Once we have the DPMO number, you can use the methodology described in section A to calculate the Sigma Level. This area can be used to estimate the DPMO. Once you have a distribution fit to the data, you can calculate the area under this curve that lie outside the specification limits. In the second approach, you can fit a non-normal distribution to the data (such as a Log-normal distribution, Exponential distribution etc) to the data. The following figure shows non-normal data that has been transformed using the Box-Cox transformation. One thing to note is that in addition to the data the specification limits should also be transformed before you calculate the Sigma Level. You could use either the Box-Cox transformation or the Johnson transformation to transform the data to a normal distribution. In the first approach, you can transform the non-normal data to a normal distribution and then calculate the Sigma Level using the methods described above. There are two approaches you can use to calculate the Sigma Level for non-normal distributions. If the data is not normally distributed, we cannot use the formulae described earlier to calculate the Sigma Level. Sigma Level for a Non-normal Continuous Distribution In the following sections, we will deal with how to calculate the Sigma Level for different types of data.ī. This Sigma Level is also called ZBench.Įven though by the strict definition, the Sigma Level only applies for a continuous data that is normally distributed, we can calculate an equivalent Sigma Level for other types of distributions for continuous data sets or even for discrete data sets. This DPMO value can be translated to the Sigma Level using the methodology described in Section A. If you have a bilateral specification, where both the USL and LSL are specified, then the Sigma Level is calculated by first calculating the total DPMO on both sides of the specification limits as follows: Note that this sigma level does not assume a 1.5 Sigma shift that is covered later in this article. This approach is shown in the following figure.įor example, if the DPMO = 45000, then Area = 0.045000 and hence Z = 1.7. Use a unit-normal distribution (with mean = 0, and standard deviation = 1) and calculate the Sigma Level that corresponds to this distribution that provides the same defect area to the right. The area under the curve is an indication of probability of defects. Divide the DPMO by 1,000,000 to get the area under the curve. If you know the capability of a process as DPMO number (see previous article on DPMO), then you can compute an equivalent value of Sigma level using the following approach. Usually, a process with a Sigma Level of 6 or greater is usually considered as an excellent process. A process with 50% defects (DPMO = 500,000) would have a Sigma Level of 0. The best possible process in the world would have a Sigma Level of +∞ (infinity) and the worst possible process in the world would have a Sigma Level of –∞ (negative infinity). A large value for the Sigma Level indicates that the process is operating far away from the customer specification limits and hence there is less chance of making defects. This can be expressed mathematically as follows:įor example, if we are interested in the capability of the temperature of the room and the temperature of the room averages around 20 degrees with a standard deviation of 1.5 degree and the customer specification limit is 23 degrees, then using the above formula the Sigma Level would be 2 (or it is a 2 Sigma process).Ī very capable process will have a large Sigma Level while an incapable process will have a small Sigma Level. If your data type is continuous and is normally distributed with a single specification limit (let’s say without loss of generality the Upper Specification Limit USL), then the Sigma Level indicates the number of standard deviations (s) that you can fit between the process average (xbar) and the customer defined specification limit. Calculating Sigma Level for Normally Distributed Continuous Data In this module, we will look at how to compute the Sigma Quality Level for different situations and also discuss some of the limitations of the Sigma Quality Level metric.Ī. Hence, in order to calculate the Sigma Quality Level, we need two pieces of information: customer requirements and process performance data. It can be used to describe if the process is capable of meeting customer requirements. It is usually indicated by the letter Z or SQL. Sigma Quality Level is a number that provides a quantitative measure of the capability of any process. What is Sigma Quality Level? View All Blogs
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