unit as the “thing” you are measuring; in this case we’re talking about days.
Figure 1-2 shows the time taken to process the orders. The cycle time varies from as short as one day to as long as seven days. Each of the data points represents a customer’s experience of the process. As well as seeing how much performance varies, you can also see the “shape” of the data. This data looks normally distributed. In a normal distribution, the shape is symmetrical around the mean, and the data has a 50-percent chance of falling either side of it. Sometimes this shape is referred to as a bell curve or a Gaussian distribution. Many things that are measured fall into this shape — for example, the heights of people, the size of snowflakes, and IQ scores.
© Martin Brenig-Jones and Jo Dowdall
FIGURE 1-2: Histogram showing the time taken to process orders.
When the data is normally distributed, we can understand the likely percentage of the population within plus one or minus one standard deviation from the average (or mean), plus two or minus two standard deviations from the average, and so on. Assuming your sample is representative, you can see how your data provides a good picture of the process cycle time. You find that approximately two-thirds of them are between 3 days and 5 days, about 95 percent are in the range of 2 days to 6 days, and about 99.73 percent are between 1 day and 7 days. This is illustrated in Figure 1-3.
The formula used to calculate the standard deviation is shown in Figure 1-4. It looks a little scary at first glance, but as with all formulas, when you start to break it down it becomes more accessible.
x in the formula represents your individual data points
xi represents each x from x1 up to xn
n represents the number of data points in your data set
represents the average (mean) of your data points
represents the “sum of”
© Martin Brenig-Jones and Jo Dowdall
FIGURE 1-3: Standard deviation.
As with most things in life, tackling the formula in stages makes it easier, so let’s have a go.
Start by adding up all of the data points you have. For example, if the data points are 5, 6, 7, 8 and 9 (we’ll demonstrate with some simple ones), the sum is 35. The number of data points we have is 5, so the value of n in the formula is 5. We can then work out the mean (average or
Next we need to work out the
Note that there are two versions of the standard deviation formula included in Figure 1-4. The first is used when we have a sample of data, and the second is used when we have the entire population. The data set we used to work through the example above was very small! If we were using the formula for a sample, instead of using n we’d use
© Martin Brenig-Jones and Jo Dowdall
FIGURE 1-4: Standard deviation formula.
In practice, when the sample size is more than 30, there’s little difference between using n or
The Process Sigma values are calculated by looking at our process performance against the customer requirements, which we cover in the next section.
Considering customer requirements
So far so good, but without understanding the customer requirements, it’s not possible to tell whether cycle time performance is good or bad.
Let’s say the customer expects delivery in five days or less. In Lean Six Sigma speak, key customer requirements are called CTQs, (Critical To Quality). We discuss CTQs in Chapter 2 and describe them in more detail in Chapter 4, but essentially they express the customers’ requirements in a way that is measurable. CTQs are a vital element in Lean Six Sigma and provide the basis of your process measurement set. In our example, the CTQ is five days or less, but the average performance in Figure 1-2 is four days. Remember that this is the average; your customers experience the whole range of your performance.
In the example provided, all the orders that take more than five days are defects for the customer in Six Sigma language. Orders that take five days or less meet the CTQ. We show this situation in Figure 1-5. We could express the performance as the percentage or proportion of orders processed within five days or we can work out the Process Sigma value.
