Theory of Control Chart
|
Interested Group |
Mean |
Standard Deviation |
Shape |
Control limit |
Process Capability |
|
Distribution of all Population |
Meu = X-doublebar |
S |
Flat, Poisson, Whatever |
UCL x = X-doublebar + 3Sx LCL x = X-doublebar - 3Sx |
Cp = Spec. Tolerance / Process Spread = Spec. Tolerance / (6Sx) = (USL – LSL) / 6S x-bar. (n^0.5) = (USL – LSL) / (UCLx – LCLx) = (USL – LSL) / [(UCLx-bar – LCLx-bar) / n^0.5 ] |
|
Distribution of Sample |
Meu x = X-doublebar |
Sx = S |
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|
Distribution of Subgroup Average |
Meu x-bar = X-doublebar |
S x-bar = Sx / n^0.5 = S / n^0.5 |
Bell-shape |
UCL x-bar = X-doublebar + 3Sx-bar = X-doublebar + 3(Sx / n^0.5) LCL x-bar = X-doublebar - 3Sx-bar = X-doublebar - 3(Sx / n^0.5) |
|
UCL x-bar |
= X-doublebar + 3Sx-bar |
|
= X-doublebar + 3(Sx / n^0.5) |
|
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[But Sx = Rbar / d2 ] Therefore ; |
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|
UCL x-bar |
= X-doublebar + 3(Rbar / (n^0.5) / d2) |
|
= X-doublebar + A2.Rbar |
|
|
A2 = 3 / [ (n^0.5). d2 ] |
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