IE 355 QUALITY AND APPLIED statistics I

LAB ASSIGNMENT 3:
PROCESS CONTROL FOR AN
AUTOMATED FILLING MACHINE

Goal

A new production process is being installed. It is an automatic filling machine that has four nozzles. The goal is to design a process control system for the filler. A process control system includes instructions for sampling, the control charts and interpretations and usage of the charts. These instructions are to be directed to those who will operate the filling machine process.

Figure 1. Automated Filling Machine

The Filler

Figure 1 shows the automated filling system. The filling process works as follows: The vessel is pressurized and the magnitude of the pressure is measured and recorded. Next an outlet valve is opened and the liquid in the vessel is dispensed simultaneously into four containers through four nozzles. After a preset length of time, the liquid outlet valve is closed and the conveyor advances to position the next set of containers to be filled. Subsequent to filling, the weight of each container is measured and recorded (the product is actually weighed twice, once before filling and then again after. The weight of the contents is then calculated as total minus the weight of container.)

The Measurements

There are two key measurements. The first is a product measurement, the weight of the contents of each container. The second is a process measurement, the pressure in the vessel.

Instructions

You may work in groups of one or two persons.

In the field, the first step would be to collect as much data as possible from the process during normal production. For this lab assignment, you will be given a dataset that you will assume has been collected in such a fashion.

You will design a proper process control system, i.e., and charts, for the filling machine for weight of liquid and vessel pressure. Once this has been done, you are ready to use your control charts to detect problems (assignable causes) in the filling system. In the field, you would put your control charts online, that is, take data from the process as it becomes available and plot it on the control charts. In the lab, you will be given an additional dataset that you are to assume comes from online production. Append the new data to the original dataset[1] and look for possible problems with the filling system. Compare pressure and weight control charts to determine where in the system a problem may have occurred. As you know, you may not be able to detect a problem immediately; several samples may be required.

Lab Report

  • Executive Summary – ½ page or less giving the punch line. The executive summary should contain a short synopsis of what was written in the entire report. “This was the problem. This is what we did. This was what we found.” Rule of thumb: if you were a busy executive and you had time only to read the executive summary, it should tell you everything that is in the report, especially what the results were, but in an abridged form.
  • Introduction – Describe the “what” of the assignment or problem. What is the problem? Describe the system. State the steps you will take.
  • Analysis: In the analysis section, remark on anything interesting or boring. For example, “For the x-bar chart in figure 1, we see nothing unusual. The points plot with no systematic patterns.” If you observe something strange or interesting, make a remark even if you do not understand why or cannot justify it with theory. Remember, we are working with random data. We will not always see what we expect.

Control Charts for Weight: Show recommended control charts constructed from initial data. Show and label your control charts. Discuss what you see whether you can justify it or not.
Control Charts for Pressure: Show recommended control charts constructed from initial data. Show and label your control charts. Discuss what you see whether you can justify it or not.
Assignable Causes: Use your online control charts to find assignable causes (if any).

  • Appendix: Put raw data here.

Notes:

Any tabular or graphical results that you include in your report must, must, must be labeled with captions and referred to in the lab report analysis. For example, “As you can see on the x-bar control chart in Figure 2, the points 3,4 and 5 are…”

StatGraphics Notes

Making Initial Control Charts:

To make initial controls chart select Special>Quality Control>Variables Control Charts>X-bar and R…. There are two ways to fill out the dialog box for the X-bar and R control charts depending on the structure of your data.

Example 1: Suppose you have 200 observations of a quality characteristic. You would like to construct control charts with a sample size of 4. In the X-bar and R charts dialog box select the Observations radio button and enter the column containing the 200 observations into the Observations field and enter a 4 in the Subgroup Numbers or Size field.

Example 2: Suppose you have two columns of sample statistics, i.e., the first column is sample averages and the second column is sample ranges. Let’s say that each sample statistic was calculated from 4 observations. In the X-bar and R charts dialog box select the Subgroup Statistics radio button. Enter the column of sample averages into the Means field, enter the column of sample ranges into the Ranges field and enter a 4 in the Subgroup Numbers or Size field.

Select OK and the chart is created along with an initial study report that tells the basic calculations (mean, std dev, control limits and the points outside the limits). Click the Graphical Options button to select the R chart too. Click Tabular Options button to select other tabular reports such as Subgroup reports and Runs Tests.

Rclick – Analysis Options allows you to enter other than 3-sigma control limits and also to exclude points that are outside control limits. Each time you exclude points, new control limits are calculated. The excluded points are indicated with X on the graphs - not with a dot like the included points.

Rclick somewhere on the graphs – Pane Options allow you to add warning limits to the control charts. Rclick somewhere on the tabular outputs to get options for each tabular report.

Click the save button (4th from left with red arrow) to save estimates of the process mean, standard deviation, and associated control limits in your data file. You can also save subgroup means and ranges. Check your data file to see that all you intended to save is there.

Adding New Subgroup Data Points to Existing Control Charts While Keeping the "Standard Limits”, i.e., Putting the control chart “online”

Once the control charts have been established, i.e., the control limits have been determined by the iterative procedure for creating initial control charts, you are ready to use the control charts online. This part of the lab assignment demonstrates adding online data to the control charts you constructed in the previous section. In the real world, the data would come to you piece by piece as subgroups are observed from the running process. In this assignment, we give you all the “online” data in one file.

First, combine the “online” (new) dataset with the current one. One way to do this is select: File>Combine>Combine Data Files…. In the open data file dialog box select the new data file. OK. StatGraphics asks if you wish to append data to end of file. Say yes. The columns of the new data file are appended to the current data file. Another way is to cut and paste using the windows clipboard.

Rclick in the X-bar and R chart Analysis window – Analysis Options. Select the Control to Standards radio button. Select either Specify Parameters or Specify Control Limits radio button. For Specify Parameters, enter the mean and variance or for Specify Control Limits enter the control limits. These are the values you calculated from the initial study above.[2]

Next, paste the new data points to the end of the original columns. Now you see the new samples plotted onto the existing control charts. The Subgroup Report lists out-of-control points. You can examine the Runs Tests for out-of-control points too. In this stage we never remove points because we are “online.” We must explain them, i.e., find assignable causes and fix the process.

1

[1] See StatGraphics Notes below.

[2] If you don’t “Control to Standards” your control chart limits will change when you append the new data. WE DO NOT WANT THIS.