Not understanding what I need to calculate, please help a. Show that a \"six-sig

Question

Not understanding what I need to calculate, please help

a. Show that a "six-sigma" process (assume a normal distribution) that is centered between specification limits produces approximately 2 part per billion outside both of the specification limits.
b. Show that a "six-sigma" process (assume a normal distribution) that has shifted 1.5 toward the upper specification limit will produce approximately 3.4 parts per million outside the upper specification limit.
c. It has been estimated that safe aircraft carrier landings operate at about the 5 level. What level of ppm defective does that imply (assume up to a 1.5 shift in one direction exists)?

Explanation / Answer

a) here probability of outside both of the specification limits =P(Z<-6 or Z>6) =P(Z<-6)+P(Z>6) =1.97*10-09

therefore numebr of parts in 1 billion =109* 1.97*10-09= ~2 parts

b) for a shift of 1.5 probability of outside both of the specification limits =P(Z<-4.5 or Z>7.5)

=3.39*10-6

therefore numebr of defective parts in 1 million =106* 3.39*10-6 =3.4

c)for a 5 sigma process with 1.5 shift probability of outside both of the specification limits

=P(Z<-3.5 or Z>6.5)=2.33*10-4

therefore numebr of defective parts in 1 million =106* 2.33*10-4 =233

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