A process is said to be of six-sigma quality if the process mean is at least six standard deviations from the nearest specification. Assume a normally distributed measurement.
(a) If a process mean is centered between upper and lower specifications at a distance of six standard deviations from each,what is the probability that a product does not meet specifications? Using the result that 0.000001 equals one part per million, express the answer in parts per million.
b) Because it is difficult to maintain a process mean centered between the specifications, the probability of a product not meeting specification is often calculated after assuming the process shifts. if the process mean positioned as in part (a) shifts upward by 1.5 standard deviation , what is the probability that a product not meeting specification ? Express the answer in parts per million.
c) Rework part (a).Assume that the process mean is at a distance of three standard deviation.
d) Rework part (b) . Assume the process mean is at a distance of three standard deviation and then shifts upward by 1.5 standard deviation.
(e) Compare the results in parts (b) and (d) and comment