Process sigma indicates the process variation (i.e., standard deviation) and is measured in terms of data units (such as seconds or millimeters), while process sigma count Z, or process sigma level, is a count with no unit of measure. Sometimes the term process sigma is used instead of the process sigma level, which may cause confusion. Z lt = Z st – 1.5 = 4.5 Clarifying Process Sigma and Sigma Level A Six Sigma process is 6 sigma in the short term and 4.5 sigma in the long term or: Referring back to the short- and long-term behavior of the process mean, there are 2 values for Z, short-term Z, or Z st, and long-term Z, or Z lt. Similarly, for a 3-sigma quality level, the process sigma must be: In general, the Z formula can be rearranged to calculate the maximum allowable process sigma, or standard deviation, for any sigma level.įor example, given a mean of 25 seconds and SL of 31 seconds, for a Six Sigma quality level, the required process sigma is calculated as: In order to bring the process to the golden Six Sigma quality level, the process sigma would have to be reduced to 1. Therefore, the process is at a 3-sigma quality level. In this example, the process sigma level for a specification limit of 31 seconds is: Given the specification limit, SL, the process sigma level, or process Z, is: The one-sided defect rate is applicable to any capable process with 1-sided or 2-sided SLs, even at a 3-sigma level. The 1.5-sigma shift makes defects approach 0 on the opposite side of the shift even at lower sigma levels. Figure 2: Process Mean Shift of 1.5 Sigma and Defect Rate Corresponding to 4.5 Sigma A Six Sigma process is actually 4.5 sigma in the long term, and the 3.4 PPM defect rate is the 1-sided probability of having a data value beyond 4.5 sigma measured from the short-term mean. A similar argument applies to the extreme case of 1.5-sigma shift to the left. The overall defect rate, therefore, is 3.4 PPM. The left specification limit is at 7.5 sigma from the mean with a defect rate of 0 PPM. The right specification limit is at 4.5 sigma from the mean with a defect rate of 3.4 parts per million (PPM). The red lines in Figure 2 (below) show the extreme case of 1.5-sigma mean shift to the right. In a stable process, the mean naturally shifts as much as 1.5 sigma in the long term on either side of its short-term value. (See Figure 1.) Figure 1: Normal Distribution With Mean, Z-score and Six Sigma Specification Limits Therefore, a process data point can be 6 standard deviations from the mean and still be acceptable. The farther the specification limits are from the mean, the lower the chance of defects.Ī Six Sigma process has a specification limit which is 6 times its sigma (standard deviation) away from its mean. Any value beyond the specification limit indicates a defect or unacceptable result. In a process, deviations from the target or mean are accepted to a certain value defined by the specification limits (SL) around the mean. Z = (31- 25) / 2 = 3 Specification Limits and Defect Rates This count is denoted by sigma level, Z, also known as Z-score, as shown below. If the standard deviation is 2 seconds, the same point is 6/2 or 3 standard deviations away from the mean. This distance can also be measured by counting the number of standard deviations in the distance. For example, a data point with a value of x = 31 seconds is 6 seconds away from a mean value of 25 seconds. The distance from the mean μ to a data value in terms of data units can be measured. Process data usually has a normal distribution. A larger standard deviation indicates that a data set has a wider spread around its mean. Standard deviation shows the extent of variation or spread of data.
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