1.4. Cumulative Cost Per Hour Calculation

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 = $\frac{3}{100} \times (900) = 27$ rupees per hour.

To find the downtime cost per hour of a machine, we take 3% of the machine's hourly equipment cost. Here, the equipment cost is given as 900 rupees. We compute 3% of 900 to find that the downtime cost per hour equals 27 rupees. This means that for every hour the machine is not operational due to downtime, it costs 27 rupees.

Imagine you own a coffee shop. If your espresso machine costs you 900 rupees per hour to operate and it breaks down, the hourly cost of that downtime is similar. If 3% of that cost addresses potential revenue lost while the machine is down, you would interpret it as losing 27 rupees for every hour the machine isn’t working.

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.

To calculate the yearly downtime cost, we multiply the downtime cost per hour by the number of operational hours in a year. Given that the machine operates for 2000 hours annually, we multiply 27 rupees (the downtime cost per hour) by 2000. The total cost of downtime for the year amounts to 54,000 rupees.

Continuing with the coffee shop scenario, if your coffee machine is out of order and not serving coffee for 2000 hours in a year, losing out on 27 rupees per hour would equate to losing a total of 54,000 rupees annually due to missed sales.

Similarly, calculate the downtime costs for the second year, where the downtime percentage is 6%. So, downtime cost is 6% of your equipment cost, Equipment cost is 900 rupees per hour.

Downtime cost per hour = $\frac{6}{100} \times (900) = 54$ rupees per hour

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

In the second year, the downtime percentage increases to 6%. We apply the same formula to find the new downtime cost per hour by multiplying 6% of the equipment cost (900 rupees). This calculation reveals that the downtime cost increases to 54 rupees per hour. Consequently, for a full year of operation (2000 hours), the yearly downtime cost escalates to 1,08,000 rupees.

Back at the coffee shop, imagine your espresso machine's parts are aging and fail 6% of the time, raising your downtime cost to 54 rupees per hour. If the shop operates for 2000 hours in a year and the machine is down during 6% of that, you'll now incur 1,08,000 rupees in downtime costs for that year.

Now, you find the cumulative downtime cost:

Cumulative downtime cost = 54,000 + 1,08,000 = 1,62,000.

To compute the cumulative downtime cost, we simply add the total downtime costs from all years. After the first year, we had 54,000 rupees, and at the end of the second year, with the new costs included, it rises to 1,62,000 rupees. This cumulative total reflects how downtime costs accumulate over time as the machine ages.

Think of it as stacking bills. In the coffee shop, if the first year's downtime costs are a stack of 54,000 rupees and the second year adds another stack of 1,08,000 rupees, your total financial burden due to machine downtime is now 1,62,000 rupees.

Cumulative cost, end of the first year = $\frac{54,000}{2000} = 27$ rupees per hour. Cumulative cost, end of the second year = $\frac{1,62,000}{4000} = 40.5$ rupees per hour.

To understand the cumulative cost per hour, we need to divide the cumulative downtime cost by the total number of operational hours across the years. At the end of the first year, it equals 27 rupees per hour. By the end of the second year, the cumulative cost rises to 40.5 rupees per hour, factoring in the increase in usage (from 2000 to 4000 hours total).

In our coffee shop scenario, if you now factor in the increased downtime costs over time, you’ll realize that each hour of operation, you’re not just losing money for one year but seeing that cumulative cost grow. Thus, over two years, the average cost of downtime per hour reflects its impact more heavily.

Now, you have to account for the loss in productivity. So, the loss in productivity is also going to result in increase in the downtime cost of the machine...

Here, the discussion focuses on the broader implications of downtime beyond just financial costs. When productivity is lost, such as when a machine is unavailable, it may require added time or resources to return to original output levels. This means additional spending for either overtime, additional machinery, or more workers is necessary to regain productivity levels.

Using the coffee shop example, if your coffee machine is down, not only do you lose sales while it's being repaired, but once it’s fixed, you may need extra staff to quickly fulfill the backlogged orders, resulting in a further strain on your budget.

Productivity adjusted cumulative cost per hour = $\frac{40.5}{0.98} = 41.33$ rupees per hour.

To adjust for productivity loss, divide the cumulative cost per hour by a productivity factor. If productivity takes a hit (for example, to 0.98), this adjustment accounts for necessary extra costs incurred due to falling behind schedule and regaining lost productivity. So, the adjusted productivity cost per hour turns out to be 41.33 rupees.

If you're back at your coffee shop and used to selling 100 cups of coffee an hour, but post-repair, you only manage 98 cups due to sluggish operations, this adjustment reflects the added costs—like hiring extra help to boost output—required to get back to where you need to be.

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