Question

6)  (10pts) Using the appropriate control chart, determine two-sigma control limits for each case:

1. An inspector found an average of 3.9 scratches the exterior paint of each of the

Automobiles being prepared for shipment dealer,

2. Before shipping lawn mowers to dealers an inspecto attempt to start each mower and

Notes any that do not start on the first try. The lot size is 100 mowers,  and an  average of 4 did not start (4 percent

Answer 1

a.

Since only the average number of scratches is known, C-chart would be applicable in this case.

Average Number of scratches or non-conformities on each automobile = C bar = 3.9

Z = 2

UCL = C bar + ( Z x √C bar) = 3.9 + ( 2 x √3.9)

= 3.9 + ( 2 x 1.975) = 3.9 + 3.95

= 7.85

LCL = Max (0, C bar - ( Z x √C bar))

C bar - (Z  x √C bar) = 3.9 - 3.95 = -0.05

So, LCL = Max ( 0, -0.05) = 0

Therefore,

UCL = 7.85

LCL = 0

b)

Since the percent defective and sample size are known, P-chart would be applicable in this case.

Percent defective = 4% = 0.04

Z = 2

Number of samples = 100

UCL = Percent defective + ( Z x Standard Deviation)

LCL = Percent defective - ( Z x Standard Deviation)

Standard Deviation = √((Percent defective x ( 1 - Percent defective)) / Number of samples)

= √ (( 0.04 x ( 1 - 0.04))/ 100) = √(( 0.04 x 0.96)/ 100)

√ ( 0.0384/ 100) = √0.000384

= 0.0196

So,

UCL = 0.04 + ( 2 x 0.0196) = 0.04 + 0.0392 = 0.0792

LCL = 0.04 - ( 2 x 0.0196) = 0.04 - 0.0392 = 0.0008