The Dynaco Manufacturing Company produces a productin a process consisting of operations of five machines. Theprobability distribution of the number of machines that willbreak down in a week is as follows:Every time a machine breaks down at the Dynaco Manufac-turing Company, either one, two, or three hours are requiredto fix it, according to the following probability distribution:a. Simulate the repair time for 20 weeks and compute theaverage weekly repair time.b. If the random numbers that are used to simulate break-downs per week are also used to simulate repair timeper breakdown, will the results be affected in any way?Explain.c. If it costs $50 per hour to repair a machine when itbreaks down (including lost productivity), determine theaverage weekly breakdown cost.d. The Dynaco Company is considering a preventive mainte-nance program that would alter probabilities of machinebreakdowns per week as follows:The weekly cost of the preventive maintenance program is$150. Using simulation, determine whether the companyshould institute the preventive maintenance program. Machine Breakdowns per Week Probability0 0.201 0.302 0.203 0.154 0.105 0.051.00
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
The Dynaco Manufacturing Company produces a productin a process consisting of operations of five machines. Theprobability distribution of the number of machines that willbreak down in a week is as follows:Every time a machine breaks down at the Dynaco Manufac-turing Company, either one, two, or three hours are requiredto fix it, according to the following probability distribution:a. Simulate the repair time for 20 weeks and compute theaverage weekly repair time.b. If the random numbers that are used to simulate break-downs per week are also used to simulate repair timeper breakdown, will the results be affected in any way?Explain.c. If it costs $50 per hour to repair a machine when itbreaks down (including lost productivity), determine theaverage weekly breakdown cost.d. The Dynaco Company is considering a preventive mainte-nance program that would alter probabilities of machinebreakdowns per week as follows:The weekly cost of the preventive maintenance program is$150. Using simulation, determine whether the companyshould institute the preventive maintenance program.
Machine Breakdowns per Week Probability
0 0.20
1 0.30
2 0.20
3 0.15
4 0.10
5 0.05
1.00
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