The specifications on an electronic component in a targetacquisition system are

Question

The specifications on an electronic component in a targetacquisition system are that its life must be between 5000 and 10,000 h. The life is normally distributed with mean 7500 h. The manufacturer realizes a price of $10 per unit produced; however, defective units must be replaced at a cost of $5 to the manufacturer. Two different manufacturing processes can be used, both of which have the same mean life. However, the standard deviation of life for process 1 is 1000 h, whereas for process 2 it is only 500 h. Production costs for process 2 are twice those for process 1. What value of production costs will determine the selection between processes 1 and 2?

Explanation / Answer

Process 1 ,mean = 7500 , sd = 1000

Z = (X -7500)/1000

P(being defective) = 1 - P(5000 <X< 10000)

=1 - P(-2.5 < X< 2.5)

= 2*0.0062 = 0.0124

total number of item produced = x

Total cost = x (10 + 5 *0.0124) = 10.062*x

For process 2

,mean = 7500 , sd = 500

Z = (X -7500)/500

P(being defective) = 1 - P(5000 <X< 10000)

=1 - P(-5 < X< 5)

= 0

Total cost = 20x

Hence Process 1 is better

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