SOLUTION: In the new Epiphyte Engineering factory 5000 light bulbs Type A are installed. Their lengths of life are normally distributed with a mean of 360 days and a standard deviation of 60
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Question 1172199: In the new Epiphyte Engineering factory 5000 light bulbs Type A are installed. Their lengths of life are normally distributed with a mean of 360 days and a standard deviation of 60 days.
a) If it is decided to replace all bulbs at one specified time, what interval must be allowed between replacements if not more than 10% of bulbs should fail before replacement?
b) What practical considerations might dictate such a replacement policy?
c) The supplier offers a new type of bulb, Type B, that has a mean life of 450 days and the same standard deviation (60 days) as the present type. If these bulbs were to be used how would the replacement time be affected?
d) Determine whether the new type of bulb is preferable given that is costs 25% more than the existing Type A. Present and explain your conclusions.
f) A rival supplier now offers a third type of bulb, Type C, that has a mean life of 432 days and a standard deviation of 45 days. If these bulbs were to be used how would the replacement time be affected?
How should the Type C bulb compare for costs if it is to be adopted? Present and explain your conclusion.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
z for the 10th percentile of failure is -1.282
length of life is z=(x-mean)/sd
so -1.282*60=x-360
-76.92=x-360
x=283 days
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Practicality is the amount of work needed--replacing may be time intensive. The cost of replacing all bulbs has to be balanced against the issues should one burn out. Where is it?
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B bulbs that lasts 450 days, 90 days longer, will require all to be replaced (same policy) in 373 days.
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If B lasts 25% longer, by the means, it is exactly 25% longer. But because the sd is less per the mean, the 10th percentile for B is 31% longer than it is for A costing 25% more. It's a close call slightly in favor of B.
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Type C would be -1.282*45=x-432
so x=374.31. It is slightly more than B, and has less variability, generally a good thing, Its costs should be similar to B although slightly less would be reasonable(0.3%).
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