The Woodmill Company reduces the dimensions of lumbers. There are two processes through which the company decides the exact width of the pieces. They determine the width manually or by the scanner. The board width of 100 boards is given for both scanner and manual processes. The main objective of the company is to determine which one of the processes will be beneficial for them. Using an optical scanner, a business in Oregon has created the ability to accurately measure the rip widths. Trim for windows and doors are produced by the Wood Mill firm. Both the manual and the scanner approaches are employed by the company in order to slice the dimension into little bits. I have tasked with finding out whether an optimal scanner is more advantageous than manual process-based data analysis.
Frequency Distribution, descriptive statistics, and their analysis
In a data set, frequency is the number of times a particular value or observation occur. The frequency distribution is a graphical or tabular depiction of the observations and their corresponding frequencies that are used in frequency analysis. The scanner data is negatively skewed and the manual data is positively skewed. From the descriptive statistics, we can see that the scanner data has a higher mean than the manual data, but the manual data has higher variability than the scanner one.
The frequency distribution of Manual values
As we can see in the chart, the frequency distribution of manual values is approximately normal as its shape is approximately bell-shaped and similar to normal curve.
The frequency distribution of Scanner values
Similarly, the frequency distribution of manual values follows a normal curve and has a roughly bell-shaped form. We can also observe it by using the box plot
Box plot also known as box-and-whisker diagrams represents the distribution of data based on the five measures like minima, maxima, first quartile, median and third quartile of the data. It contains a box whose bottom side represents the first quartile and the top side represents the third quartile.
The desired box plots are shown in the Chart diagram
As the box plot of both has no outliers and whisker’s line of both boxes’ plots appear be same, thus the distribution of both process is approximately normal with no outliers. Obtain the descriptive statistics of both measures, manual and scanner which includes Average, Minimum, Maximum, Quartiles, Median, and Standard Deviation etc.
Use the Minitab technology to obtain the descriptive statistics of the manual and scanner values with following steps:
Enter the data values with column names, “Scanner Value” and “Manual Value” as few values are shown below:
- Go to Stats-> Basic Statistics-> Display Descriptive Statistics.
- Select Scanner and Manual values under Variables and check the desired statistics.
- Press Ok.
Thus, the obtained results are:
Thus, the average value of Scanner Value and Manual Value is 30.009 and 22.837 respectively while the standard deviations are 7.444 and 8.501 respectively. As the standard deviation shows the variability of the data i.e., it indicates how far are the data points from its sample mean. Thus. The manual value has more variability as compared to scanner value since the standard deviation of the manual process, 8.501 is greater than the standard deviation of the scanner process, 7.444.
The process generates more value
As the scanner process has smaller standard deviation and forms a bell-shaped distribution thus the optical scanner process generates more values. It shows that the manual process is less reliable as it has larger variability in the values while the scanner process has less relative variability due the lower standard deviation.
The process has less variability
From the frequency table, we can see that the values in the manual data vary more than the values of the scanner data. Manual data are dispersed more sparsely. Some are very low and some are towards the high end. So, the scanner data has less relative variability.
From the descriptive statistics, we use the formula for the relative variability.
Relative variability = SD / absolute value of mean.
Relative variability for scanner = 0.2454
For manual values = 0.3772
Hence, the scanner data has less relative variability.
An optical Scanner is the best option
Thus, it concludes that the scanner process (optimal scanner process) is the best option for the company as compared to the manual process since the scanner process has no outliers and is normally distributed and has less variability in the values. Scanner has the lower variability since the standard deviation of the process is lower.
As we see that the optical scanner has less variability, so we can see that this is the best option. Because for any data, less variability is always acceptable which indicates that the data is more consistent. Also, the SE is less for the scanner data which tells us that the error in this data is lower than the manual data.
By using excel data analysis
Secondly, Go to Data and data analysis
Input values as shown in the image
Output for Scanner and manual process
Again, put the data in excel and go to data, data analysis and Descriptive statistics
Putting the values as shown below
The scanner is programmed to detect flaws and calculate the best rip widths to maximize the board’s resale value. The tear widths of 100 test boards were measured using a scanner. There was no actual ripping done to the boards. Each of the 100 boards was graded by a lumber grader, presuming that the rips detected by the scanner had been made. These 100 boards were then manually ripped in accordance with standard procedure. Each board was graded by a grader after the manual ripping process had been completed.
Therefore, approximately 3 values are more than 2 standard deviations from the mean. The mean value (Mu) is 22.8372 and the standard deviation (SD) is 8.5014. The limits for the 2 SD’s from the Mu are 5.8344 and 39.84. Therefore, approximately 2 values are more than 2 standard deviations from the mean. The scanner process generates more values than the 2 SD’s from the mean. Here, the scanner process has less variability than the manual process due to lower SD. Therefore, the scanner process has less variability. By observing the above conclusion, it can be concluded that the optical scanner process will help the process to give better results than the manual process. Therefore, the scanner process is the best option.
As a result, we can observe that the optical scanner aids in the creation of better boards and outperforms the manual approach. As a result, there were four values in the case of the optical scanner, but only two values beyond the two standard deviations threshold in the case of the manual method. Optical Scanner has a lesser variability because the process’s standard deviation is lower.