Normal Variation

Quick reference

• 00:04 Hi, I'm Ray Sheen.
• 00:06 SPC relies on monitoring normal variation within a process.
• 00:10 Now we'll be using this concept in many other modules,
• 00:13 so let's explain just what that means. >> All processes have
• 00:17 some level of variation.
• 00:19 And that variation is often described using the normal curve.
• 00:23 Normal variation is represented by the normal curve or
• 00:26 as it is commonly called the bell shaped curve.
• 00:29 There are some characteristics of this variation.
• 00:32 First, it is symmetrical.
• 00:34 There are about the same number of data points above and below the mean or
• 00:37 average value.
• 00:39 Second, the curve is higher in the middle.
• 00:42 The means most of the data points or
• 00:44 variation is centered near the middle of the range of points.
• 00:47 So what's the term used to describe this curve?
• 00:50 In the statistical world,
• 00:51 it's often called a Gaussian distribution, named after the German
• 00:55 mathematician Carl Gauss who was a pioneer in the study of statistics.
• 01:00 With respect to variation in a process, the normal curve has several implications.
• 01:05 First, there will be a center point of variation
• 01:08 that is the most commonly occurring value.
• 01:11 Also, approximately the same amount of variation points will be above the center
• 01:15 point as below the center point.
• 01:17 Since the center point is the most common point, it is the peak of the curve.
• 01:21 And theoretically, the curve never gets to zero at the extremes,
• 01:24 although there is a practical limit.
• 01:27 The curve is used for
• 01:28 random variation because it represents a typical uncertainty.
• 01:33 In fact, you'll see that in SPC,
• 01:35 we will check the distribution of variation in a process.
• 01:39 Once we see a normal distribution,
• 01:40 we know that the only effect that is present is random variation.
• 01:45 This leads to a principle of process control.
• 01:47 It assumes that the only variation in a process is normal variation.
• 01:52 Predictable variation can be controlled because we understand its limits.
• 01:56 Unpredictable variation is uncontrollable.
• 01:59 The process is uncontrollable because there are special effects acting on
• 02:04 the process that are not part of random variation.
• 02:07 When a process has standard systems resources activities,
• 02:10 it is more likely to exhibit normal variation.
• 02:14 Now let me talk about what I mean by predictable.
• 02:17 When the process only has normal variation,
• 02:19 a plot of the variation will be a normal curve.
• 02:22 That means that there's a stable center point to the variation,
• 02:25 which is called the mean.
• 02:26 There is a stable shape to variation.
• 02:29 Normally, the bell shape of a normal curve.
• 02:32 And there is a stable spread to the data from the minimum to the maximum.
• 02:36 The magnitude of the spread is often described using the standard deviation for
• 02:41 the data distribution.
• 02:43 That means a predictable and
• 02:44 stable process lends itself to statistical analysis and control.
• 02:49 We'll be using statistical definitions for the distribution of the variation, so
• 02:53 let's define some of these terms.
• 02:56 When the variation is a normal variation,
• 02:58 the statistical terms that apply to the normal curve can be used.
• 03:02 There are four statistical definitions that are used in our SPC calculations.
• 03:07 The first one is the mean or
• 03:09 average point, this will be the center of the curve.
• 03:12 We can calculate it by adding the value of all the variations and
• 03:16 dividing by the number of points.
• 03:18 Another point is the median.
• 03:20 This can be found by taking all of the values of the variation and
• 03:23 putting them in order from the smallest to the largest.
• 03:26 The middle point is the median.
• 03:28 In a perfect normal curve, the median and the mean are the same.
• 03:33 The range value is the span from the smallest value to the largest value.
• 03:38 It helps us to understand the boundaries of the variation.
• 03:41 Finally there is the Standard Deviation.
• 03:44 This is a measure of the spread.
• 03:46 Unlike the span, it indicates the typical spread in the uncertainty.
• 03:49 This is the most complex calculation of the ones just mentioned.
• 03:54 It is the square root of the sum of all the deviations squared.
• 03:58 The deviation is the difference between the actual variation and the mean or
• 04:02 average value of the variation.
• 04:04 In fact, let me go a little deeper into this discussion of standard deviations
• 04:09 by looking at the standard normal curve measured using standard deviations.
• 04:14 As previously mentioned, the center point of the curve is the mean value.
• 04:18 All of the variation points that are within -1 standard deviation two plus one
• 04:22 standard deviation around the mean will represent 68.27% of the variation.
• 04:29 If we expand our perspective out to + or- 2 standard deviations,
• 04:34 we're now up to 95.45% of variation.
• 04:38 By the time we get to a + or- 3 stand deviations,
• 04:42 we have included 99.73% of all variation.
• 04:46 The + or- 3 standard deviation point will be an important one for
• 04:50 us to use with control charts, because that was the value that Walter Shewhart
• 04:54 was focused upon when he developed control charts.
• 04:58 As we continue on,
• 04:59 + or- 4 standard deviations represents 99.9937% of all variation.
• 05:06 + or- 5 standard deviations represents 99.999943% of all variation.
• 05:13 And + or- 6 standard deviations represents
• 05:17 99.9999998%. >> Normal variation can
• 05:21 be represented by the normal curve.
• 05:24 This statistical curve is the foundation for our statistical process control.

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