Which of the following statements are not correct? A) For a 3-sigma $\bar { X }$ Chart, where the process mean $\mu$ And standard deviation $\sigma$ Are known, the probability that a point on the chart falls above the UCL is .013, as is the probability that the point falls below the LCL. B) For a 3-sigma S chart, $P \left( S _ { i } U C L \right) = P \left( S _ { i } U C L ) = P ( R _{i}

Question

Which of the following statements are not correct? A) For a 3-sigma $\bar { X }$ Chart, where the process mean $\mu$ And standard deviation $\sigma$ Are known, the probability that a point on the chart falls above the UCL is .013, as is the probability that the point falls below the LCL. B) For a 3-sigma S chart, $P \left( S _ { i } > U C L \right) = P \left( S _ { i } < L C L \right) = .0013$ C) For a 3-sigma R chart, $P ( R_{i} > U C L ) = P ( R _{i} < L C L ) = .0013$ D) Only B and C are not correct. E) Only A and C are not correct.

Quizplus · Accepted Answer

B and C are incorrect because the probabilities they mention (.0013) do not align with the standard properties of control charts. For a 3-sigma control chart, the probability of a point falling outside either the upper control limit (UCL) or the lower control limit (LCL) is approximately 0.0027 (or 0.27%) for each tail, summing to about 0.0054 (or 0.54%) for both tails combined, not 0.0013 as stated in options B and C.

Which of the Following Statements Are Not Correct? A) for a 3-Sigma

Which of the Following Statements Are Not Correct?
A) for a 3-Sigma