# The road towards perfect flow: flow velocity (part 2)

There are many approaches and methods that focus on improving flow. And for good reason, as improving flow yields improved profitability and returns. But how, in fact, can we determine our level of “flow”? In the first post, the typical ‘flow rate’ measure turned out to be unsuitable to do so. In this second post in a series of three, I, therefore, introduce flow velocity as a first measure to evaluate the level of and the progress towards flow.

## The need for a better measure of flow

In the previous post, I have described the state of ‘flow’ as a state in which products advance continuously, steadily, smoothly and effortlessly towards the state in which they actually provide value for the customer. I then asked myself the question of how to determine a certain level of flow and how to measure our progress towards better flow. A first, well-known measure of flow, called ‘flow rate’ (also referred to as ‘throughput rate’ or ‘running rate’), was investigated. But I concluded that flow rate would not be a good measure of flow. Flow is not about how many units can pass a certain point in the flow in a given period. Flow is about every single unit of product progressing continuously and steadily at the same speed. Therefore, we need another check item to be able to determine the level of flow that exists in a value stream.

At this point, I would, therefore, like to introduce the check item of ‘flow velocity’ to quantify the level of flow in a value stream.

We need another check item to be able to determine the level of flow of a value stream.

## Flow velocity

In general, speed is the measure of movement. Speed can be defined as the distance traveled per unit of time. It is the rate at which an object has covered the distance that it has traveled. There is a slight problem, however, with this definition of speed that comes from the concept of distance traveled. I can travel around the world, but not change of position as a result. Distance traveled is the total length of the path traveled between two positions, whereas I am more interested in the distance between two positions.

Now we indicated earlier that flow also involves advancement into a specified and particular direction. So, I am not even interested in just distance, but in the distance covered in a certain direction. This is typically referred to as displacement. Displacement is distance in a certain direction and therefore has a sign, whereas distance is only the magnitude of the displacement. In physics, displacement in time is not referred to as speed but as velocity. Velocity is the speed of something in a given direction; it is displacement per unit of time. In everyday language, however, most people will use the terms speed and velocity interchangeably.

In our context, velocity can, therefore, be translated as the product’s advancement or progress towards completion per unit of time.

So how can we measure velocity? To do so, you need a time frame and a measure of the product’s progress towards completion. Let’s discuss both, starting with product advancement.

## Product advancement

As discussed in the first post of this series, in Lean we speak of the ‘flow of work’, not so much the ‘flow of product’. So, within the framework of measuring velocity, we are first looking for a measure of the progress of this work on a product.

At Toyota, the verb “to work” is defined very precisely. It means that we make an advance in the process, and enhance the added value (Lu, 1985). Within work, Ohno subsequently separates non-value-added work and value-added work (Ohno, 1978).

Value-added work, finally, means some kind of processing — changing the shape or quality, nature or character of a product or assembly. Processing adds value and these processing operations are sometimes also referred to as net operations. In processing, the raw materials or parts are made into products to generate added value. Examples of processing are assembling parts, forging raw materials, press forging, stamping metal plates, welding, tempering gears and painting bodies.

So, a measure of a product’s advancement could well be the standard time that would have been required on value-added work (net operations) to achieve the product’s current state in the process.

Next question would be whether to use standard labor time content or elapsed clock time during which net processing has taken place.

Imagine our product has advanced to a state where we — according to standard — would have expended 14 manhours on the product. And imagine we have done so using two people in a 7-hour shift on one working day. So, the time that elapsed while adding value (performing value-added work according to standard) was seven hours, one shift or one working day. If we would have done the work with only one person the elapsed time would have been two shifts or two working days. In the first case, it would progress faster than in the second, but also using more resources during that shorter period of time. The labor time spent on the product in both cases would still have been the same of course.

Now in our case, we would of course only be interested in adding more resources in such a short period of time, when in the end this proves to be useful overall. In other words, when the higher rate of local advancement does not lead to a reduced throughput time overall, it only reduces velocity.

Therefore, in the velocity measure we should take the elapsed clock time during which net processing or value-added (VA) work takes place, independent of the actual number of resources used and independent of the actual labor content.

## Throughput time

The second element in measuring velocity is a time frame. This time frame is used to evaluate the product’s advancement relative to this time frame, typically the elapsed time that it took to achieve this advancement (i.e., a duration).

Shingo writes that the production lead time or lead time at Toyota is defined as the time from the first process (start) to the last (finish) (Shingo, 1981). Similarly, Hall (1983) defines a concept called throughput time as the elapsed time from when material starts into a process until it finishes — through a work center, through a plant; usually in days (or weeks or even months). Later, he also sometimes referred to this time as flow-through time (Hall, 1998).

Now we should be careful here as lead time is also often used as the span of time required to perform an activity that may include time for administrative activities like order preparation as well as physical activities like production, queuing, inspection and transport (Hall, 1983). For instance, the term lead time is often used in measuring the so-called Order-to-Delivery or OTD lead time, defined as the elapsed time between a customer putting in an order and receiving the product. The use of the concept of lead time should therefore be clearly distinguished from lead time as it is typically being used in just-in-time (JIT), sometimes also referred to as throughput time. Here we will also make use of the concept of throughput time to avoid confusion with the many uses of lead time. Throughput time can be defined more specifically as the elapsed time from entry of a material into the production system under consideration until its current state (using the same calendar as in measuring product progress).

So, now we have defined product progress or product advancement as the elapsed net processing or VA time used for the standard value-added work (standard net operations or processing) to achieve the product’s current state in the process. And in measuring velocity we defined the time frame relative to the product’s progress as throughput time as the elapsed time from entry of a material into the production system under consideration until its current state (using the same calendar as in measuring product progress).

Therefore, a product’s velocity can now be defined as the elapsed VA time to achieve the product’s current state, divided by the elapsed time from entry of a material into the production system under consideration until its current state.

Or in short:

Velocity = elapsed VA time / throughput time

Flow velocity is the elapsed VA time until now, divided by the throughput time until now.

## An example of determining flow velocity

Let’s look into an example. Imagine we want to know the velocity of a product that we found in our finished goods inventory. So, the product has completed all of its value-added work. Now assume the elapsed working time used for the standard value-added work for the product is 14 hours (or 2 working days of 7 hours). Now also assume that the product (in its raw material form) was physically received 20 working days before. This is the time frame in the velocity measure. Consequently, the product’s velocity is 2/20 or 0.1.

Now the typical unit of measure of speed (or velocity) is of course meters per second [m/s] or miles per hour [mph] or something similar. In our case, as both the numerator and denominator are units of time, velocity is dimensionless, typically indicated as [1]. To facilitate discussion, however, the velocity of a manufacturing process in Lean is typically indicated in the form of a percentage [%]. In our example, the velocity of the process is said to be 10%. This implies that, until now, the product was actually only making real progress in 10% of the time it has spent in the system under consideration. The other 90% of the time it spent in the system, it did not advance (even though people and/or machines could have been “working” on it partially).

So, a product may be said to take a month to produce but, when we have a closer look, we may discover that, in reality, the actual time the production processes take may be extremely short. The time spent for manufacturing typically is far shorter than the time the product lies idle in storage. This ratio between the time required for net processing and the time the product is in storage may become as high as 1:100 (Lu, 1985). According to Shingo, velocity typically is between 2 and 15% (Shingo 1981).

Now in Lean literature (more than in Toyota literature though) you may come across the concept of Process Cycle Efficiency (PCE) or Process Efficiency Ratio (PER) or Value-Added Ratio (VAR). What is typically meant with these measures is the amount of value-added time divided by the throughput time. And this ratio is typically expressed in the form of a percentage. So, when looking closer, Lean’s well-known process (cycle) efficiency indicator is, in fact, a measure of flow velocity.

So, is this it? We can use flow velocity to measure our level and our progress towards perfect flow? Not so fast! Because there are many different ways in which one can achieve a certain level of flow velocity. One can run in one burst and then rest, or one can run in four smaller bursts and wait in between. Velocity is the same, but flow?

This raises the question of how to measure the smoothness and steadiness of the flow velocity, as an additional measure of flow. This will be dealt with in the third and last post of this series on flow.

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