Process Excellence Coaching & Consulting

I dare to say that in some situations, simple average works as an effective capability index!

Process

The concept is applicable to specific group of processes, most often transactional, where time is the most important: “the sooner the better”.

These processes should be part of business-to-business model rather than a business-to-consumer model: what matters is the total business effect, not the ‘perception’ of the process by the individual user.

Example: Shared Service Centre (accounting, purchasing, etc.) providing these services to other companies or branches of the same corporation.

Process Indicator

The most common metric (KPI) of such processes that I have come across is the percentage of orders/services completed in a given time (“this month, the invoicing department processed 95% of invoices in less than the required 6 business days“)

I was not (and am not) a fan of this metric for several reasons:

• Two processes with the same “percentage in a given time” can be significantly different (the missing 5% from the example above can be processed in both 7 and 70 business days)
• People working and managing such a process have no interest in taking care of cases exceeding the required time (“It does not matter whether we process this particular invoice in 7 days or 70 days; It’s lost anyway“)
• I was “raised” on production processes and capability metrics like Ppk and Cpk 😉

Better (?) Indicator

Looking for a better metric of the effectiveness of the processes discussed here, I followed two paths.

The first path was terribly uphill:

• The times of individual orders in these processes have a log-normal distribution rather than a normal one
• At the same time, we usually have the luxury of having a complete set of data (information about all processed invoices), so we do not have to assume a specific population distribution, but we can determine/plot the “Empirical Cumulative Distribution Function” (CDF) for our specific process (as in the attached picture)
• Looking at the CDF of various processes, I found that a good metric would be the area between the curve and the Y axis (time = zero). The ‘closer to zero’ the curve is, the better the process (more invoices processed with less time). The ideal we are aiming for is a curve practically parallel to the Y axis, close to zero (“all invoices are processed almost immediately“)
• But how to calculate such an area of the area? It’s probably some kind of integral, on a function related to probability and log-normal distribution – magic and higher mathematics…
• However, I was determined and tried to figure something out on a simple example. And maybe I’ll discover some new, unknown Ppk indicator??
• I did it. I managed to calculate that this surface area is equal to … the arithmetic average of the process. My daughters were laughing out loud: “Dad, so you managed to determine the formula for the arithmetic mean, right? You should have said that you were looking for it, we would have helped!” 😂
• Now, after help from experts on LinkedIn I know that I have ‘discovered’ known feature of the cumulative distribution function…

The second path was simpler (and of course I came up with it later 🤦):

• Since we are interested in the time of processing orders (“the sooner the better”) and we work in the B2B mode – a fairly obvious indicator of the process is the total time spent on a given service, on all orders in a given month (“We processed 1000 invoices. How much time did it cost us in total?”)
• Since the volume of orders varies from time to time, let’s normalize this total time by the number of orders, i.e. let’s determine the average time per order – which is exactly arithmetic average.

Average as a capability metric for (selected) processes

Once I came to the usual average as a measure of the effectiveness of the processes we are talking about here, I realized many of its advantages:

• Super easy to calculate
• Independent from the actual distribution of the data behind (log-normal, normal or any other)
• Unlike the “percentage of orders over a given time” indicator, it is affected by each order. Therefore, it is “profitable” to fight for all, even the “lost” orders, because the average will “notice” whether overdue invoices are processed in 7 or 70 days
• Similarly to the Ppk indicator for “production” processes (usually with a normal distribution), the average here includes both variability and the location of the data. The features of the log-normal distribution show that each reduction in the variability of such a process automatically reduces its average. So we can treat the average here in the same way as the Ppk in normally distributed processes: as a single number summarizing how efficient the process is, how close we are to the ideal state (“ all invoices are processed almost immediately”).

The last point is unfortunately also a disadvantage of this approach. But more in terms of acceptance than the mathematics behind it: we are so used to treating the mean as something separate from variation that it is difficult to convince ourselves to a different interpretation.

What do you think about this approach? What indicators do you encounter in this type of processes? What do you use?