You are the mechanical engineer in charge of maintaining the machines in a factory. The plant manager has asked you to evaluate a proposal to replace the current machines with new ones. The old and new machines perform substantially the same jobs, and so the question is whether the new machines are more reliable than the old. You know from past experience that the old machines break down roughly according to a Poisson distribution, with the expected number of breakdowns at 2.5 per month. When one breaks down, $1,500 is required to fix it. The new machines, however, have you a bit confused. According to the distributor brochure, the new machines suppose to break down at a rate of aproximately of 3.0 per month (and do coast $1,700 to fix). (In either events, the number of break downs in any month appaers to follow a posson distribution.) On the basis of this information, you judge that it is equally that the rate is 3.0 or 1.5 per month.
A. Based on minimum expected repair cost, should the new machines be adopted?
B. Now you learnt that a third plant in a newby town has been using these machines. They have experienced 6 breakdowns in 3 months. Use this information to find the posterior probability that the breakdown rate is 1.5 per month.
C. Given your posterior probability should your comany the new machines in order to minimize expected repair cost?
D. Consider the information given in part b. If you had read it in the distrubtor's brochure, what would you think? If you had read it in a trade magazine as the result of an independent test, what would you think? Given your answers, what do your think about using sample information and Bayes' theorem to find the posterior probabilities? Should the source of the information be taken into consideration somehow? Could this be done in some way in the application of Bayes' theorem?