deviations, what is the expected number of defects per million opportunities?

math   Statistics-And-Probability   
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Answer #1

if there is a shift of 1.5 standard deviations , new specification will be between -4.5+1.5 =- standard deviation to 4.5+1.5 =6 standard deviation

therefore probability of defect =P(Z<-3)+P(Z>6) =1-P(-3<Z<6)=1-(1-0.0013499)=0.0013499

therefore DPMO or expected number of defects per million opportunities =np=106*0.0013499

=1349.899 ~ 1350

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