A manufacturing process at your company produces a polymer film that is in the s

Question

A manufacturing process at your company produces a polymer film that is in the shape of a rectangle. For each film produced, as a quality control measure the thickness (in microns) is measured in four specified locations, "Bottom Left", "Bottom Right", "Top Left" and "Top Right", labeled 1, 2, 3 and 4, respectively. From a production run of 3000 pieces, 160 films were randomly selected and the four thickness measurements were made for each of those selected. Thus, the outcome of this set of measurements was four sets of 160 thickness measurements, each set corresponding to a specific location on the films. Box plots for the four data sets, 1, 2, 3 and 4, are shown above. These plots were generated in Matlab using the same convention that we discussed in class. Answer the following questions for data set 4, corresponding to a position on the "Top Right" of each film. Indicate on the plot the value of the median, the 25th percentile, 75th percentile and the Inter-quartile range (IQR). Does the upper whisker appear to extend to its maximal value of (75th percentile + 1.5*IQR)? Does the lower whisker appear to extend to its minimal value of (25th percentile - 1.5*IQR)? Circle or otherwise identify any outliers. Based on these box plots, do you think there is any significant difference in the median values of the four locations that were tested? Explain your reasoning. A histogram of the thickness data at one of the locations (1, 2, 3 or 4) is shown above. The histogram was generated using a bin width of 50 microns. As mentioned, there are 160 total observations in each data set. Compare the histogram to the box plots and indicate which data set (1, 2, 3 or 4) the histogram is presenting: _____ What are the features of the histogram and box plot that support your answer. The customer for these films has an application in which the tolerance for thickness requires the film to be between 450 and 550 pm. Do you think they are going to be very happy with the product your company is providing? Explain your answer.

Explanation / Answer

8b) Ans: Based on the box plots, it does not show large significant differences between the median of the four data sets. Also, they have slightly positive skew and most of the data fall within a specific range in these four data sets.

8c) Ans: Compare the histogram to the box plot, data set 2 presents this histogram. Both the histogram and box plot have similar skewness, same maximum and minimum values and median value of histogram is near to 500 it is near to 490 of box plot 2.

8d) Ans: No, they will not very happy with the product of this company which is provideing because the variance of these data set is significantly larger that their requirement.

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