I am very confused. Any help will be greatly appreciated. Thank you. You’ve just

Question

I am very confused. Any help will be greatly appreciated. Thank you.

You’ve just started a business using a laser tool to etch designs in copper. It’s called Groovy Signs and Name Plates (GSNaP). Your suppliers sell copper in pre-cut sheets of various thicknesses and because of the current value of commodities they charge you for the copper by the weight of the roll. Consequently, you want the sheeting to be thin to keep the weight down, but thick enough to hold your etchings. The manufacturer of the etching equipment has established guidelines suggesting the equipment will not work with sheets thinner than 0.00097 meters (i.e., .97mm) or thicker than 0.00121 meters (1.21mm). To choose between two suppliers – A and B - you get a shipment of 100 sheets each day for a month from each supplier. At the end of the month, you find supplier A provided sheets with a mean thickness of 1.10mm and a standard deviation (?) of .4mm. Supplier B provided sheets with a mean thickness of 1.05mm and a standard deviation (?) of .3mm.

Determine the values of Cp, CPU, CPL and Cpk for each supplier. Which supplier would you prefer? Explain

Explanation / Answer

The values given in the question are:

LCL = 0.97mm

UCL = 1.21mm

Mean (A) = 1.1 mm and Std dev(A) = 0.4mm

Mean(B) = 1.05mm and Std dev(B) = 0.3mm

Cp::

Cp = (UCL-LCL)/(6*Std dev)

Cp(A) = (1.21-0.97)/(6*0.4) = 0.1

Cp(B) = (1.21-0.97)/(6*0.3) = 0.133

CpU::

CpU = (UCL -Mean)/(3*Std dev)

CpU(A) = (1.21-1.1)/(3*0.4) = 0.092

CpU(B) = (1.21-1.05)/(3*0.3) = 0.178

CpL::

CpL = ( Mean - LCL)/(3* Std dev)

CpL(A) = (1.1-0.97)/(3*0.4) = 0.108

CpL(B) = (1.05 - 0.97)/(3*0.3) = 0.089

CpK ::

CpK = min(CpU,CpL)

CpK(A) = min(0.092,0.108) = 0.092

CpK(B) = min(0.178, 0.089) = 0.089

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