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This assignment required you to use statistical process control and

specifically, the X-bar and the R chart.

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

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

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

a difference between the two shifts.

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

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

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

And the details that you were given,

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

These are filled using an automatic pourer and

the bags are also included in veins.

So in order to make sure that you keep the variation

in the bag weight out of the equation.

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

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

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

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

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

And each of those times there are ten bags.

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

of a sampling and sample size.

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

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

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

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

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

as well as the smallest and the largest.

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

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

check whether to process is in statistical control computing limits for

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

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

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

And you were asked to not,

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

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

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

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

doing the SPC analysis, what can you say?

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

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

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

not being supported based on the data and

based on the analysis that you can do using SPC?

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

the calculations that we can do for the control charts.

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

Just the partially converted data into averages and

maximum and the minimum to give you a shortcut.

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

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

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

the control limits and even practicing drawing the control charts.

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

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

So let's start with shift one.

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

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

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

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

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

The average range is going to be used.

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

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

Then we might have to eliminate that and

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

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

Although when you do this using software,

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

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

therefore you shouldn't be calculating the others.

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

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

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

5:19

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

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

The ranges are calculated by max minus min.

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

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

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

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

So that's 1.77 is the D4 value and

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

the lower control limits are 61.59 and 7.73.

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

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

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

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

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

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

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

So make a note of that as we go forward.

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

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

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

the 25 samples for shift one, and

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

in terms of the range fall within 7.73 and 61.6.

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

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

everything stays in statistical control as it is right now,

you can expect there to be variation between 7.73 and

61.60 grams from this process.

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

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

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

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

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

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

7:59

the means of the 25 samples.

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

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

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

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

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

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

So what are we saying here?

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

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

We are calibrating the upper and

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

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

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

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

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

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

inherent potential of this process and

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

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

9:32

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

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

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

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

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

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

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

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

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

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

let's take a look at shift two.

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

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

And I came up with these using Minitab.

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

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

the R and X-chart.

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

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

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

11:04

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

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

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

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

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

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

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

And what you'll find is that they do.

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

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

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

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

Very similar, if you remember from shift one.

So this range is very similar.

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

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

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

So here we get a center line of 481.8, so

this should be giving you some cause for

concern if you are thinking about 500 grams.

Center line itself is much lower than 500 grams and

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

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

we're multiplying it by A2.

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

samples of size ten.

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

you can see that the upper control limit is 492.

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

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

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

You look at the lower control limit and that 471.17.

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

the means from those 25 samples that you had from shift

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

And simply looking at that chart that was already prepared for

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

So they are all between 471 and 492.

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

under the way that it's currently performing.

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

No point's out of statistical control.

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

471 grams and 492 grams which tells you that

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

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

are going to be less than the upper control limit.

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

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

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

if you were actually compute the control charts.

Again, giving us the same information that we had

based on the calculations that we did.

Once again,

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

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

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

down, you can think about that.

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

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

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

The upper control limit is also not reaching that average.

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

is going to be underweight.

So overall the interpretation that we can get from this and

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

But overall we can say that the ranges for

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

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

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

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

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

But shift one is not doing very well either

because there the center line was at 500.

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

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

Shift one also has a problem here.