Mathematics, 13.04.2021 04:10 kaylorb8284
A machine is used to produce precision tools. The machine can be considered in one of three possible working conditions: good, fair, poor. If the machine is in good condition today, then 40% of the time it will be good tomorrow and 30% of the time in fair condition. If the machine is in fair condition today then it will be in fair condition tomorrow 10% of the time and poor 20% of the time. If the machine is in poor condition today then it will be poor tomorrow 40% of the time and good 60% of the time. A machine in good condition will produce about 156 tools/day, one in fair condition will produce about 69 and one in poor condition only produces 40.
a. Define states and construct the one-step transition probability matrix P.
b. Assume that long-run probabilities (IT vector) are given. In terms of these probabilities, write a mathematical expression for the expected production of tools per day.
c. Assume that long-run probabilities (Ä«t vector) are given. In terms of these probabilities, what is the expected daily loss in production due to the machine not always operating in the good condition?
Answers: 3
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