Determine the steady-state probabilities

Assignment Help Operation Management

Reference no: EM131741605

A company owns three CNC machines. Although they go through a well-planned preventive maintenance program, each working machine breaks down five times per week, on the average. A repairperson is available to repair the machines when they break down. If a machine breaks down, it is served immediately if the repairperson is idle; otherwise, it waits for service. The repairperson can repair machines at an average rate of ten machines per week. The times that working machines take to breakdown and their repair times are continuous random variables which distributions possess the memoryless property. Thus, this system can be modeled as a continuous-time Markov chain.

a) Define the states of the Markov chain and draw the state transition diagram including the transition rates

b) Determine the steady-state probabilities.

c) What is the utilization of the repairman (i.e., fraction of time the repairman is busy)

d) What is the average number of working machines?

e) What is the average number of machines waiting to be repaired?

Reference no: EM131741605

Questions Cloud

Traditional on the job productivity estimation method : Use the traditional on-the-job productivity estimation method.

Calculate mean and median normal daily minimum temperature : The Mount Washington Observatory (MWO) in New Hampshire claims to have the world's worst weather. Below are some data on the weather extremes recorded.

Elements in an organization internal environment : Considering the elements in an organization’s internal environment, which do you think are most important for an organization to grow and prosper?

Create a comic book based on tangible interpretation : Develop an in-depth character study (utilizing research) or a presentation on a cultural event or a theory connected to the literature.

Determine the steady-state probabilities : Determine the steady-state probabilities. What is the average number of working machines?

Main program prompts the user for the amount of money : Modify the program in Exercise 3a so that the main program prompts the user for the amount of money and passes it to the interest-calculating function.

Can osha cite an employer for a mobile crane operator : Question number 1. Can OSHA cite an employer for a mobile crane operator that has not had a physical exam prior to operating a mobile crane?

Future of social media and social media marketing : How do you view the future of social media and social media marketing? Write a description citing trends or developments you think may evolve.

Proportion of time clerk is working on task : We are trying to estimate the proportion of time a clerk is working on a task.

User Account

All Pages