Classes of Distribution

Quick reference

• 00:04 Hi I'm Ray Sheen, it's often very helpful to recognize the type of distribution that
• 00:09 you're working with.
• 00:10 Different physical phenomena create different types of distributions.
• 00:14 When you can recognize the distribution,
• 00:16 it provides insight into the process performance characteristics.
• 00:21 >> Let's start by looking at some of the more common distributions
• 00:25 that we see with discrete data.
• 00:28 Keep in mind that discrete data can only take on a limited number of values.
• 00:32 So often our distribution will be a plot of,
• 00:35 a count of different discrete value buckets.
• 00:37 By that I mean, how many times did it occur on Monday?
• 00:40 How many times on Tuesday?
• 00:41 How many on Wednesday?
• 00:43 So let's look at some typical distributions.
• 00:46 The first is the binomial distribution.
• 00:48 In this case, the data is pass failed type of data,
• 00:52 what is plotted is the number of counts of fails per standard size subgroup.
• 00:57 Once you've characterized this distribution, you can predict the number
• 01:01 of failures that will occur in the next batch or subgroup.
• 01:04 The next one that consider is the Poisson distribution.
• 01:08 The distribution counts the number of occurrences within a bucket or category.
• 01:13 It is quite often used to count the number of occurrences within a set time period,
• 01:18 such as defects per day or hour.
• 01:21 In this distribution, we can picture what a typical level of process performance
• 01:25 looks like, the normal condition, and the min and max values.
• 01:29 Again, we're dealing with the discrete data because it
• 01:32 is a count of the defects per day.
• 01:35 We can't have 7.4 defects occurring, it's either seven or it's eight.
• 01:39 But we can use this to set expectations about the process performance and
• 01:44 predict the probability of failures or defects.
• 01:47 The geometric distribution shares some similarities with the binomial and
• 01:51 Poisson distribution, but there are some differences.
• 01:54 Like a binomial distribution,
• 01:56 it's often associated with pass fail data or data that can only pick on two states.
• 02:00 But like the Poisson distribution, is often tied to time increments or buckets.
• 02:05 So in this case, we determine how much time does it take before the item
• 02:09 first changes state from compliant to defective.
• 02:12 It is often used to predict failure rates.
• 02:15 Now let's change our focus from discrete data to continuous data.
• 02:19 Continuous or variable data can take on any value.
• 02:22 By that, I mean that a data point could occur between any two data points.
• 02:26 There's not a finite number of values, rather,
• 02:29 there's a possibility of an infinite number of values.
• 02:31 We can always take a fraction between any two data points,
• 02:34 our only limitation is the discrimination of our measurement system.
• 02:38 The first one is a distribution that we've already seen and discussed, and
• 02:42 that's the normal distribution.
• 02:43 This characterized in a form that is symmetric, a high peak in the middle, and
• 02:48 tails that approach zero.
• 02:49 As we have often noted in the past,
• 02:52 this represents the common cause of variability within a process.
• 02:56 The next one is a uniform distribution,
• 02:59 this is symmetric because it is essentially a flat or a horizontal line.
• 03:03 This represents no relationship between the variables being plotted.
• 03:07 No matter how you change the factor that's on the x-axis, the y factor is unphased.
• 03:13 Our next distribution is bi-modal, or, for that matter,
• 03:16 we could have had a tri-modal or even a quad-modal distribution.
• 03:20 This is normally asymmetric, when you see this type of distribution,
• 03:24 it indicates that there are actually multiple independent distributions in your
• 03:29 data set.
• 03:29 You need to analyze this to identify the factor that can separate out the two
• 03:34 distributions.
• 03:35 Once they've been separated, they can each then be analyzed.
• 03:38 This will sometimes occur when you have multiple products,
• 03:42 multiple locations, multiple suppliers, multiple processes,
• 03:47 multiple people, multiple factors that are involved in the process.
• 03:52 Next I would like to discuss the exponential distribution.
• 03:56 This is definitely asymmetric, one end will occur at some point on the y-axis and
• 04:01 the distribution will then trend down when approaching the y value of zero.
• 04:06 There are a number of physical phenomenon that behave in an exponential fashion,
• 04:10 one that is commonly found is failure rates.
• 04:13 Now let's look at the log normal distribution.
• 04:16 This is also asymmetric, but it reflects a value of zero on both the left and
• 04:21 the right side of the curve.
• 04:22 However, unlike the normal curve, it heavily skewed to one side or the other.
• 04:28 It also is a good measure of some physical phenomena such as machine down time.
• 04:32 The last distribution I wanna mention is actually a family
• 04:36 of distributions known as the Weibull curve.
• 04:38 The Weibull curve represents multiple effects, and
• 04:41 therefore, can take on multiple shapes, including exponential or log-normal.
• 04:46 The actual curve is based upon the selection of some parameters in
• 04:49 the formula.
• 04:50 But these will often change over time.
• 04:52 The Weibull distribution is most commonly used for reliability analysis and
• 04:57 predictions.
• 04:58 Let's warp up our discussion of distributions looking at two different
• 05:02 ways to represent a distribution.
• 05:04 These different methods are really just different data visualizations of
• 05:09 the same information.
• 05:10 The Probability Density Function or PDF view, is the format of the distributions
• 05:15 that I have been showing you on the previous slides.
• 05:18 The x-axis takes on a value from the lowest to the highest of
• 05:21 that particular variable, and the y value represents the probability
• 05:25 that a given data point will have that value.
• 05:28 In other words, the higher the y value,
• 05:30 the higher the probability that a data point will be occurring at that x value.
• 05:35 We contrast this with a Cumulative Distribution Function, or CDF.
• 05:39 This is a graph where the x-axis shows the range of the x variables just like PDF.
• 05:46 And the y-axis always starts on the left side at 0, and
• 05:50 rises to a value of 1 on the right side.
• 05:52 What is being plotted is the likelihood that the next x value is equal to or
• 05:57 less than the x value on the axis.
• 06:00 So the far left, it is 0 because there are no other points further to left.
• 06:05 And at the far right, we're up at 1 or
• 06:07 100% because all of the data points are equal to or less than that value.
• 06:13 Let's look at an example, here's the PDF and CDF for
• 06:17 a normal or Poisson distribution.
• 06:19 The histogram is the Poisson view and the curve is the normal view.
• 06:23 As you can see, PDF is the form for what we have and looking at.
• 06:27 It's symmetric and peaked at the center and the tail approaching zero,
• 06:32 while the CDF is a great s-curve plot.
• 06:35 The curve starts at 0, has a gentle upslope, and then in the center,
• 06:40 where the PDF is heaviest, the curve becomes quite steep.
• 06:44 And as it approaches the right tail of the bell shaped curve,
• 06:48 the CDF begins to flatten out again.
• 06:50 Let's contrast that with the geometric or exponential distribution.
• 06:53 The geometric is the histogram and
• 06:55 the curved line is the exponential distribution.
• 06:58 In either case, the PDF is heavy on the left side and
• 07:02 then tapers down to very small values on the right side.
• 07:05 Now when we look at the CDF, it starts at 0 and when we get to the first value
• 07:11 of the x-axis where the distributions starts it quickly shoots up.
• 07:16 Then as the level of the PDF gets smaller and smaller the CDF gets flatten out and
• 07:22 only very minor changes until it gets to the final value of 1.
• 07:26 Now I tried to put an S curve onto the CDF
• 07:29 plot just to show you that it doesn't fit very well at all.
• 07:33 The S curve shape will occur on CDF with a symmetric distribution,
• 07:38 but definitely does not with an asymmetric one.
• 07:41 >> You definitely need to be familiar with these different types of distributions if
• 07:46 you plan to set for the IASSC exam.
• 07:48 And it's also helpful to understand them so
• 07:50 as to spot likely physical phenomena in the data.

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