0:14

This assignment required you to use statistical process control and

Â specifically, the X-bar and the R chart.

Â And compare two shifts and first of all look at the two shifts

Â that are being used to fill bags of cereal in a particular line.

Â And see what's going on there in terms of the two shifts whether there's

Â a difference between the two shifts.

Â As well as to check what is the capability of the process

Â if the process is in statistical control during these two shifts.

Â So that was pretty much the question that you were asked.

Â And the details that you were given,

Â were that these are supposed to be 500 gram bags of cereal.

Â These are filled using an automatic pourer and

Â the bags are also included in veins.

Â So in order to make sure that you keep the variation

Â in the bag weight out of the equation.

Â The quality control manager started to check based on tearing the bags and

Â checking the weight of the cereal inside the bags to see whether it was 500 grams.

Â And he has collected data from the filling process over five days.

Â So there are two shifts and he has collected data over five days.

Â And each day, he has collected data at five different times.

Â And each of those times there are ten bags.

Â And that's the information that you're given in terms of the frequency

Â of a sampling and sample size.

Â So a sample size is ten bags every time he takes a sample.

Â What he has done is he has done some of the work for you.

Â He has provided you with the sample averages and he has provided you with

Â the smallest and the largest value in each of those samples.

Â So the averages for each of the samples has already been calculated

Â as well as the smallest and the largest.

Â And once you have the smallest and the largest, the range can be calculated.

Â The question that's being asked is based on the data that's given to you

Â check whether to process is in statistical control computing limits for

Â both the X-bar and the R charts for shift one and shift two separately.

Â And compare the sample averages and ranges that you have from all of the samples to

Â see whether each of these shifts, the process is statistical control or not.

Â And you were asked to not,

Â you are not required to draw the control charts although if you wanted to get more

Â insight into any kind of trend you would be drawing the control charts as well.

Â The second part of the question was, what can you say?

Â Once you have these results from doing the statistical process control analysis,

Â doing the SPC analysis, what can you say?

Â Because you're also told that there is some kind of a hunt that

Â the second shift has a particular issue in terms of under filled back.

Â So what can you say about that whether that is a hunch that's being supported or

Â not being supported based on the data and

Â based on the analysis that you can do using SPC?

Â So let's go ahead and see what we can find based on

Â the calculations that we can do for the control charts.

Â So first of all, although in the problem statement you are given.

Â Just the partially converted data into averages and

Â maximum and the minimum to give you a shortcut.

Â What you're also given is the Excel spreadsheet with the complete data.

Â So if you wanted to get practice into what would the complete data set look like?

Â And then he'd be able to calculate the averages and calculate from that,

Â the control limits and even practicing drawing the control charts.

Â You could possibly do that as well, based on the data that's provided to you.

Â In addition to what's being provided in the problem.

Â So let's start with shift one.

Â And let's start with the range chart for shift one.

Â So if you remember from a statistical process control when you're talking about

Â continues distribution charts, measurement charts, they always go in pairs.

Â So we are going to compute the R and the X-chart.

Â We do the R chart first, because the R is going to be used.

Â The average range is going to be used.

Â In order to compute the upper and lower control elements of the X-bar charts if

Â the range chart details you that there's something that's out of control.

Â Then we might have to eliminate that and

Â re compute the range before we go to the X-bar chart.

Â So that's why we typically do the R chart first.

Â Although when you do this using software,

Â it's just going to quickly run both of them.

Â It's not going to tell you that one is not in control and

Â therefore you shouldn't be calculating the others.

Â So that's something that you need to keep an eye on in terms of both the R chart and

Â the X-bar chart should give you results of it being in,

Â instead of statistical control, if that's the result you're looking for.

Â 5:19

So let's take a look at the range chart for shift one.

Â The center line is gonna be based on the mean of the ranges.

Â The ranges are calculated by max minus min.

Â Max and min are given to you, smallest and largest values.

Â The upper control limit is going to be based taking that mean range and

Â multiplying by the D4 value and the lower control limit is going to be taking

Â that mean range of 34.66 and multiplying by the D3 value.

Â So that's 1.77 is the D4 value and

Â 0.223 is the D3 value and what you get as the upper and

Â the lower control limits are 61.59 and 7.73.

Â So you may recall where these D3 and D4 values come from, it's

Â from this chart that we had seen when we talked about statistical process control.

Â And you can see that because we have sample size of ten, so

Â we're taking the table that's on your right and

Â we're taking the first row from that with a sample size of ten.

Â We're using the D3 and D4 value and this is where

Â you will also get the A2 value that you're going to use for the X-bar chart.

Â So make a note of that as we go forward.

Â So coming back to the R chart that we've calculated for

Â shift one, what can you say from this R chart?

Â Well, you go back to all of the range values that you have calculated for

Â the 25 samples for shift one, and

Â what you'll see is that all of the values that you have there

Â in terms of the range fall within 7.73 and 61.6.

Â So the serial bag weights are expected to vary by between 7.73 grams and 61.6 grams.

Â So if this process works as it is working right now and

Â everything stays in statistical control as it is right now,

Â you can expect there to be variation between 7.73 and

Â 61.60 grams from this process.

Â That seems to be a little bit high when you're aiming for

Â a 500 gram bag, that it can be varying by this much.

Â However we still need to look at the X-bar chart to see how much short or

Â how much higher it's gonna be compared to the 500 gram target that we have.

Â So let's take a look at the X-chart or the X-bar chart of for shift one.

Â So we again, we get the center line which is based on taking

Â 7:59

the means of the 25 samples.

Â So get the mean of means or the x double bar of 500.2244 for shift one.

Â The upper control limit is based on taking that mean and adding 0.308, which is

Â the A2 value which we got from that chart based on a sample size of ten and

Â multiplying that by the average range that we got when we did the range chart.

Â So we take that, we get an upper control limit of 510.9.

Â We take a look at the load control limit and that works out to 489.55.

Â So what are we saying here?

Â We are saying that the upper and lower control limits are 489.55 and 510.9.

Â So first thing we need to do is because we are calibrating this control chart.

Â We are calibrating the upper and

Â the lower control limits, we need to check whether this calibration's going to work.

Â And for that we go back and we look at the 25 means.

Â And what you'll find is that those means are fall within

Â these two limits between the lower and the upper control limits.

Â So the averages of all 25 samples are fall within these control limits.

Â So we can go ahead and state something about the inherent capability,

Â inherent potential of this process and

Â we can say that cereal bags are expected to weigh between 490 and 511 grams.

Â If you were to round up, 490 and 511 grams.

Â 9:32

What you can note from here is that although everything is in statistical

Â control, the center line for this chart was 500.22 grams.

Â So in a sense, what this is telling us is that they will be 50%

Â of the output from shift one that is going to fall below 500.22 grams.

Â So there will be underweight bags coming from shift one in terms of

Â weighing those bags and checking what the weight of those bags is.

Â So why it's happening we don't know but

Â there seems to be a propensity for under weighed bags from the shift as well.

Â Now, let's take a look at shift two because if you remember.

Â There was a hunch about shift two being the culprit behind this whole thing, so

Â let's take a look at shift two.

Â But before we do that, although you weren't asked to come up with charts for

Â these bags, here are the charts that you would have come up with.

Â And I came up with these using Minitab.

Â And these confirm what we found earlier that all of the points are within

Â the upper and lower control limits and the control limits are what we have found for

Â the R and X-chart.

Â So given the data that you have you can actually go ahead and

Â compute these charts if you have access to software such as Minitab or

Â any other software that can be used to compute control charts.

Â 11:04

Now, let's take a look at shift two.

Â So we're looking at the second shift here and again, we start with the range chart.

Â Similar process that we had earlier, we get the center line 34.39,

Â we get the upper control limit of 61.29 and the lower control limit of 7.69.

Â So our control limits are gonna be 7.69 and 61.29 and the first thing

Â that you would want to check is, go back and look at all of the ranges.

Â The 25 ranges that you have for second shift and do they fall between these two?

Â And what you'll find is that they do.

Â So we can take these control limits and depend on them.

Â We can say that given the way that the process is currently performing,

Â we can say that there's going to be a range of between 7.69 and 61.29 grams.

Â It's going to be variation between 7.69 and 61.29 grams.

Â Very similar, if you remember from shift one.

Â So this range is very similar.

Â So in that sense, we can say that there's not much difference between shift one and

Â shift two when you look at the range and the control charts for the range.

Â So let's go ahead and move onto the X-bar chart now for shift two.

Â So here we get a center line of 481.8, so

Â this should be giving you some cause for

Â concern if you are thinking about 500 grams.

Â Center line itself is much lower than 500 grams and

Â when you look at the upper control limit, similar calculations as the previous ones.

Â We're using the range that we got from the second shift and

Â we're multiplying it by A2.

Â The A2 remains the same as sift one because everywhere we had

Â samples of size ten.

Â So we're staying with that same A2 number, but

Â you can see that the upper control limit is 492.

Â Again, there should be alarm bells ringing in your mind because the upper control

Â limit is telling you that even if this process isn't statistical control, it's

Â not gonna give us output that is greater than 492 which itself is less than 500.

Â You look at the lower control limit and that 471.17.

Â The first thing that you need to do is check whether all of

Â the means from those 25 samples that you had from shift

Â two are size ten are giving you values that fall between 471.17 and 492.

Â And simply looking at that chart that was already prepared for

Â you tells you that none of those means are outside these limits.

Â So they are all between 471 and 492.

Â So this is how the process would perform under usual circumstances,

Â under the way that it's currently performing.

Â And we can rely on it because nothing is out of statistical control.

Â No point's out of statistical control.

Â However, we can also say that the cereal bags are expected to weigh between

Â 471 grams and 492 grams which tells you that

Â all of the bags in the second shift are going to be less than 500 grams.

Â The upper limit itself is 492 grams, so it's telling you that all of the bags

Â are going to be less than the upper control limit.

Â So putting the information that we got from shirt one and shift two together, and

Â given that they have a hunch about shift two, what can we say about all this?

Â Well first, let's take a look at the control charts that you would've got

Â if you were actually compute the control charts.

Â Again, giving us the same information that we had

Â based on the calculations that we did.

Â Once again,

Â you were not asked to come up with these control charts but it gives you a nice

Â pictorial representation of how the data would look in terms of a control chart.

Â And if you had more information as to what particular day things are going up or

Â down, you can think about that.

Â But here the main point is that you're aiming for

Â bags to be at 500 grams and even the upper control limit

Â of the X-chart is not reaching that level, let alone the average.

Â The upper control limit is also not reaching that average.

Â So it is telling you that most of the outputs from shift two

Â is going to be underweight.

Â So overall the interpretation that we can get from this and

Â we've interpreted each of those shifts as we went along.

Â But overall we can say that the ranges for

Â the two shifts are similar but they appear to be quite high.

Â When you think about how much variation you're expecting from taking

Â a sample of ten bags, they appear to be quite high because you're getting

Â an upper control limit of around 67 and that's quite high.

Â Shift two is certainly worse than shift one in terms of under-filling the bags.

Â But shift one is not doing very well either

Â because there the center line was at 500.

Â So it's telling you that 50% of the bags would be under 500 grams.

Â So yes, shift two has a problem, but it's a bigger problem than shift one.

Â Shift one also has a problem here.

Â