The Six Sigma Deviation

Using Six Sigma -- suppose you want to estimate the height of people in your organisation, and measuring everyone is not practical, so you take a representative sample of 30 people’s heights.You work out the mean average height for the group – as an example, let’s say this is five foot, 7 inches.

You then calculate the difference between each person’s height and the mean average height.

In broad terms, one sigma, or standard deviation, is the average of those differences.

The smaller the number, the less variation there is in the population all things you are measuring. Conversely, the larger the number, the more variation.

Sigma Population Percentages

Let us suppose that when measuring the heights of those 30 people, the standard deviation is 1 inch.

The likely percentage of the population within plus one and - one standard deviation from the mean, plus two and -two standard deviations from the mean, and so on.

Assuming your sample is representative, you can see how your information provides a good picture of the heights of all the people in your organisation.

You will find that approximately 2/3 them are between 5 foot 6 inches and five fours 8 inches tall. About 99.73 percent our between 5 foot 4 inches and 5 foot 10 inches.

Here is the standard deviation formula:

The Sigma Formula

Using n-1 makes an allowance for the fact that we are looking at a sample and not the whole population.

In practice though, when the sample size is over 30, there is little difference between using n or n-1.

When we referred to a ‘population’ this could relates to people or things that have already been processed.

So, for example, a population of completed and dispatched insurance policies or hair dryers.

The process sigma values are calculated by looking at our performance against the customer requirements – more of that in a moment.

The Workplace Process Sigma

In the real world you probably do not measure the height of your colleagues.

Imagine instead that in your organisation you issue products that have been requested by your customers.

You take a representative sample of fulfilled orders and measure the cycle time (the time taken from receiving the order to issuing the product) for each order.

Critical To Quality (CTQ)

You can see the range of your company’s performance. The cycle time varies from as short as one day to as long as seven days.

But the customer expects delivery in five days or less. In lean six sigma speak, a customer requirement is called a CTQ – Critical To Quality.

CTQ’s express the customer’s requirements in a way that is measurable.

CTQ’s are a vital element in lean six sigma and provide the basis of your process measurement set.

In my example, the CTQ is five days or less, but the average performance is four days.

It is important to remember that this is the average – your customers experience the whole range of your performance.

Measuring Six Sigma Defects

Many organizations use averages as a convenient way of making their performance sound better than it really is.

In my above example, all the orders that take more than five days are defects for the customer in six sigma language.

All those that take five days or less - meet the CTQ.

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.

The process sigma value is calculated by looking at your performance against the customer requirement, the CTQ, and taking into account the number of ‘defects’ involved where you fail to meet it (all those cases that took more than five days).

Calculating Process Sigma Values

Process sigma values provide a way of comparing performances of different processes, which can help you to prioritised projects.

The process sigma value represents the population of cases that meet the CTQ’s right first time.

Sigma values are often expressed as defects per million opportunities (DPMO), rather than per hundred or per thousand, to emphasize the need for world-class performance.

First Pass Sigma Performance

Not all organizations using six sigma calculate process sigma values.

Some organizations just use the number of defects or the percentage of orders meeting CTQ’s to show their performance.

Either way, if benchmarking is to be meaningful, the calculations must be made in a consistent manner.

Recognizing that you are looking at ‘first-pass’ performance is important.

If you make an error but correct it before the order goes to the customer, you still count the effect because the rework activity costs you time and effort.

Your customer may have several CTQ’s relating to an order – for example, speed, accuracy and completeness. So there may be more than one defect in the transaction.