History of some SPC

In this article, I will describe how helpful the SPC charts were for me. The names of people listed here have been changed for their safety (just joking :-)).

It was over 10 years ago. I had just started a new job and after a few days I was given a serious task. It was a beautiful day to die - it was enough to not cope with the "simple" task and all this hocus pocus and Six Sigma would be worthless.

“We have a problem with the filling,” my boss told me. "We use the best equipment in the world, the best flowmeters, but we’re still having problems. Maybe you can determine what the problem is?"

What is the answer in such situations?

My answer - of course, I will gladly do it (however I did have doubts).

What do you do when you do not know the process, do not know the machines, and do not know the people? Has that ever happened to you before? Fortunately, I had something up my sleeve - a few years of experience as the Black Belt. Six Sigma works basically everywhere.

I need to explain how the filling machine works (see Fig. 1). The liquid is fed to the filling machine under constant pressure from the tank. The filling machine has a flowmeter whose task is to measure the volume. It can be set with an accuracy of 0.1 cm3, with a tolerance of 5 cm3 (e.g. 65-70 cm3).

There are 2 nozzles working independently in the filling machine. Usually, the work looks like this: the first nozzle fills one product, while the second nozzle is fitted and waiting to fill another product. When filling ends on one side, after activating the button, the filling on the other side starts. The volume setting is the same for both nozzles. However there are independent diaphragms, valves and solution supply tubes.

I made a simplified version of MSA because I would be doing all the measurements myself on the scale. It can be assumed that 1cm3 of solution = 1g of solution and the accuracy of the weight is 0.1g.

Some background information on the "simple" problem. It was unresolved for several years. It continuously disappeared and reappeared. The problem was protected by labor-intensive and expensive controls. I think it was waiting for me.

I decided to use SPC. In Minitab thera are several SPC charts to choose, e.g. I, I-MR, Xbar-S, Xbar-R, P, NP, C, U. First, the charts must be adapted to the type of data. The data can be either continuous or discrete. If I add that I want to collect data in the shortest possible time, then only the I chart or I-MR chart can be used.

How big should be the sample?

This is a good question, especially when you do not know the standard deviation. One can assume that the "big" sample has about 30 pieces. The Central Limit Theorem says, that regardless of the distribution of data in the population, the distribution of means tends to normal distribution. In the case of 30 items, regardless of the type of distribution in the population, the mean of the sample should be a good estimate of the population mean.

If there were 8 filling machines and in each 2 nozzles, how would you calculate the sample size of 30 items?

I will give you several versions of the answer:

1. 30 items in total for all filling machines, which would mean about 3-4 items per filling machine.
2. 30 items for each filling machine, which means 30 x 8 = 240 items.
3. 30 pieces for each nozzle, which means 30 x 8 x 2 = 480 items.

Let us analyze each option:

1. The least time consuming, but the most risky. It would make sense if all machines worked identically, but can we accept such an assumption?
2. Workload about 1-2 hours. A good option if we assume that both nozzles in each filling machine give the same results. One can be tempted to make such an assumption, especially because this is the most important part of the filling machine, i.e. a flowmeter, is shared to both nozzles.
3. The most labor-intensive version. Workload about 4 hours. There is a chance to check whether there is variability between filling machines (as in version 2), but also whether there is variability between nozzles in each filling machine.

I chose version 3, which meant that I spent half a day weighting samples, but I do not regret it. The content of the article will explain why it was the best choice. In addition, I asked to setup all filling machines identically to about 67.5 cm3 (in the middle of the tolerance range), except that the number of pulses is set on the controller (one pulse is about 0.1 cm3) and this number was the same for each filling machine. Let us follow the data analysis (I use the word "analysis", although SPC charts should be used in the Measure phase) using different charts and different options.

I encourage you to copy data from Tab. 1 and self-analysis in Minitab.

Tab. 1. V - volume for all 16 nozzles. 30 pcs. X 8 filling machines x 2 nozzles.

First, the samples must be arranged in chronological order. In principle, for each nozzle we could (should) have a separate graph. Let me start with the simplest chart - Time Series Plot, which is in Fig. 2. I made a certain simplification showing all the samples on one graph. We can do it, but it is necessary to maintain the order of data. In this case, data 1-30 are for the 1st nozzle in the 1st filling machine, 31-60 are for the 2nd nozzle in the 1st filling machine, 61-90 are for the 1st nozzle in the 2nd filling machine, 91-120 are for the 2nd nozzle in the 2nd filling machine, etc. The same order is in Tab. 1.

All data was split into individual nozzles as can be seen in Fig. 3. On the left side, for example, you can see data for the Nozzle C1_1 and C1_2, which belong to the C1 filling machine. A similar nomenclature is used for all filling machines. The filling machines are: C1, C2, C3, C4, S1, S2, S3, S4.

The Time Series Plot even in the version where data is split into nozzles does not give us much statistical information. It is time to go one level higher, to select SPC chart (see Fig. 4). If we do not set any additional options we will get a graph like in Fig. 5 - I-MR chart, i.e. Individual - Moving Range.

The top chart "Individual Value" (short I) in Fig. 5 shows the individual measurements, while the lower chart "Moving Range" (short MR) shows the consequent differences between measurements. 1st MR point is the absolute value of the difference between 2 and 1 Individual, 2nd MR point is the absolute value of the difference between 3 and 2 Individual, etc. (MR1 = |Y2 - Y1|, MR2 = |Y3-Y2|, where Yi are individual values, i = 1, 2, ..., 480).

Important elements appeared on the chart in Fig. 5. I will describe the top "Individual Value" chart:

• Green line - marking the mean of all measurements.
• Upper red line marked UCL (Upper Control Limit). UCL = mean + 3 sigma.
• Lower red line marked LCL (Lower Control Limit). LCL = mean - sigma.
• Some points are marked in red. This means that special causes are responsible for those values. Minitab allows detecting 8 types of special causes (set the option "I-MR Options" and set tests like in Fig. 6). Each red dot is described by a number indicating the number of the test that failed. No. 1 means that the point is beyond the control range - it is either above UCL or below LCL.
• How sigma (standard deviation) is determined? Let us say that the standard deviation is one, but there can be many estimators. The sigma estimation method would need to be part of a separate article. I will mention only that it depends on the MR values from the bottom chart.
• Sudden increases (peaks) or decreases of values on the chart I appear as peaks on the MR chart. Some peaks (in red) are so large that they go beyond the control limits of the MR chart.

The time has come for the next step. One needs to select the "Stages" tab and insert the "Machine" variable (Machine equals Filling machine), like in Fig. 7. We will get a graph shown in Fig. 8. It can be seen that different filling machines are characterized by different variability, what is marked by wider or narrower control ranges, which are individually determined for each filling machine. The biggest problem can be seen for the S4 filling machine.

Creating the SPC chart again, but this time by selecting "Nozzle" in Stages we will get a chart visible in Fig. 9. This diagram reveals another problem - for the S3 filling machine we notice big differences between the 1st and 2nd nozzle.

Let us summarize all the conclusions coming from the SPC chart analysis:

• Equal setting of filling machines does not ensure uniform filling, more specifically, the average volumes are different for each filling machine. It should be mentioned here, that the flowmeters are calibrated in such a way that each set at the same value allows to obtain the same volume with an accuracy of approx. 0.2 cm3. Calibration, however, takes place in laboratory conditions. Therefore, there must be a different factor than the flowmeter that influences the filling volume. Later on this factor was detected during the Six Sigma project.
• For several filling machines, e.g. S3 or C2, there are significant differences between the nozzles. For the S3 filling machine the variability within the nozzle and between the nozzles is so large, that it takes up the whole tolerance range. It is almost certain that once out of several dozen fillings go beyond the tolerance range. The introduced control (once every 30 minutes, or about 150-200 fillings) does not ensure the detection of this problem.
• For the S4 filling machine the difference in mean between nozzles is negligible, while the spread within each nozzle is so large, that practically covers the tolerance range. This filling machine probably from time to time fills outside the tolerance range.

As for a few hours of work, it is probably a lot of conclusions (what is your opinion?). In addition to the conclusions, I initiated the following activities:

• Immediate replacement of membranes and review of valves in filling machines.
• Systematic membrane replacement and valve review after a fixed number of cycles.
• Replacement of flowmeters in the machines with the biggest variation.
• Periodic checks (once a month) carried out as described here. ATTENTION: normal control of the filling took place every 30 minutes, but due to the change of production volumes and, consequently, adjustment of volume, the phenomena described in this article could not be detected.
• Standardization of the settings of the filling machines in order to know how to set each filling machine to the given volume. Previously, it was secret knowledge (the biggest enemy of standardization) - in the case of less experienced people, this resulted in an extended set-up time for filling machines and additional controls.

Finally, the presentation of the least favorable scenario. Let us assume that I took a sample of 30 pieces for all the filling machines in total. To simulate this, I randomly selected from a sample of 480 measurements several samples for each filling machine (see Fig. 10). Basically, the diagram says it all. On its basis, we cannot draw any of the previously presented conclusions. In this case, the choice of the most labor-intensive version of filling analysis using SPC paid off.

SPC charts can be a very effective tool. However, attention should be paid to sample size and data collection plan.

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Author: Adam Cetera (LeanSigma.pl)
Creation date: 2018-07-03
Modification date: 2018-07-03

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