Minitab software is the pioneer in providing statistical software and services for the fields of quality improvement, education and research application. It has powerful functions and a simple visual operation interface, and is highly favored by quality scholars and statistical experts. After the 1990s, Minitab's general statistical products entered the field of statistical application of industrial enterprises, providing rich functions such as statistical process control , statistical analysis, statistical graph drawing, experimental design, efficacy and sample size calculation. With the improvement of the software version, more statistical functions have been added and have been favored and adopted by the majority of users. The third stage of
Six Sigma Management DMAIC model is analysis (A). After identifying what happened (Y) in the measurement stage, the next work is to find the cause of the problem through analysis. That is, a set of factors that affect Y arranged by importance are finally determined. The method used in the analysis stage of
depends to a large extent on the problem solved and the business process faced. It usually adopts a combination of data analysis and process analysis. Data analysis mainly uses data that have been collected or data that needs to be collected for analysis to distinguish problem patterns, problem development trends or other relevant factors; process analysis mainly distinguishes inconsistent, unrelated, or certain areas that may cause problems or cause problems from the perspective of the entire process operation. Put together the conclusions of various methods and gain a comprehensive understanding of the influencing factors.
From the perspective of Six Sigma management, there are three specific goals achieved in the analysis stage: find out all factors that affect project Y; identify the key few factors; and evaluate predictive improvement benefits. Tools in the analysis stage are divided into three categories according to the type of tools, including qualitative analysis methods composed of brainstorming methods, quantitative analysis methods supported by statistical techniques, and graphic tools supported by statistical techniques and management techniques.
graph analysis tools mainly include: box charts that compare the differences between two groups of data, scatter plots that describe the correlation relationship between factor variables, histogram that displays influencing factors, multivariate plots that describe the relationship between influencing factors, quality function development for comprehensive analysis from the perspective of customer requirements, technology and product requirements, contour charts that analyze the relationship between three variables through two-dimensional charts, and flow charts for finding reasons through process. The following is a focus on box charts, scatter plots, margin charts, matrix charts, contour charts, multivariate charts, etc. in conjunction with Minitab software. The structure of the box plot of
box plot is shown in the figure above. This is the data provided by Minitab software, and the samples have 4 Q values corresponding to the sample. The 4 Q values are: Q1, Q2, Q3, and Q4. The arithmetic average of the data located in the middle or the two data is called median .
Open the Boxplot main dialog box from the Graph drop-down menu. Through the selection input of variables, you can draw a box plot, or you can draw the box plot of each category value in the same window according to the category variable. The Datadispaly option can select the type of box: InterquartileRange Box chart (IQRangeBox), median confidence interval box plot (CIBox), and sample full distance box plot (RangeBox). Edit Attibutes sub-dialog, which can change the attribute values of the box, such as fill color, edge type, color, size, width, display of tentacles, and setting the box width to proportional to the sample size. The Annotation option can also set marking properties for exception points, medians, mean values, etc.
Box chart is a drawing tool that describes the characteristics of data distribution through one or several box shapes. In Six Sigma quality management, its main function is in the following two aspects: comparing the degree of dispersion and concentration of data between different samples, and finding differences to provide a basis for the next step of judgment and decision-making.
For each independent box plot, determine whether the data has an outlier existence. The exception points should be analyzed and the reasons should be summarized.
To create and analyze box graphs, you must first understand the Q value.Q is the abbreviation of quartile, representing 1/4 of the data. Each sample has 4 Q values. When the sample data is sorted from small to large, the data are divided into 4 parts, that is, Pulse in the Sata directory. The mtw dataset is derived. The method of interpretation and analysis of box chart is as follows:
rectangular box represents sample data from the first quartile Q1 to the third quartile Q3, and the position of the median is marked in the box, so that the box includes half of the sample data. In this example, select I QRange Box.
Comparison of the upper tentacles and the lower tentacles shows whether the data is symmetrical. When the lower tentacle is larger than the upper tentacle, the data is in a left-sided distribution. On the contrary, when the upper tentacle is larger than the lower tentacle, the data is in a right-sided distribution. Only when the upper and lower tentacles are equal can the data be symmetric. Compared with the box plot of normal data, it can also be seen whether the sample data complies with normal distribution . Obviously, in this example, the sample data on the left is left-sided distribution, while the one on the right is right-sided distribution.
exception point interpretation. If the observed values are located outside the three times the interquartile distance on the upper and lower sides of the rectangular box, they become an abnormal point and are marked with an asterisk* in the box chart. These values have a significant impact on the analysis of mass characteristics , and special attention should be paid. No exception points appear in this case.
In order to examine the relationship between the two variables X and Y, the N pair of observation data values of (X, Y) are depicted in the two-dimensional rectangular coordinate system , forming a scatter plot.
In the scatter plot Plot dialog box under the Graph drop-down menu of Minitab, enter the dependent variable to be analyzed and the independent variable under the Y and X columns respectively. If there is a causal relationship between the two variables, then let the cause variable be X and the result variable be Y. If you want to analyze the relationship between multiple pairs of variables, enter them according to the rows under the column. The Data display option can specify grouping variables to group data, and you can select display content (such as symbols, areas, etc.) for each pair of data or each group of data or each chart.
Set the attribute value of the displayed content and select implementation in Edit Attributes. Annotation is used to specify the attribute values of the drawing's title, annotation, data marks, outlier marks, median and mean marks, straight lines, polygons and bookmark marks. Frame can be used to specify attribute values such as coordinate axes, multi-chart display, and axes value range. Regions options can set the region attribute values for data, charts and legends.
From the scatter plot, you can observe the relationship between variables X and Y: Positive correlation: Y value increases with the increase of X value; negative correlation: Y value decreases with the increase of X value; uncorrelation: There is no rule in the change between Y value and X value.
In addition, the scatter plot can also know the degree of correlation between the two variables; check whether there are abnormal points, etc.
The example here uses the Minitab software's own data Pulse.mtw, which analyzes the relationship between variable Weight and Pulse 1, and a box graph that reflects the respective distribution of the two variables. From the two-dimensional scatter plot, it can be seen that there is no correlation between the variable weight and pulse 1, that is, the pulse of the human body will not be different due to weight differences, which is also in line with the physiological characteristics of the human body in reality. From the box graph of the variable weight, one can see that one point is an outliers, which is outside the upper limit, indicating that one person is relatively large. Through the Brush option of the chart editing function, you can view specific information about the point, and the individual should pay attention to it. In the box chart of the variable pulse 1, no abnormal points appear, indicating that there are no adverse phenomena in the pulse of the observed object.In Six Sigma quality management analysis, especially relevant statistical analysis, it is necessary to combine the actual situation to prevent errors in judgment. For example, from the data, some variables have correlations and strong correlations, but in reality, the two variables are not related, and this correlation also becomes a pseudo-correlation.
matrix graph is also a type of scatter plot. The distribution relationship diagram between multiple variables can be displayed in a two-dimensional plot. This allows you to observe the correlation between multiple variables in a chart, which facilitates data analysis between multiple data and saves a lot of time. A matrix graph can analyze up to 20 variables.
Marginal graph is actually a type of scatter plot. By attaching a histogram, box chart or point plot of variable Y and variable X in a direction parallel to the Y and X axis, the distribution of the two variables can be individually analyzed.
generates a marginal graph, and select it in the MarginalPlot dialog box under the Graph menu. In the dialog box, enter variables Y and X as the Y axis and X axis respectively, select the type of marginal graph, and you can choose one from the histogram, box chart or point chart. At the same time, you can select the variables to be used as marginal graphs. You can only make the marginal graphs of variable Y or variable X, or you can make a marginal graph for both variables. In addition, you can also select the marks of the Y axis and X axis and the title of the chart to replace the default value.
In the Symbol option, you can display the data point's attribute values, such as displayed symbols, colors, etc. In the
Options dialog box, you can set the scale value of the coordinate axis, mark attribute value, etc. If the maximum scale value of the two coordinate axes is the same as the minimum scale value, under certain circumstances, two variables with the same unit of measurement can be made more comparable.
marginal graph includes a two-dimensional scatter plot and a distribution plot of each variable. The two-dimensional scatter plot can be used to analyze the correlation between two variables and the joint distribution between the two variables, and the distribution plot of each variable can be used to analyze the distribution of each variable. The
Graph variables option is used to specify the variables to be analyzed, where at least two variables are to be selected, but no more than 20 are allowed. Use the Minitab software to bring its own data Pulse.mtw, and in this option, Pulse1, Pulse2, Height, and Weight are selected from the variable list on the left, so that the correlation between these four variables can be analyzed. The optional options in the
Options sub-dialog are: list all the matrix (default value) or the contents of the lower left or upper right corner; place the variable name in the diagonal position of the matrix (default value) or on the boundary; to distinguish overlapping data points, add "Jitter" as the offset of the data points, and the system defaults to no display information. The variables that reflect the correlation relationship of each scatter plot in the
matrix graph are the variables corresponding to the horizontal and vertical directions of the scatter plot. For example, the scatter plot in the upper right corner of the matrix graph in this example corresponds to the variable Pulse1 horizontally and the variable Weight vertically, so the scatter plot reflects the correlation between the variable Pulse1 and Weight.
can be seen from this matrix diagram that the variable Pulse 1 is not related to the variable Weight and Height, and the variable Pulse2 is not related to the variable Weight and Height, indicating that the pulse has nothing to do with weight and height, that is, the body shape of a person, and is in line with the actual situation in reality. In the scatter plot of variable Weight and Height, the value of one variable increases with the increase of the value of the other variable, and the two show a significant positive correlation, reflecting the actual situation. Generally, weight will increase with the increase of height.
scatter plot, marginal plot, and matrix plot are all used to describe the correlation between two variables. When only analyzing the relationship between two variables, choose a general scatter plot; when describing the distribution of each variable at the same time, choose a margin plot; if you want to analyze the relationship between multiple variables at the same time in a chart, choose a matrix plot. The analysis of correlations in each chart is consistent.
contour chart is to depict three variables in a two-dimensional chart. If the horizontal coordinates and the vertical coordinates represent the variables X and Y respectively, then the third variable Z can be regarded as an extension inside/outside the drawing plane, and the shadowed part in the figure represents the value of the variable Z. The Contour Plot under the
Graph menu is used to make contour graphs. In its main dialog box, enter variables X and Y and Z respectively. The variables X and Y are set as the horizontal and vertical coordinates of the contour graph respectively, and the variable Z is used as the third variable. The Data Display option specifies the display form of data: Area or Connect, and can also specify the fill color and size of the area and the type, color and size of the connection line.
Use the Minitab software's own data Exh_grph.mtw, in the main dialog box of Contour Plot, select Enter Alt under the Z column, enter Lat under the Y column, and enter Long under the X column. Select the Area block and click Attributes to enter the dialog box. Enter 1 in Filltype (1=solid), and enter 4 15 2 5 3 in Fill color, representing blue, gray, red, cyan and green respectively.
In the contour chart, the shadow is composed of lines or areas surrounded by lines equal to z values. The analysis of connoisse graphs is also mainly carried out from this perspective.
This example analyzes the relationship between longitude, latitude and altitude.
6,
6 Six Sigma Quality Management, when studying multiple indicators, multivariate graphs can be used to vividly depict the relationship between variables. Multivariate graphs are used to present continuous numerical variance data using a graphical method. These graphs can also be used to have some preliminary image understanding of the data before doing ANOVA . The implementation of this diagram is not in the Graph menu, but in the Multi-Vari Chart under the Quality Tools under the Stat menu. In its main dialog box, the functions that each option and sub-dialog box can realize are:
Response: Enter the data column name of the interpreted variable, which must be numerical;
Factor: Enter the factor variable, and up to four can be input. The factor variable can be numerical, font-type or date/time;
Options Sub-dialog box: Drawing displays each data point, connects the sample mean of each factor with a straight line, and sets the drawing output title instead of the default value.
uses the Sinter.mtw, the built-in data of Minitab software. This data is used to evaluate the effect of the slag time of three metals under strong pressure. The data collection process is to measure 5 samples of each metal in each slag time: 100, 150 and 200 minutes respectively. Before performing data analysis, we first want to use a multivariate graph to see if there is a clear trend or interaction.
In the output multivariate diagram, there are three points connecting lines on each metal type. These three points represent the average compression strength of the metal in each time period under the corresponding metal type type, and also reflect the information in each metal type group. The points on the horizontal connection in the figure represent the average compression strength of the three metals, representing the information between each metal type group.
The results show that the compression strengths of the three metals correspond to the slag time are quite different, indicating that the type of metal interacts with the length of the slag time. The slag time corresponding to the maximum compression strength of the three types of metals is: 100 minutes, 150 minutes, and 200 minutes, respectively.
If you want to quantify the interaction between factors and the effects of other factors, you can further use methods such as analysis of variance or general linear patterns.
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