Anything between these two measurements is considered to be a good product. In the case of the 32 inch waist size jeans, this would mean that 31 inches will be the lower spec limit (LSL) and 33 inches will be the upper spec limit (USL).
2 SIGMA NORMAL DISTRIBUTION PLUS
If we go back to the jeans example, the customer might be willing to accept jeans that are plus or minus 1 inches from the target (this is of course very lenient, but let's say this is the case for this six sigma tutorial). Therefore they give their suppliers tolerances in their specifications. The distribution curve of the jeans example may look like the picture below.Ĭustomers understand (at least most do) that there is variation in everything in life and that it is close to impossible to hit the exact same measurement every time. That is why the normal distribution curve is highest in the middle and gets lower and lower on the sides. As the measurement moves away from the center, it becomes less and less likely that the corresponding value will occur. Extremely rarely, they could be 30 inches or 34 inches (2 inches more or less than the target). Rarely, the process could come out with 31 inches our 33 inches (1 inch more or less than the target). Sometimes, they may be 31.9 inches…or perhaps 32.1 inches (0.1 inches more or less than the target). If your process is meant to produce jeans of 32 inches waist size and assuming that the process is not broken - you should be getting jeans with 32 inches waist size coming out of your process most of the time. One of the important outputs of your process will be the waist size of the jeans. The two curves below have the same mean, but the curve on the right has a higher standard deviation since it is a wider curve.įor an example in this Six Sigma tutorial, let's say your factory is producing jeans. The higher the standard deviation, the wider the curve. The standard deviation defines how wide or narrow the curve is. The mean defines where the curve is centered around. The normal distribution curve is defined by two numbers - the mean and the standard deviation. The normal distribution curve is an illustration of the frequency or count of the number of times a value is recorded for a process. To the lay man, it's known as the bell curve. To understand this, we will have to revisit the concept of the normal distribution curve. Reduce the variation in the process to the point that +/- 6 standard deviations (sigma) of your process are in between the upper and lower specification limits. Center the process to match the target.Ģ. Under this traditional view, Six Sigma has two main objectives:ġ. Traditionally, Six Sigma's focus has always been on reducing variation and improving process capability to reduce defects. We can then see if the observed data point falls within the normal variation we expect (i.e. within 1.96 standard deviations for 95% confidence) or outside it, and is therefore the result of something not within the normal range.This Six Sigma tutorial will guide you through the basic building block of Six Sigma's two main objectives. The other, related, way we can use this information is if we have a mean and standard deviation and observe a data point, we can calculate how many standard deviations from the mean this data point is. This is why we used the figure 1.96 when calculating our confidence interval earlier, and this is the property that allows us to infer information about the population from Typically we calculate a 95% confidence interval (although 99% is also common), and this tells us the likely range the population mean falls within. Therefore if we know the mean ( \(\mu\)) and standard deviation ( \(\sigma\)) of our sample we can calculate the confidence interval of our sample mean (as we did above). These are about 68%, 95%, and 97.5% respectively. Because the normal distribution is symmetrical we know that 50% of cases fall below and 50% of cases fall above the mean.Īnother useful property of the normal distribution is we know, or can calculate, how many cases fall with 1, 2, 3, or more standard deviations of the mean (these are shown as \(\mu \pm \sigma \mu \pm 2\sigma \mu \pm 3\sigma\) on the figure). Lots of data follow this pattern: the height or weight of a population The mean of the normal distribution ( \(\mu\) on the diagram above) is the centre. The normal distribution was discovered by Gauss (which is why it’s also sometimes called the Gaussian distribution) and described an ‘ideal’ situation.
The normal distribution looks like this (by Dan Kernler from Wikimedia Commons, CC BY-SA 4.0): The normal distribution is central to our ability to infer about a population from a sample. Import pandas as pd import matplotlib.pyplot as plt import numpy as np import math import scipy.stats food = pd.
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