Question

(Use Excel to calculate the probabilities.) 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? (Use Excel to calculate the probabilities.) Thank You

Answer 1

Suppose the sample mean follows normal distribution with mean and standard deviation = .

It is given that the lower and upper specifications are mapped to +/- 4.5 standard deviations from the mean.

So that LSL =

and the USL =

If the mean is sifted up by 1.5 standard deviations from the mean, then the new mean is

First we need to find

where is shifted sample mean.

Plugging the values of LSL, USL and , we get

....(1)

Let's use excel:

The command is as "=NORMSDIST(3)-NORMSDIST(-6)"

= "=NORMSDIST(3)-NORMSDIST(-6)" = 0.998650101

So that the proportion of defective items when we shift the process up by 1.5 standard deviation is

So the expected number of defects per million opportunities = 1000000*0.001349899 = 1349.899 = 1350

So the answer is 1350