In the new Epiphyte Engineering factory, 5000 light bulbs Type A is 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 it 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.