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, you're getting a binary answer and

Â 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 counter defects, we're looking at a sample and

Â seeing how many defects did we find in that data.

Â So a single product or 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 discreet distribution.

Â So we're getting a count.

Â You cannot have 2.5 defects, for example.

Â So it can be either two defects or three defects, so

Â 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 common 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 5 linear yards of material and

Â count the number of flaws, right?

Â So each of the samples is a sample of 5 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.

Â In a daily sample of 5 linear yards, what is the upper limit of

Â the defects, the number of defect that you can find?

Â And we treat that as infinity.

Â We say that the upper limit for the number of defects that you can find

Â is going to be infinity, because we're simply not defining what a defect is.

Â It could be many different things.

Â And we're going to say that you can find many,

Â many different defects in every sample of 5 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 that has meaning in terms

Â of computing the upper and lower control limits for this type of control chart.

Â So moving on with the problem.

Â 5 linear yards of data everyday, collected data for 20 days, so what we'll

Â have is the number of defects that you can see over a 20 day period, right?

Â So here's the data that we have, we can see that we have 20 days worth and

Â how do we use this to computer, 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 for the C chart, a center line is simply going to be the mean

Â of all the defects that you found in all of the samples.

Â So you're gonna take an average and

Â if you remember how many samples we had, we had 20 samples.

Â So it's gonna be the total number of defects divided by 20,

Â is going 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 as being C bar,

Â that's the mean of the count of defects that you got.

Â And the standard 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 you are looking at the standard deviation.

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

Â based on 240 effects in 20 samples.

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

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

Â that gives us our upper and lower control limits.

Â So we take this and we can compare it

Â with the number of defects that we saw in each of the samples.

Â And if it is below 1 or above 20,

Â in fact, if it's going to be above 20, we're going to call it out of control.

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

Â and that, it needs to be between 2 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 limit

Â to be a negative number based on the calculations.

Â Here, that's not the case.

Â 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 equidistance 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

Â lower control limits based on data that we got from the process.

Â 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, 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 5 linear yards of cloth.

Â If you're talking about a sample, if you take off any kind of a product,

Â let's say you're looking at cell phones.

Â If you're taking a sample of ten cell phones, and

Â 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