1. Problem Markov Chains
A manufacturer has one key machine at the core of its production process. Because of heavy use, the machine deteriorates rapidly in both quality and output. Inspection is done at the end of each week classifying the condition of the machine into one of 4 possible states. State Condition Expected cost due to defective units produced. 0 good as new $ 0 1 minor wear $1,000 2 major wear $3,000 3 inoperable $6,000 due to lost production The IEEM analyst models the machine as a markov chain and determines the following steady probabilities for the state of the machine. p0 = 0.2, p1 = 0.5, p2 = 0.2, p3 = 0.1 You are to find the expected cost of defects and lost production per week for this machine.