Question

Consider a manufacturing system that follows the following steps: a part to be manufactured will begin the process by entering step A. After step A, 15% of the parts must be reworked, i.e., returned to step A, 5% of the parts are salvaged, and 80% proceed to step B. After step B, 10% of the parts must be returned to step A, 2% are salvaged, 88% of emerged to be sold for a profit. Define an appropriate Markov Chain that represents the production process for a part (define the state variable and the state space).

Answer 1

A manufacturing system with different steps and probabilities of transitioning between them as a Markov Chain, we can define the state variable as the step in the production process and the state space as the possible steps. The transition probabilities can then be defined based on the given percentages for returning to a previous step or emerging as finished parts.

Step-by-step explanation:

For this manufacturing system, we can define the state variable as the step in the production process that the part is in. The state space will consist of four states: A, B, Returned to A, and Salvaged.

To represent the production process as a Markov Chain, we can define the transition probabilities between states. From step A, 15% of the parts return to step A, 5% are salvaged, and 80% proceed to step B. From step B, 10% return to step A, 2% are salvaged, and 88% emerge as finished parts for sale.