Machines in a factory break down at an exponential rate of six per hour. There is a single repairman who fixes machines at an exponential rate of eight per hour. The cost incurred in lost production when machines are out of service is $10 per hour per machine. What is the average cost rate incurred due to failed machines?
In a factory, machine breakdowns are a common and costly issue. The cost of machine failures can have a significant impact on a factory's operations and bottom line. In this blog post, we will explore the average cost rate incurred due to failed machines in a factory where machines break down at an exponential rate of six per hour and there is a single repairman who fixes machines at an exponential rate of eight per hour.
Calculating the Average Cost Rate:
To calculate the average cost rate incurred due to failed machines, we need to take into account the cost of lost production when machines are out of service. In this case, the cost incurred in lost production is $10 per hour per machine. To calculate the average cost rate, we need to know the average number of machines that are out of service at any given time.
The average number of machines that are out of service can be calculated as follows:
Average number of machines out of service = (Breakdown rate) / (Repair rate – Breakdown rate) = (6) / (8 – 6) = 6
The average cost rate incurred due to failed machines can then be calculated as follows:
Average cost rate = (Average number of machines out of service) * ($10 per hour per machine) = (6) * ($10) = $60 per hour
The cost of machine failures can have a significant impact on a factory's operations and bottom line. By understanding the average cost rate incurred due to failed machines, factories can take steps to minimize these costs and improve their operations. In this example, the average cost rate was found to be $60 per hour, which highlights the importance of having an efficient repair process and minimizing machine downtime.
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