I need the Upper Control Limit ?(UCL Subscript Upper X overbarUCLX?)equals=4.669

Question

I need the

Upper Control Limit

?(UCL Subscript Upper X overbarUCLX?)equals=4.6694.669.

?(Enter your response rounded to three decimal? places.)

Lower Control Limit

?(LCL Subscript Upper X overbarLCLX?)equals=3.6993.699.

?(Enter your response rounded to three decimal? places.)

Upper Control Limit

?(UCL Subscript Upper RUCLR?)

?(Enter your response rounded to three decimal? places.)

Lower Control Limit

?(LCL Subscript Upper RLCLR

Thanks

X Problem 9 ! Question Help AnderSet Laboratories produces rough lenses that will ultimately be ground into precision lenses for use in laboratory equipment. The company has developed the following thickness measures, based on 15 samples of four lenses that were taken when the process was under control: Click the icon to view the sample data. F Click the icon to view the values of the A2, D3, and D4 constants. i More Info a. X is . (Enter your response rounded to three decimal places.) More Info Minimum Maximum Sample Size N A2 D 3 D4 3.27 - 2.57 OWN --- 1.88 1.02 0.73 0.58 0.580 0.48 0.480 0.42 0.08 0.37 0.14 0.34 0.18 0.31 0.22 0.29 0.26 0.26 0.27 0.28 2.28 2.11 2.00 1.92 1.86 1.82 1.78 1.74 1.74 Mean (Microns) (N= 4) 3.785 4.217 4.254 3.788 3.851 4.176 3.177 5.491 3.756 6.373 4.112 4.045 4.175 3.797 4.172 3.643 3.869 4.021 3.771 3.527 3.517 2.924 3.768 2.879 5.183 4.095 3.986 3.954 3.698 4.006 3.987 4.286 4.407 3.984 4.081 4.579 3.973 5.616 4.202 6.393 4.248 4.314 4.382 3.831 4.272 11 0.29 1.72 Print Done Print Done

Explanation / Answer

It is mentioned that :

Sample size = n = 4 lenses

Following are the value of constants for n = 4 :

A2 = 0.73

D4 = 2.28

D3 = 0

iIt is to be noted that :

UCLx = Xbar + A2.rbar

LCLx = Xbar – A2.Rbar

Therefore ,

UCLx – LCLx = 2 .A2.Rbar

Or, 4.669 – 3.699 = 2 x 0.73 x Rbar

Or, 0.97 = 1.46.Rbar

Or, Rbar = 0.97/1.46 = 0.6643

Therefore ,

CONTROL LIMITS FOR RANGE ( R ) CHART :

Upper Control Limit ( UCLR ) = D4.Rbar = 2.28 x 0.6643 = 1.5146

Lower control Limit ( LCLr ) = D3.rbar = 0

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