Answer :
Answer:
True
Step-by-step explanation:
A six sigma level has a lower and upper specification limits between [tex] \\ (\mu - 6\sigma) [/tex] and [tex] \\ (\mu + 6\sigma) [/tex]. It means that the probability of finding no defects in a process is, considering 12 significant figures, for values symmetrically covered for standard deviations from the mean of a normal distribution:
[tex] \\ p = F(\mu + 6\sigma) - F(\mu - 6\sigma) = 0.999999998027 [/tex]
For those with defects operating at a 6 sigma level, the probability is:
[tex] \\ 1 - p = 1 - 0.999999998027 = 0.000000001973 [/tex]
Similarly, for finding no defects in a 5 sigma level, we have:
[tex] \\ p = F(\mu + 5\sigma) - F(\mu - 5\sigma) = 0.999999426697 [/tex].
The probability of defects is:
[tex] \\ 1 - p = 1 - 0.999999426697 = 0.000000573303 [/tex]
Well, the defects present in a six sigma level and a five sigma level are, respectively:
[tex] \\ {6\sigma} = 0.000000001973 = 1.973 * 10^{-9} \approx \frac{2}{10^9} \approx \frac{2}{1000000000} [/tex]
[tex] \\ {5\sigma} = 0.000000573303 = 5.73303 * 10^{-7} \approx \frac{6}{10^7} \approx \frac{6}{10000000} [/tex]
Then, comparing both fractions, we can confirm that a 6 sigma level is markedly different when it comes to the number of defects present:
[tex] \\ {6\sigma} \approx \frac{2}{10^9} [/tex] [1]
[tex] \\ {5\sigma} \approx \frac{6}{10^7} = \frac{6}{10^7}*\frac{10^2}{10^2}=\frac{600}{10^9} [/tex] [2]
Comparing [1] and [2], a six sigma process has 2 defects per billion opportunities, whereas a five sigma process has 600 defects per billion opportunities.