16-02-02 - n:= 1 μ =.65 μ 3 ⋅σ n =.695 μ 3 ⋅σ n...

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16.2.2 A production process making chemical solutions is in control when the solution strengths have a mean of μ 0 := 0.650 and a standard deviation of σ := 0.015 Suppose that it is a reasonable approximation to take the solution strengths as being normally distributed. At regular time intervals the solution strength is measured and is plotted on a control chart. (a) What are the center line and control limits of a 3-sigma control chart that you would construct to monitor the strengths of the chemical solutions?
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Unformatted text preview: n := 1 μ = .65 μ + 3 ⋅σ n = .695 μ- 3 ⋅σ n = .605 (b) If a randomly sampled solution had a strength of x := 0.662 would you take this as evidence that the production process had moved out of control? μ- 3 ⋅σ n < x and x < μ + 3 ⋅σ n = true This value falls within the acceptable control range. What if x := 0.610 μ- 3 ⋅σ n < x and x < μ + 3 ⋅σ n = true This value falls within the acceptable control range. page 1...
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