Understanding the Basic Six Sigma Concept

Six-Sigma is a fairly simple concept, but has been made complicated by over use of statistics. Here is a simple step by step explanation of the six-sigma process that is easy for a non-technical person to follow.

Once you gain a good understanding of the concept, you can start learning some of the six sigma tools that can be used to implement the methodology in practical projects.

Let consider a process. Every process has some sort of a performance target.

E.g.:

• Number of days it takes for a mail piece to reach its destination (Target – 3 days)
• Time taken to complete reviewing a loan application (Target – 30 minutes)
• Number of bad widgets in a manufacturing shop etc (Target – 3 out of 100)

It is rare that the process meet this target 100% of the time. There is always some variation associated with the process. This variation will cause the process to be off the target a little bit. This is perfectly normal and every process is permitted a certain amount of variation from the target. As long as the process performance stays within this permitted variation, the process is considered good.

E.g. Time to make a pie is supposed to be 7 minutes, but is allowed a variation of plus or minus 1 minute. This means that the time to make the pie could be anywhere between 6 – 8 minutes, even though the expected time is 7 minutes.

Sigma value is a standardized way of stating how often your process performance will lie within that permitted variation. The higher the sigma value is, the better the process.

E.g. A 6-sigma process has a 99.99966% chance of staying within the permitted variation limits.

Statistics

Now, let’s get to the statistical part of the process. Lets get to know the important terms first

1. The theoretical target for the process is the TARGET MEAN. E.g. Diameter of a hole should be 3 feet.
2. The permitted variation for the process from the Target Mean is TOLERANCE. E.g. the diameter of the above mentioned hole could vary by plus or minus 1 foot. So the diameter could be anywhere between 2 feet and 4 feet.
3. The range of this tolerance is called the CONTROL LIMIT. The lower value (in the above case, 2 feet) of this range is called the LOWER CONTROL LIMIT (LCL) and the upper value (4 feet in the above case) is called the UPPER CONTROL LIMIT (UCL)

Now we take a look at the process and collect some data on how the process is performing. E.g. measure the diameter of a number of holes mentioned in the previous example.

The sigma (σ) of the process is calculated based on these measurements. σ is nothing but the standard deviation of the process, which, in simple terms, is the variation that we expect to see in the actual process.

Here, x would be the diameter of each hole, X is the average of all diameters measured and n is the number of holes measured.

The goodness of your process is determined by comparing the variation of your process with the permitted variation. If you have a low value for your σ in comparison to the permitted variation, it is highly unlikely that your process would go beyond the permitted variation.

The σ level for your process is nothing but the ratio of permitted variation to the process variation and indicates the capacity of your process to not stray outside the control limits on either side.

i.e. σ Level = (UCL – LCL) / 2 σ

Now, you have noticed that the control limit has been divided by 2 σ to calculate the sigma level. This is because we assume that the process mean is in the centre of the control limit and your sigma level is the capacity of your process to stay in limit to either side of the mean. Based on this assumption, the sigma level cal also be calculated as,

σ level = (Mean – LCL) / σ OR (UCL – Mean) / σ

Where (Mean – LCL) and (UCL – Mean) gives you the same amount of permitted variation (equal distance to both sides of the mean)

Now, if your process has only 1 control limit (E.g. a process with an expected success rate of 100% and a tolerance of 10%; no UCL, Mean = 100% and LCL = 90%), the same formula can be used to calculate the sigma level.

Sigma level tells you the probability of our process staying in the permitted variation. E.g. a sigma level of 3 means that 93.31% of the time, your process would stay in the permitted range. i.e. if you make 1 million pieces, 66,800 pieces will be defects (outside the permitted variation)

Here is a table with the probability associated with each sigma level. These values have been calculated using probability functions.

Now you must have noticed the bell shaped charts that represent the processes. Here is the reason.

If you plot all the measurements for the process, there is a good chance that most of the measurements lie close to the mean.

The bell shaped curve is nothing but the probability of occurrence for each measurement. So there is a high probability for a measurement to lie close to the mean and as we move sideways from the mean (closer to the control limit), there is a lower probability of measurements. The area outside the control limits represent the probability of measurements falling outside the control limits.

The shift of the mean

Now, it is not necessary for the process mean to be right in the centre of the control limit. This is called the shift of the mean.

What this means is that the distance between the control limit and the mean is not even on both sides. So to be on the safe side, the sigma level is calculated based on the shorter side.

I.e. Sigma level = Lower of (UCL – Mean OR Mean – LCL] / σ

This gap divided by the sigma will give the sigma level of the process. Say for the above 6 sigma process, the mean has shifted by 1.5 σ, now the shorter gap is 4.5 sigma and the process now becomes a 4.5 sigma process instead of a 6 sigma and the defects is now 3.4 ppm.

There is a notion that the six sigma process means 3.4 ppm. This is not true, the 6 σ process yields 0.002 ppm. The 3.4 ppm concept came from a Motorola process where they decided a process will be called six sigma if the USL – LSL / 2 σ = 6 and the Mean has shifted by 1.5, yielding an actual sigma value of 4.5 and corresponding 3.4 ppm.

Six sigma is a statistical term indicating how much you have deviated from your target. The notion behind the idea is that if you can measure your defects, you can systematically identify the causes for the defect and eliminate them.