READ THIS Density Functions - Mystery of the Sticking Handle This Lab is to be done Individually. A local company produces labeling tools used by food and retail stores. These tools are 99% plastic parts manufactured using plastic injection molding. Plastic injection molding is the most efficient and cost-effective method of making parts for many manufactured products. Although there may be many different types of plastic parts used in one labeling tool, they all are produced (molded) in basically the same way. Typically, the process consists of the following steps: 1. A mold is mounted in a plastic injection molding machine. 2. Molten plastic is injected into the cavities of the mold. 3. The plastic solidifies. 4. The mold opens and the part (or parts) are ejected. 5. After inspection and further cooling, the parts are either assembled or stored as inventory. In evaluating the quality of batches of molded parts, it is necessary to measure or visually inspect samples of parts for adherence to specifications. These specifications are preset so that when the parts are assembled with other parts they will fit and operate correctly. The quality evaluation of the process that manufactures these parts requires knowledgeable people using micrometers, calipers, fixtures and gauges to determine the exact measurement of the dimensions of the parts being produced. Quality problems can still be present even after the parts are sent on for assembly. If these problems result in poor operation, it will be dissatisfied customers that will bring it to the company s attention! Note: Recall from Lab 1 (Kisses) that there are no two things exactly alike and there will always be some variation. The goal in manufacturing is to make sure your process is in control and working within preset specifications. The following is a real problem that occurred in the early development of a certain model of labeling gun (see picture above). Customers began calling and complaining that the labeling gun's trigger handle was "sticking". Applying lubricant to the trigger as a quick fix did not help the problem. Quality control people needed to find the cause and correct it. READ THIS Initial Investigation: Some ready-to-ship units were tested, but they were all working well. READ THIS Initial Investigation: Some ready-to-ship units were tested, but they were all working well. Bins of pre-assembled parts that could cause this sticking problem were sampled and checked. As a result, one part was considered the most likely culprit, the trigger itself. This part also had one critical dimension with tight specifications (+/- .037 inches) and was notorious in the Molding Department as being a headache part. This dimension was the trigger's length (see photo further down this page). In the manufacturing of the triggers, three are created at once using a mold with three cavities. (Why make three at once? Remember that not only should the variation between parts be made as small as possible but also the time in making them. Three at a time is faster that 1 at a time. Time is money!!) Note: Multicavity molds make it possible to produce more than one copy of the part at a time. Since it is impossible for any two things to be exactly alike, a cavity number, molded on the part, is often used for control purposes so that parts can be easily traced back to their particular cavity. (If you ever get a chance to look closely at a plastic part from something around the house, see if you can find the "hidden" cavity number.) 111 A sample of parts was taken. The critical dimension of the part (the length that was mentioned above as the likely culprit in causing the trigger to stick) was measured and recorded on the following data sheet. The target length in the manufacturing of the trigger was originally 3.701 inches. However, as we learned from the Hershey Kisses, Hershey could never hit their target Kiss perfectly. Although 3.701 is the target, it is expected that there will be some smaller than that and some greater. However, problems could occur if the parts are too much greater. The table below shows how the manufacturers of the labeling gun were doing as they tried to hit their target - a trigger that was 3.701 inches in length. Click the Excel file containing this data and save it to your computer: Sticking Handle Data Dimension Cavity Dimension Cavity Dimension Cavity 3.709 3 3.728 2 3.692 1 3.683 3 3.73 2 3.702 1 3.701 1 3.699 1 3.694 3 3.699 1 3.684 1 3.71 1 3.699 3 3.694 3 3.716 2 3.718 2 3.726 2 3.72 2 3.702 1 3.731 2 3.683 3 2710 2 2721 2 2400 1 3.702 1 3.731 2 3.683 3 3.719 2 3.731 2 3.689 1 3.699 1 3.704 1 3.692 1 3.721 2 3.694 3 3.696 3 3.694 3 3.709 1 3.693 3 3.736 2 3.726 2 3.692 3 3.69 3 3.686 3 3.734 2 3.731 2 3.716 2 3.696 3 3.721 2 3.698 1 3.701 3 3.704 1 3.728 2 3.695 3 3.693 3 3.732 2 3.686 3 3.711 1 3.711 2 3.704 1 3.689 1 3.734 2 3.734 2 3.693 1 3.732 2 3.683 3 3.695 3 3.692 3 3.721 2 3.673 1 3.697 1 3.693 1 3.686 33.701 3 3.73 2 3.721 3 3.682 3 3 3.699 1 3.689 3 3.718 2 3.73 2 3.727 2 3.721 | 3 3.722 2 3.698 1 3.729 2 3.725 2 3.69 3 3.703 1 3.69 1 3.727 2 3.721 3 3.722 2 3.698 1 3.729 9 2 3.725 2 3.69 3 3.703 1 3.69 1 3.712 23.727 2 3.704 1 3.683 3 3.686 3 3.682 3 3.699 1 3.708 1 3.725 2 3.697 3 3.693 3 3.723 2 3.701 1 3.721 2 3.692 1 3.704 1 3.692 3 3.686 1 3.697 1 3.694 3 3.702 1 DO THIS 1. Can you determine any trends as you quickly scan the table? Load all the data above into 2 columns on an Excel spreadsheet. Separate the parts by cavity number. To do this, select the two columns of data, including the labels: Dimension & Cavity, and go to Data/Sort on Excel s menu. Then Sort by: Cavity 2. The target dimension for this part is: 3.701. At the time when the parts were being manufactured, Engineering had determined that a tolerance of 0.037 would be acceptable. i.e. the part would work well if it measured somewhere between 3.664 inches and 3.738 inches. Anything beyond the 3.738 in. would cause "sticking problems". Looking over the collected data, would any of the triggers cause the labeling gun to stick? NOTE: A measurement that was a little under 3.664 inches usually wasn't a problem. It may cause the trigger to be a little "loose" in the stamper but didn't interfere with its operation. It was determined by technicians that a trigger length above 3.738 inches would cause the stamper to jam. Anything below 3.738 inches and the trigger should be fine allowing the stamper to work well. NOTE: A measurement that was a little unger 3.004 Inches usually wasn't a propiem. It may cause the trigger to be a little loose in the stamper but didn't interfere with its operation. It was determined by technicians that a trigger length above 3.738 inches would cause the stamper to jam. Anything below 3.738 inches and the trigger should be fine allowing the stamper to work well. 3. Obtain descriptive statistics and a histogram for each cavity using identical calibrations on the x-axis for all histograms. You can do this by using the same bin range for all three cavities. Create one file containing these three labeled histograms stacked vertically so they can be easily compared (Click on the Link Kisses Have Changed to see an example of how to display histograms in this way.) ... Summarize your findings. Since these are manufactured parts, what shape did you expect for the distributions? Is this the shape you discovered in the histograms? From the investigation thus far, what cavity or cavities do you think appear suspicious? Why? 4. As mentioned before, the specification range for this part is between 3.664 and 3.738 inches. Investigation determined that any triggers with lengths greater than 3.738 in length will cause the gun to stick! Any triggers with lengths less than 3.738 inches would not cause problems. As you saw from the collected data, there were no bad triggers in the samples. However there is still enough information to help us solve this mystery! Determine what cavity or cavities are producing triggers that stick and the percentage of triggers that are sticking! (When turning in the answer to this question, show all your work in finding the answers including calculations you made.) Hint: The histograms of the trigger lengths for each cavity appear mound-shaped. This should not be a surprise since these are manufacturing processes. Use what you learned in section 4.5 & 4.6 (Normal Distributions) to calculate the needed probabilities/ percentages to answer this question. NOTE: When doing any of the calculations DO NOT ROUND OFF the descriptive statistics such as average and standard deviation obtained from Excel! You are working with very small values. What you might consider a small amount of rounding could result in a great amount of error!! Example: Click on the link Modeling the Normal Distribution to see how a standard normal probability model can be used to estimate probabilities/percentages using collected data. 5. Assuming that each cavity produces the same number of triggers, estimate the percent of all the labeling guns (triggers from all cavities) that could be sticking. In the end, the company will decide, based on your findings, whether or not the cavity or cavities in the mold should be repaired. Changing a mold is very costly! You will want to make sure that the information you present is accurate. Submit an Excel file or Word document containing your 3 vertically displayed histograms and your answers to the questions 1 through 5 in the category Lab 3 Dropbox.