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So, downtime cost per hour equal to 3% of your equipment cost. Equipment cost is nothing but 900 rupees per hour.

Downtime cost per hour = 3 / 100 × (900) = 27 rupees per hour

Your machine is going to operate in a year for 2000 hours. So, what is your yearly downtime cost? Yearly downtime costs for the first year is,

Downtime cost per year = 27 × 2000 = 54,000 rupees.

In this chunk, we calculate the downtime cost associated with a piece of equipment. Downtime cost is defined as the loss incurred when the equipment is not operational. The first step is to determine the cost of downtime per hour, which is calculated as a percentage (3%) of the equipment's hourly cost (900 rupees). This gives us a downtime cost of 27 rupees per hour. To find the total downtime cost for a year, we multiply the hourly downtime cost by the total operational hours in a year (2000 hours), resulting in a total of 54,000 rupees for the year.

Imagine you have a vending machine that earns you 900 rupees every hour it operates. If it breaks down for 3 hours, that's 3% of your income lost per hour. So, you lose 27 rupees per hour due to that downtime. If the vending machine is inactive for a whole year but operates for 2000 hours, you'd lose 54,000 rupees overall. This is similar to losing earnings during repairs in any business.

Similarly, calculate the downtime costs for the second year, in which the downtime percentage is 6%. So, downtime cost is 6% of your equipment cost, which results in:

Downtime cost per hour = 6 / 100 × (900) = 54 rupees per hour.

Downtime cost per year = 54 × 2000 = 1,08,000 rupees.

In this part, we assess the downtime costs for the second year. As the downtime increases to 6%, we first recalculate the downtime cost per hour using the updated percentage applied to the equipment's hourly cost (900 rupees), leading to 54 rupees per hour. Next, to compute the total downtime cost for the year, we multiply this hourly rate by the full operation time of 2000 hours, resulting in an annual downtime cost of 1,08,000 rupees.

Consider the same vending machine scenario, where now we've found that it breaks down more often, leading to a 6% downtime over the year. Instead of earning 27 rupees for every hour it’s working, now it earns 54. If it only worked for 2000 hours, your losses could rise to 1,08,000 rupees. Think of it as a restaurant that starts needing repair work more frequently due to age, increasing their non-functioning hours and corresponding losses.

So, now you find the cumulative downtime cost by adding it.

Cumulative cost, end of the first year = 54,000 Cumulative cost, end of the second year = 54,000 + 1,08,000 = 1,62,000 rupees.

This section discusses how to compute the cumulative downtime costs over multiple years. To do this, you begin with the downtime cost from the first year and then add the downtime cost from subsequent years. After the second year, the cumulative cost adds up, totaling 1,62,000 rupees at the end of year two by combining the previous year's cumulative cost and the new year's downtime costs.

Think of it like keeping track of expenses in a personal budget over two years. If you spent 54,000 rupees in the first year due to your vending machine downtime, and then 1,08,000 rupees in the second year, your cumulative spending for both years would be the total of these two amounts combined. It's akin to tracking cumulative debt — each year's losses add to the previous total.

Now, you have to account for the loss in productivity, which increases downtime costs. Loss of productivity results in additional costs because the machine has spent time in repairs.

Here, we examine the impact of lost productivity on overall costs. When a machine is down for repairs, it doesn’t only incur direct downtime costs but also leads to an indirect loss in productivity. This is because the project may fall behind schedule, leading to additional expenses to meet deadlines, such as engaging more workers or machines.

Consider a factory where machines are supposed to run continuously to meet customer orders. If a machine breaks down, not only do they incur repair costs, but they might need to hire extra shifts or even rent additional machines to keep up with production, leading to unanticipated higher costs. It’s similar to a chef scrambling for extra help if their main stove goes out.

So, this is how we estimate the economic life of the machine. We have optimized the productivity with respect to cost. If you are going to hold onto the machine for more years, beyond the optimum replacement point, the losses per hour are reflected in the total operational costs.

In the concluding part, the discussion shifts towards how to assess the optimal time to replace a machine. By considering all accrued costs, including downtime, productivity loss, and obsolescence, businesses are encouraged to identify the point at which maintaining a machine becomes more costly than replacing it. Continuing to use the equipment beyond its economic life leads to higher costs each hour of operation.

Think of it like driving an older car that frequently breaks down. While it may seem cheaper to hold on to it, the ongoing repair costs and time lost from being unable to drive can outweigh the price of investing in a newer, more reliable vehicle. The goal is to find that sweet spot where owning and operating your equipment costs the least.

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