0:14

This lesson is about control charts for count kind of data.

Â So count kind of data is different from proportion kind of data

Â in the sense that when you're looking at proportion defective,

Â you're only looking at whether a product is defective or non-defective.

Â You're getting a yes-no answer.

Â You're getting a binary answer and it's based on a binomial distribution.

Â Whereas what we're doing here is we're looking at count data, so

Â we're looking at the count of defects.

Â We're looking at a sample and seeing how many defects did we find in that data?

Â So a single product or a single unit of a product can have multiple defects,

Â and that's going to have meaning in count kind of data,

Â while it did not have any meaning in proportion kind of data.

Â So count kind of data is still dealing with attribute kind of measurement,

Â with discrete distribution, so we're getting a count.

Â You cannot have 2.5 defects, for example, so it can be either two defects or

Â three defects.

Â So it's still a discrete distribution that we're dealing with.

Â So let's take a look at an example here to get a sense of getting the upper and

Â lower control limits and then using a control chart based on count data.

Â So we have a textile manufacturer who wants to determine the quality level

Â of their weaving process.

Â They take daily samples of five linear yards of material and

Â count the number of flaws.

Â So each of the samples is a sample of five linear yards.

Â They've decided to take one sample per day, and

Â they're going to count the number of flaws.

Â So if you think about this for a minute, in a daily sample of five linear yards,

Â what is the upper limit of the number of defects that you can find?

Â And we treat that as infinity.

Â We say that the upper limit for

Â the number of defects that you can find is going to be infinity.

Â Because we're simply not defining what a defect is.

Â It could be many different things, and we're going to say that you can find many,

Â many different defects in every sample of five linear yards.

Â Why is this important?

Â It's because we are going to use what is known as the Poisson

Â distribution as the underlying distribution for this kind of data.

Â So the count data is coming from a Poisson distribution, and

Â that has meaning in terms of computing the upper and lower control limits for

Â this type of control chart.

Â So moving on with the problem, 5 linear yards of data every day,

Â collect the data for 20 days, so what we'll have

Â is the number of defects that you can see over a 20-day period.

Â So here's the data that we have.

Â We can see that we have 20 days' worth.

Â And how do we use this to compute the control limits for a control chart?

Â So let's take a look at the numbers and the calculations for that.

Â 3:12

So what you have here is for the C chart, the center line is simply going

Â to be the mean of all the defects that you found in all of the samples.

Â So you're going to take an average, and if you remember how many samples we had,

Â we had 20 samples so it's gonna be total number of defects divided by 20 is going

Â to give us our center line.

Â And the nice part about this kind of distribution is that

Â the standard deviation is simply the square root of the mean.

Â So you have the center line that's being C bar,

Â that's the mean of the count of defects that you've got,

Â and the center deviation is simply the square root of that.

Â So the upper and lower control limits are going to be based on the mean plus or

Â minus 3 times the standard deviation which is the square root of the mean.

Â So in that sense the calculations are going to be much more easier here

Â when we are looking at the standard deviation.

Â The center line for the control chart works out to be 10.2

Â based on 204 defects in 20 samples.

Â And the upper control limit is going to be based on the square root of 10.2 and

Â you take plus or minus 3 times the standard deviation.

Â And that gives us our upper and lower control limits.

Â So we take this and we can compare it with the number

Â of defects that we saw in each of the samples and

Â if it is below 1 or above 20.

Â In fact, if it's going to be above twenty, we are going to call it out of control.

Â So we can see that right from here without even plotting on the control chart

Â in that it needs to be between two numbers, right?

Â 5:02

Now one point of caution before we move on to look at the chart

Â is that although we did not get a negative value for the lower control limit here,

Â based on the calculations, you might get a negative value for a different problem.

Â As we cannot have a negative count of defects, it's not going to make any sense.

Â We'll do the same thing that we did in the case of the P chart,

Â in the case of the proportions, we'll bump it up to a 0.

Â So we change it to 0 if we do find the lower control

Â limit to be a negative number based on the calculations.

Â Here that's not the case, so we don't need to make any change.

Â We have a nice symmetrical control chart here.

Â The upper and lower control limit are equidistant from the center line, and

Â then when we look at the plot, everything seems to be doing fine.

Â So what can we say from this control chart?

Â Based on the idea that we were calibrating the upper and lower control limits

Â based on data that we got from the process based on these 20 samples,

Â we can say that the current process will produce between 1 and 19 defects, right?

Â So our inherent capability of the process

Â is to produce as many as 19 defects the way it's running right now, right?

Â Less than 1 would be something that's extraordinary, and

Â greater than 19 would be something that's extraordinary.

Â That's what we said earlier.

Â That's exactly what we're saying here.

Â 6:28

If we do get numbers that are above or

Â below, we need to figure out what happened.

Â It could be root causes of something that has gone wrong.

Â Or if it's on the lower side,

Â it's how did we manage to get points that were lower than the lower control limit?

Â Because we're talking about count of defects,

Â lower numbers are going to be better.

Â 7:12

The condition here is that each sample has to be of an equal size.

Â So in this particular example, we talked about five linear yards of cloth.

Â If you're talking about a sample that you take of any kind of a product.

Â Let's say you're looking at cell phones, if you're taking a sample of

Â ten cell phones and you're counting the number of defects in the ten cell phones,

Â the sample size has to be constant when you're counting the number of defects.

Â Just simply to give them the same opportunity for having defects,

Â to be fair in that sense to the sample.

Â