Normal Distribution

Quick reference

• 00:05 Hi, I'm Ray Sheen, and I've already used the term normal distribution several times
• 00:09 in other modules and I'll be using it a lot more throughout the course.
• 00:13 So let's explain what this really means.
• 00:16 The normal distribution is at the heart of statistical process control and
• 00:22 therefore it is of major importance to Lean Six Sigma.
• 00:26 The normal distribution is what you have probably referred to as the bell
• 00:30 shaped curve.
• 00:31 It is a distribution of data values in a data set for a process parameter.
• 00:36 The distribution is symmetrical with a peaked center.
• 00:40 That is also known as a Gaussian curve,
• 00:42 named after Carl Gauss who was a prominent mathematician in the early 1800s.
• 00:48 To be a little more precise, since the normal curve is symmetrical, there
• 00:52 are an equal number of data points both above and below the center peaked value.
• 00:57 That would not be true of a skewed distribution.
• 01:00 There's only one peak, and it is at the center of the curve.
• 01:04 There are not multiple peaks, nor is the top of the curve flat.
• 01:08 And the ends of the curve approach the value of zero.
• 01:11 Although theoretically it never reaches zero,
• 01:14 from a practical standpoint, it does.
• 01:17 The area under the curve represents all of the data in the data set.
• 01:21 That is what we mean by the form of a data distribution.
• 01:24 It is the form of the curve that covers over all of the data points.
• 01:29 The reason this curve is so
• 01:30 important is that it represents normal, random uncertainty in a process.
• 01:35 Once all the special effect causes are removed from a process,
• 01:39 what is left is the random uncertainty,
• 01:42 which will inevitably take on the shape of this normal curve.
• 01:46 Remember in Lean Six Sigma, we want to remove variation.
• 01:49 So our goal is to remove the special cause variation and
• 01:52 limit the amount of remaining random variation.
• 01:56 Let's look at some very important characteristics of this curve.
• 02:00 For the illustration, I will set the mean value or
• 02:02 center point at a zero value on this horizontal scale.
• 02:07 The horizontal scale will use the units of sigma or standard deviations.
• 02:11 Now based upon the shape of the normal curve,
• 02:14 if we were to draw a line one standard deviation above the mean and
• 02:19 another one standard deviation below the mean, 68.27% of
• 02:23 all the data points of our data set would fall between those two lines.
• 02:28 So, roughly two-thirds of all data values in a standard normal curve,
• 02:32 meaning random variation,
• 02:34 are within one standard deviation of the average value of that data set.
• 02:39 Let's jump out to two standard deviations.
• 02:42 Now, I can see that 95.45% of the data points of that data set
• 02:47 will fall between -2 standard deviations and +2 standard deviations.
• 02:54 The -3 standard deviation to +3 standard deviation is a significant point for
• 02:59 us to consider.
• 03:00 You can see that 99.73% of all data points are within this range.
• 03:06 That means that from random variation,
• 03:08 we should only see 3 data points out of a 1,000 that go beyond these lines.
• 03:14 The reason this is of interest is that the process capability ratios and
• 03:18 statistical process controls strategies, that were developed by professor Shewhart were
• 03:23 based upon achieving the + or - 3 standard deviation level of performance.
• 03:29 Now, more about that will come up in our course on statistical process control.
• 03:33 Moving out to +4 sigma and -4 sigma levels, as you can see,
• 03:39 we are now at a point of 99.9937% of the data points are between the data values.
• 03:46 Continuing onto the + or - 5 sigma level, it's 99.999943% of all data.
• 03:51 And finally, at + or - 6 sigma,
• 03:54 99.9999998% of the data points would be
• 03:59 underneath the curve and within those limits.
• 04:04 And we'll come back to these numbers in the Statistical Process Control course and
• 04:09 focus in on what this means for process control and process yield.
• 04:14 Let me wrap this up with some comments about the characteristics of normal
• 04:17 distributions.
• 04:19 The normal distribution is an excellent model for random variation in nature.
• 04:24 This could apply to random variation on the inputs to a process.
• 04:27 Such variations in material or in environmental conditions.
• 04:31 It also represents the random variation within the process itself,
• 04:35 that means a variation of output such as variation in timing, or quality or cost.
• 04:40 This variation has no clearly assignable cause, it's just part of the system.
• 04:45 Now if you go back and follow the item through the process, you can find several
• 04:49 factors that led to a particular final value of a process parameter.
• 04:53 But those factors can and do vary slightly.
• 04:56 And if the variation is within the normal range, it is still random variation.
• 05:01 We'll talk a lot more about this in the session on special cause and common cause.
• 05:05 The bottom line is that in order to change the level of variation
• 05:09 there needs to be a fundamental change to the process.
• 05:13 But a great characteristic of this type of variation is that it is predictable.
• 05:18 We can calculate a mean and a standard deviation.
• 05:21 As I've shown on the last slide, we can with confidence predict what percentage
• 05:25 of the process outputs will fall within the different standard deviation or
• 05:29 sigma levels.
• 05:31 The predictable center, spread and shape will allow us then to set
• 05:35 up statistical process control charts, and track our process performance,
• 05:40 be able to detect when abnormal conditions are occurring.
• 05:46 The normal distribution is used throughout the Lean Six Sigma process for
• 05:50 both analysis and control.
• 05:53 It is the most commonly found distribution and we will be referring to it often.

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