Question

 Chicken Eggs

 A farmer focusing on the production of eco-friendly chicken eggs collects the following data about his output. In a sample of 50 eggs, the farmer finds the average egg to weigh 47 grams. The standard deviation of the egg weight is 2 grams and the distribution of weights resembles a normal distribution reasonably closely. The farmer can sell the eggs to a local distributor. However, they have to be in the interval between 44 grams and 50 grams (i.e., the lower specification limit is 44 grams and the upper specification limit is 50 grams).

 What is the capability score of the eco-friendly chicken egg operation?

 What percentage of the produced eggs fall within the specification limits provided by the local distributor? By how much would the farmer have to reduce the standard deviation of the operation if his goal were to

 obtain a capability score of Cp=2/3 (i.e., get 4.5% defects)?

Answer 1

Sample = 50

Mean = 47 grams

Standard devaition == 2 grams

Lower specification limit = LSL = 44 grams;Upper specification limit = USL = 50

Capability score is given by parameters Cp

Cp= ==0.5

The process is not capable since Cp<0.667

TO find % outside limits, we find z for LSL and USL

Z_USL==50-47/2 = 1.5

from z table, we get corresponding value for z=1.5 as 0.9332. This falls under spec

For ZLSL==1.5

z=0.9332

Hence total % out of specification =(1-0.9332 + 1-0.9332)=13.36%

If Cp=2/3 = 0.667=(50-47)/

Therefore = =1.5

Hence the standard devaition has to be reduced to 1.5 for Cp = 2/3