Assignment Follow Up 2 - Dilpreet Singh

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Grand Canyon University *

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Feb 20, 2024

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Assignment Follow Up Dilpreet Singh 1) Open the document with the answers provided by Professor Hillmer and read through his answers. Compare the answers that Professor Hillmer came up with for each problem to the answers you obtained. Q.1 Dilpreet - About time 30, there is a single extraordinarily high value that represents a unique reason. The remaining data seem to show only common causes aside from this value. Investigating differences between the moment the specific cause is notified and the moments just before and following might be a suitable course of action Q1 Professor Hilmer - There is one extremely large value around time 30 that is a special cause. Other than this value, the remaining data appear to only contain common causes. An appropriate action is to find out what is different when the special cause is signaled compared to the time immediately before and after when the special cause is signaled. Q.2 Dilpreet – A) The data grows at a reasonably steady rate over time B) Two values that are higher than the rest of the data are close to the beginning of the data; these could be unique reasons. Additionally, many values are below the bulk of the data. C) Given that most of these values correspond to the month labeled "h" in the plot including the labels for each month, there appears to be some seasonality in the data. Throughout the year, the month-to-month variation from July to August is consistently less than the other month-to-month variations. Last but not least, the first month-to-month change in this data, labeled b, is significantly less than the other values designated b. Q.2 Professor Hilmer – A) The data increases over time at a fairly consistent rate. B) There are two values near the beginning of the data that are higher than the rest of the data, these may be special causes. Several values are lower than the majority of the data. C) From the plot with the labels for each month it is evident that most of these values are for the month labeled “h”, therefore there is evidence of some seasonality in this data. The month-to- month change from July to August is consistently lower than the other month-to-month changes for the same year. Finally, there is one month-to-month change (this first one is labeled b) that is much lower than the other values labeled b in this data. Q.3 Dilpreet – A) This data follows a seasonal trend in several ways. Certain months have greater data sets than others.

B) January (a) and February (b) typically have higher sales, while July through December typically have lower sales. This data exhibits a seasonal pattern. March's first occurrence (c) has a far higher value than the other March values. Q.3 Professor Hilmer - There seems to be somewhat of a seasonal pattern to this data. The data for some of the months is larger than other months. B) Higher sales tend to occur in January (a) and February (b) and lower sales occur in July through December. There is a seasonal pattern in this data. The first occurrence of March (c) is much higher than the other values of March. Q.4 Dilpreet - This data exhibits an increasing tendency over time as well as a clear seasonal pattern. The data might have slightly shifted downward at time 72. Following this change, the data keeps growing. Q.4 Professor Hilmer - This data has a distinct seasonal pattern and the data has an increasing trend over time. There may be a slight downward shift in the data around time 72. After this shift, the data continues to increase. Q.5 Dilpreet – A) This data meanders with multiple trends, containing both common and unique causes. The data starts with an increasing trend and continues to do so until about time thirty. After that, it drops steadily until time sixty, at which point it increases until the end of the data. Given that the data trends point to specific reasons rather than a stable system of common causes, this system is unstable. B) The fact that the data primarily lies within horizontal parallel lines indicates that it only includes common causes. Compared to the original plot, the time series plot of the month-to- month variations appears to be a far more stable system of common causes. Though it doesn't seem to be significant enough about the other data to constitute a special cause, there is one large value at time 18 that may be a special cause. C) There is symmetry in the histogram. If there are only common causes in the data, then plotting a histogram is suitable. The time series plot indicates that this presumption is logical. The histogram suggests that the data has some special causes around the value of 300. This histogram resembles a data histogram from a system with just common causes and is extremely near to being symmetric. This data's mean is quite near zero. The chronological sequence of the data would not matter, and the histogram would be suitable if the data followed a stable system with only common causes. This assumption appears to be about correct for this data based on the time series plot; there is just one somewhat large value that could indicate a special cause.

Q.5 Professor Hilmer – A) At the beginning of the data there is an increasing trend until around time 30, then the data decreases fairly steadily until time 60, and finally the data increases to the end of the data. This is not a stable system of common causes because the trends in the data are evidence of special causes. B) The time series plot of the month-to-month differences looks much more like a stable system of common causes than the original plot. There is one large value around time 18 that might be a special cause; however, it does not appear to me to be large enough compared to the other data to be a special cause. C) This histogram is very close to being symmetric and it looks like a histogram of data that comes from a system containing only common causes. The mean of this data is close to 0. If the data followed a stable system of only common causes, then the time order of the data would not matter and it would be appropriate to draw the histogram. From the time series plot, this assumption seems to be approximately true for this data, there is only one somewhat large value that could be a special cause. Q.6 Dilpreet - The graphic shows that the first six values all of which were negative and significantly lower than the remainder of the data—show that the output from this industrial process was not what was expected. The procedure did not meet the goal at the start of the data. The deviations often fluctuate consistently around 0 after the first six measurements. Given that the shift represents a unique cause, it would be wise to investigate what made the first six values distinct from the remaining data. Q.6 Professor Hilmer - The plot indicates that the output from this industrial process was off target for the first six values – these values were all much lower than the rest of the data and they were all negative. At the beginning of the data, the process was below the target. After the first 6 values, the deviations tend to vary around 0 consistently. Since the shift is a special cause, it would be a good idea to investigate what was different about the first 6 values compared to the rest of the data. 2) List the instances where your answers were different from Professor Hillmer’s answers. For each instance where you identified a difference which of the two approaches do you believe is a better answer to the question asked? Why? By comparing my answers to Professor Hilmers solutions, the answers are similar.

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3) Describe what you have learned, if anything, by comparing your answers to Professor Hillmer’s answers. I learned that I need to give a more meaningful and good explanation for my answers rather than giving a small direct answer.

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