Suppose that the lifespan of a piece of equipment is normally distributed with mean 10 years and standard deviation of 3 years. A particular piece of equipment’s current age is 11 years. The firm is considering two options; i) replace it now, ii) wait until age 13 to replace it (unless it dies before then, in which case an unscheduled replacement is necessary). Suppose that immediate replacement will cost the company a TL. Replacement at age 13 (if the equipment lasts that long) will cost b TL, where b < a. An unscheduled replacement between now and age 13 (that is, if the equipment dies suddenly during the next two years) will cost c TL, where c > a. • What is the probability that, barring replacement now, the equipment will last until age 13? What is the expected cost of replacement if the equipment is not replaced now? • Under what condition a, b and c, is expected cost lower if equipment is replaced now, rather than under the age 13 policy?
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Suppose that the lifespan of a piece of equipment is
deviation of 3 years. A particular piece of equipment’s current age is 11 years. The firm is considering
two options; i) replace it now, ii) wait until age 13 to replace it (unless it dies before then, in which case
an unscheduled replacement is necessary).
Suppose that immediate replacement will cost the company a TL. Replacement at age 13 (if the equipment lasts that long) will cost b TL, where b < a. An unscheduled replacement between now and age 13
(that is, if the equipment dies suddenly during the next two years) will cost c TL, where c > a.
• What is the probability that, barring replacement now, the equipment will last until age 13?
What is the expected cost of replacement if the equipment is not replaced now?
• Under what condition a, b and c, is expected cost lower if equipment is replaced now, rather than
under the age 13 policy?
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