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Chart Based on Standard DeviationsAn chart based on
Chapter 14, Problem 14 BSC(choose chapter or problem)
14. \(\mathrm x\ ^{-}\) Chart Based on Standard Deviations An \(\mathrm x\ ^{-}\) chart based on standard deviations (instead of ranges) is made by plotting sample means with a centerline at x ̄ ̄ and control limits at \(\mathrm {x\ ^{- \ -}+A\ 3\ s\ ^-}\) and \(\mathrm {x\ ^{- \ -}-A\ 3\ s\ ^-}\), where A 3 is found in Table 142 and \(\mathrm s\ ^{-}\) is the mean of the sample standard deviations. Use the data in Table 141 to construct an \(\mathrm x\ ^{-}\) chart based on standard deviations. Compare the result to the \(\mathrm x\ ^{-}\) chart based on sample ranges (as in Example 5).
Equation Transcription:
Text Transcription:
x ^-
x ^-
x ^{- -}
x ^{- -}+ A 3 s ^{-}
x ^{- -}- A 3 s ^{-}
s ^-
x ^-
x ^-
Questions & Answers
QUESTION:
14. \(\mathrm x\ ^{-}\) Chart Based on Standard Deviations An \(\mathrm x\ ^{-}\) chart based on standard deviations (instead of ranges) is made by plotting sample means with a centerline at x ̄ ̄ and control limits at \(\mathrm {x\ ^{- \ -}+A\ 3\ s\ ^-}\) and \(\mathrm {x\ ^{- \ -}-A\ 3\ s\ ^-}\), where A 3 is found in Table 142 and \(\mathrm s\ ^{-}\) is the mean of the sample standard deviations. Use the data in Table 141 to construct an \(\mathrm x\ ^{-}\) chart based on standard deviations. Compare the result to the \(\mathrm x\ ^{-}\) chart based on sample ranges (as in Example 5).
Equation Transcription:
Text Transcription:
x ^-
x ^-
x ^{- -}
x ^{- -}+ A 3 s ^{-}
x ^{- -}- A 3 s ^{-}
s ^-
x ^-
x ^-
ANSWER:
Solution 14BB
There is a small difference in control limits of formula and Minitab due to rounding off. This chart which is based on standard deviation suggests that the process mean is in the statistical control because none of the three out-of-control criteria is violated. Therefore, the process is in-control and there is no need for quality control for this process.
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