OIM 350 HW#4

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University of Massachusetts, Amherst *

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350

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Mechanical Engineering

Date

Jan 9, 2024

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docx

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Problem 1 1. Construct an X-bar R chart using subgroups of size 6. 2. Comment on the results from this analysis. As you can see above in the X-bar & R chart, all points fall within the control limits and there does not seem to be any trend or pattern within the control limits. This tells us that the process is stable. We can say that any variation that occurs is due to the common variation of the process. 3. Plot the data as a time series and comment (hint: sample/head on the x-axis and height on the y- axis). Do you see any patterns or assignable causes? By using the data as a time series, we can observe that the patterns are repeated. Every bottle created according to their rank in manifaturing is the almost the same as the

product created 30 later but with the same rank. For ex. A bottle created 1 st has the same Hight as the 7 th bottle and the 13 th bottle and so on. You can see it better in the data table labeled Time series height by sample in JMP (check JMP data table). 4. Construct a comparison boxplot (compare box plots of the 6 “heads”). Comment on the graph. As you can see in the box plot the height when compared to the head is very similar. Other than no.2 most of the highest fall within 0.05 of each other and in some cases the height is the same. This tells us that if a bottle is produced in the 1 st head all the 1 st head bottles are going to be of similar height. 5. Perform a one-way ANOVA. What does this analysis tell you (and how did you get to your conclusion)? Looking at ANOVA we can tell that Since the p-value is less than 0.05 we reject the null hypothesis and conclude that not all means are equal (at least one mean is different). We can also tell that head 4 has the heist mean and the lowest amount of gap between each bottle produced. (Graph was too long see JMP file attached to look at the graph and data table for ANOVA).

6. Using the output in 3-5 to comment on what you think the problem is as well as any assignable causes and how the shampoo company can resolve the label variability problem. Why do you think the X-bar R chart did not provide obvious clues as to what the problem was? I think our problem is a malfunction in the production line where the height of the bottle is determined by which head the bottle belongs in. the bottle produced 1 st is going to have different 1 st has different height than other bottles but the bottle produced 1 st in the second batch has similar height as the first one. So, to fix the problem we need to fix the malfunction in the production line or maybe do the following: all products produced 1 st will go in the same box, all bottles produced second should go in the same box, so on and so forth. This will lead to all the heights in being same as the rest when a supplier gets their boxes of shampoo. You could also produce all the bottles same as head 4 since it has the least distribution resulting in all the bottles being similar. X-bar & R chart could not provide us with this data because it cannot scale the difference when the input in very tiny. It only looks at whether the process is within the control limit or not. Problem #2 1. After watching the video (and/or read the transcript), briefly summarize the problem that the company encountered (what is tin dust? Why do they want to reduce it?...) and what did they do to solve the problem . Make note of who participated in the project and which steps did they take (refer to DMAIC or PDCA). Focus on the solution process. You will analyze the data in the subsequent questions The problem the company encountered was having tin dust in their production lines. Tin dust is the dust produced by tin. The company used lots of tin. The y wanted to reduce tin dust because it resulted in them having to clean tin dust-off production line all the time. To address this issue, the quality manager, Marcus, assembled a cross-functional team consisting of individuals from production, technical, and maintenance departments. The team adopted a problem-solving approach inspired by the Six Sigma DMAIC (Define, Measure, Analyze, Improve, Control) framework. To solve the problem by following these steps: Define:  Identified the problem: Excessive tin dust in production lines causing frequent cleaning.  Goal: Reduce tin dust to enhance production efficiency. Measure:  Established a baseline by observing and measuring tin dust production after 25,000 lids.

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 Determined that more than two kilograms of tin dust triggered the need for line cleaning. Analyze:  Formed a team to brainstorm potential root causes for tin dust.  Identified key variables, including thickness of tin sheet, piston measurements, and coating presence on the piston. Improve:  Utilized SAS JMP to set up a Design of Experiments (DOE) to analyze the impact of variables on tin dust.  Executed experiments over a week, collecting data on tin dust with varying settings.  Analyzed the data using statistical tools to identify significant factors affecting tin dust. Control:  Conducted further trials to validate the proposed changes.  Implemented optimal solutions, including coating the piston and adjusting Measurement 3 to 2.0, based on statistical analysis.  Emphasized the importance of controlling the production process to maintain reduced tin dust levels. 2.