Question An appliance manufacturer needs a resistor that has to have a resistanc

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An appliance manufacturer needs a resistor that has to have a resistance of 100±5 ohms. Three suppliers have submitted bids for the resistor. Supplier A is able to supply resistors with a mean resistance of 102 ohms with a standard deviation of 2 ohms. Supplier B is able to supply resistors with a mean of 99 ohms and a standard deviation of 1 ohms. Finally, supplier C’s resistors have a mean resistance of 100 ohms and a standard deviation of 5 ohms.

(a.) Which one or more of these suppliers is capable of supplying the manufacturer’s needs? Answer by calculating an appropriate process capability measure for each supplier.

(b.) The manufacturer needs these resistors in quantities of 100,000 units. For each of the three suppliers calculate the number of units that might not meet the specification limits set by the manufacturer. Assume that resistance of the resistors follows a normal distribution with means and standard deviations as given for the supplier.

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Explanation / Answer

a)

We need to find Cpk to determine which supplier best suits the requirements

USL = 105 ; LSL = 95

>> For Supplier A , Mean = 102 , Std dev = 2

CpU(A) = (USL-Mean)/(3*Std Dev) = (105-102)/(3*2) = 0.5

CpL(A) = (Mean -LSL)/(3* Std Dev) = ( 102-95)/(3*2) = 1.167

CpK = min(CpU, CpL)

CpK(A) = min(0.5,1.167) = 1.167

>> For supplier B,

CpU = (105 - 99)/(3*1) = 2

CpL =(99-95)/3*1 = 1.333

CpK(B) = min(2,1.333) = 1.333

>> For Supplier C,

CpU =(105-100)/(3*5) = 0.333

CpL =(95-100)/3*5 = -1.667

CpK(C) = min(0.333, -1.667) = -1.667

The higher the value of CpK , the more the process is capable of meeting specification .

Therefore process B is most capable

(b)

We need to determine percentage above upper specification and percentage below lower specification. For this ,we need to find Z values first and then corresponding percentages

For A,

Z upper = USL - mean/(std dev) = (105-102)/2 = 1.5

Percentage above upper limits = 6.68%

Z lower = (Mean -LSL)/ Std dev = (102-95)/2 = 3.5

Percentage below lower limits = 0.02%

Units that don't specification limits = 100000*(6.68%+0.02%) = 6700

>> For supplier B

Z upper = (105-99)/1 =6

Percentage above upper limits = 0%

Z lower = (99-95)/1 = 4

Percentage below lower limits = 0.00317%

Units that won't meet specifcations = 0.00317% of 100000 = 3.17 units

>> For C,

Z upper = (105-100)/5 = 1

Percentage above upper limits = 15.865%

Z lower =(100-95)/5 = 1

Percentage below lower limits = 15.865%

Units dont meet specifications = 100000*(15.865%+15.865%) = 31730 units

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