let's now take a look at how we actually analyze and interpret a control chart you remember we had our data plotted over time time is on the horizontal axis and our measure of interest is on the vertical we're going to have as our centerline the mean X bar and we're going to have our upper and our lower control limits UCL L Co now the way we start interpreting the control chart is that we place zones on the chart now there are three Sigma limits above the center line and there are three Sigma limits below the center line and most software will label these zones emanating from the center C be a same above C be a now that we have these zones we can apply what are called the test for special causes this is being able to look at the data and ask do I have special causes things that knock a process out of whack or do I have just what is called random common cause variation typically data that vacillate between the upper and lower control limits is common cause variation but there are ways to detect if you have special patterns in the data so when we look at data that looked like this line it's up it's down its back at fourth and it's between the upper and lower control limits that's a classic demonstration of what is known as common cause variation now on the other hand if we had a data point that went and exceeded the upper control limit that's a demonstration of a special cause that is data that have exceeded the upper estimation of the variation in the process by the upper lower upper control limit or similarly you could have a data point that exceeded the lower control limit several the other tests that we use statistically are whether or not there's been a shift or a trend those are two classic ways to think of out the data as they lay themselves out a shift in the data occurs when you get a certain number of data points that hang above or below the center line so if we have our mean and we had our data that went here here here and hung above the center line for eight or more data points in a row that would signal a shift that is the data were randomly arraying themselves and then all of a sudden for some reason they stayed at a particularly high level or low level you could have a shift up or shift down eight data points or more constitute a shift in the process the other classic test that is used to apply statistical thinking to the chart is whether or not you have a trend now a trend is when you have six or more data points constantly going up or constantly going down so we would see data one two three four five six that would be an upward trend and similarly you could have a downward trend note that if you have data points that go up up but then repeat you don't count the repeats but what you do is see if in fact at some point they start going back up if it goes up up repeat repeat and then drops then that cancels the trend so we have these two key tests one is for a shift and one is for a trend now there are a couple other tests and I'm just going to clean things up here a bit to show you what those look like we often times will look to see if we have data that form abnormal patterns so let's have our upper and our lower control limit with our mean and then we have data that start arraying themselves around these zones and there's two key tests that we look at to understand whether or not data that fall even B the control limits are demonstrating abnormal patterns the first one relates to how the data array themselves in these zones and I'm going to again put the C B and a zones on here when you get two out of three data points in Zone A or beyond that's a signal of a special cause so here are two out of three data points you could have it lay itself out like this and you could actually have a third data point here you still have two out of three in zone a of the chart now people say I understand where data point that exceeds an upper lower control limit is extreme variation now you're telling me that you can have patterns within a chart between the control limits that actually demonstrate special causes an abnormal pattern and the answer is yes here's the simple explanation if I took the data and squish them all over and I had over here a normal curve as you move out this curve you should see less data as you move out the tails of a distribution and the two-out-of-three test of a special cause is indicating you're getting too much data bunching in the tails of your distribution now the other test which relates to this is almost the converse it's when you get too much data bunching around the center so we would have data that essentially are random and then all of a sudden 15 data points in a row hug the center line and then break out again when you have 15 data points or more hugging the center line that is falling between zone C's plus and minus 1 Sigma on other side of the mean this is a signal that there's too little variation and this gets to the fact that if we looked over here to our static display of data you'll remember from basic statistics that about 68% of the data fall between plus and minus one standard deviation of the mean on a normal curve well when you get a pattern like this you're exceeding the 68% you're getting too much data hugging this bell curved part of the distribution and that's not a normal pattern a random pattern as we've said before is just up and down back and forth and when you get a pattern like this where you had random variation very little variation and then random again that's a signal that there's something strange going on in the in the process itself so we have these different rules we have a trend we have a shift we have two out of three and we have 15 or more hugging the center line the classic rule that we started with is when you have a single data point that exceeds the upper or lower control limit and that is classically known as a three sigma violation of special cause okay so in a quick overview that shows you how we use the special cause tests related to the zones on the chart and it gives you the ability to understand how we actually interpret the chart once we had it so now we have actually built a control chart we have plotted the elements of it the mean the upper and lower limits and we now know how to interpret it you