# Question: A production process contains a machine that deteriorates rapidly in

A production process contains a machine that deteriorates rapidly in both quality and output under heavy usage, so that it is inspected at the end of each day. Immediately after inspection, the condition of the machine is noted and classified into one of four possible states:

The process can be modeled as a Markov chain with its (one-step) transition matrix P given by

(a) Find the steady-state probabilities.

(b) If the costs of being in states 0, 1, 2, 3, are 0, $1,000, $3,000, and $6,000, respectively, what is the long-run expected average cost per day?

(c) Find the expected recurrence time for state 0 (i.e., the expected length of time a machine can be used before it must be replaced).

The process can be modeled as a Markov chain with its (one-step) transition matrix P given by

(a) Find the steady-state probabilities.

(b) If the costs of being in states 0, 1, 2, 3, are 0, $1,000, $3,000, and $6,000, respectively, what is the long-run expected average cost per day?

(c) Find the expected recurrence time for state 0 (i.e., the expected length of time a machine can be used before it must be replaced).

## Relevant Questions

The example in Sec. 2.1 summarizes an award-winning OR study done for Merrill Lynch. Read Selected Reference A2 that describes this study in detail. (a) Summarize the background that led to undertaking this study. (b) Quote ...Refer to Selected Reference A4 that describes an OR study done for Yellow Freight System, Inc. (a) Referring to pp. 147–149 of this article, summarize the background that led to undertaking this study. (b) Referring to p. ...Read Selected Reference A3 that describes an OR study done for Swift & Company. (a) Summarize the background that led to undertaking this study. (b) Describe the purpose of each of the three general types of models ...Consider the following gambler’s ruin problem. A gambler bets $1 on each play of a game. Each time, he has a probability p of winning and probability q = 1 p of losing the dollar bet. He will continue to play until he ...Reconsider Prob. 29.2-1. (a) Use the procedure Chapman-Kolmogorov Equations in your IOR Tutorial to find the n-step transition matrix P(n) for n = 2, 5, 10, 20. (b) The probability that it will rain today is 0.5. Use the ...Post your question