Statistics
Statistics is Work in Progress and is currently offered as an Early Access Feature. If you are interested in this feature please reach out first to your internal Seeq contact for guidance.
Overview
The Statistics tool provides statistical summaries and comparisons that enable users to assess the statistical properties of a sample set, to determine the baseline operation of their process, and to detect subsequent changes from the baseline operation. The functions are integrated into Workbench.
Opening the Statistics tool
Figure 1
The Statistics tool can be opened from the tools panel, or by using the search term Statistic in the Tools search field, as shown in Figure 1.
The Statistics tool comprises Statistics Summary for creating summaries, and View Statistic Summaries, which presents a list of summaries.
Using the Statistics Tools
Figure 2a
Figure 2b
Statistics Summary Tool
Title and color: The title field allows the user to select a title for the Statistics Summary. Right clicking on the colored square gives the option to select a color to be used in the summary.
Input signal: The signal to be summarized should be selected.
Window of interest: By default, the window of interest is the display range of the workbook. If the display range changes, clicking the Refresh button updates the window of interest.
Limit summary to a condition: Optionally, a condition in the window of interest can be selected. If no condition is selected then all samples within the window of interest will be included.
Histogram bins: The histogram bins to be used are specified by Size of bin (the bin width) or by Number of bins. The default is size of bin, and the recommended size is pre-filled.
Specification limits: The optional Lower specification limit (LSL), Upper specification limit (LSL) and Target fields can be set. The LSL, USL and Target, are needed for the calculation of metrics for process performance such as Ppk.
Open Summary Report View: Clicking this link opens the Summary Report tab in the display panel of the worksheet.
Execute: Clicking the Execute button creates the Statistics Summary.
View Statistics Summaries Tool
List of summaries: The list of summaries shows the summaries associated with the workbook.
Card content: Each summary in the list is displayed in a card showing the window of interest, the signal name, and any limiting condition.
Action item icons: The action items allow a user to edit, duplicate or delete a Statistics Summary. Hovering the mouse on an action icon gives a tool tip.
Search box: The search tool can be used when seeking or filtering statistics summaries that are local to the current workbook and, optionally, in other workbooks.
Operationalize Statistic Summary Tool
The Operationalize Statistics Summary tool converts an existing Statistics Summary into operational time series outputs for continuous monitoring. The tool generates SPC (Statistical Process Control) charts and periodic statistics that can be used to detect process variations and track performance over time.
Key capabilities:
Generate I-Chart (Individuals) and MR-Chart (Moving Range) control charts
Apply Western Electric run rules for automated variation detection
Create periodic statistics calculations (CPK, PPK, and P-values)
Configure output organization with lane management
Customize timestamp placement and interpolation methods for statistics
To open the tool, select Tools > Statistics > Operationalize Statistics Summary from the Tools panel.
For detailed instructions, see Operationalize Statistic Summaries.
Content of a Statistics Summary
Figure 3a shows the output of the Statistics Summary in the Summary Report view. The components within a summary are:
Histogram: The Histogram shows how the sample values values are distributed across intervals.
Box Plot: The Box Plot shows the median and quartiles of the sample values, and potential outliers.
Bell Curve: The Bell Curve shows a Normal distribution with the same mean and standard deviation as the sample set. This gives a visual indication of how similar the distribution is to a Normal distribution.
Table: The Table lies below the Box Plot. It shows the statistics for the sample set grouped into various categories in accordion-style row groups that expand or collapse. It may be necessary to scroll to see all the values (Figure 3b). Mathematical details of the statistics are given in a later section.
Figure 3a Figure 3b
Viewing Options
Summary Report
The Summary Report tab in the Display Pane of the worksheet opens when a user clicks the Open Summary Report view link or the Execute button in the Statistics Summary tool. The summary appears in the Summary Report tab in the display area.
Tabbed viewing
The Trend and Summary Report tabs can be selected to view the Summary Report or to display the signal trends. The tabs can also be opened side-by-side using flexible layouts ("Seeq Your Way") in Workbench to drag the Trend and Summary Report tabs into new docked positions, as shown in Figure 4.
Figure 4
Summary report controls
Figure 5
Action icons
Statistics Summaries can be edited, duplicated, or removed from display using the action icons in the title card (Figure 5). Hovering the mouse over an icon gives a tool tip for each action.
Figure 6a
Figure 6b
Summary Report Toolbar
The toolbar in the Summary Report view allows further customization:
Overlay: The Overlay button presents the histograms in overlaid format for detailed comparison. The box plots are presented one above another for easy comparison.
Histogram: The Histogram button toggles the display of the histogram.
Box Plot: The Box Plot button toggles the display of the box plot.
Table: The Table button toggles the display of the table of statistics.
Bell Curve: The Bell Curve button toggles the display of the bell curve.
Stats: The Stats button opens a menu of the available statistics (Figure 6a), where a selection can be made of which to include in the table.
Labels: The Labels button opens a menu where the histogram and content of the header card can be customized (Figure 6b)
Baseline: The Baseline field is used when comparing summaries.
Histogram tool tips: Hovering the pointer on one of the histogram bins shows the boundaries of the bin, the total count of samples falling in that bin and also the percentage of the samples in the sample set that fall into that bin.
Working with multiple statistics summaries
Views
Figure 7
Figure 8
Side-by-side view
Statistics summaries can be viewed side-by-side, as shown in Figure 7.
Overlay view
Statistics Summaries can alternatively be overlaid to give a qualitative visual comparison (Figure 8).
Quantitative comparisons
Figure 9
Selection of baseline
The baseline for comparison is selected from the Summary Report toolbar.
When a baseline is selected, an extra row called Comparison Tests appears in the table of statistics.
Comparison tests
Equal Mean p-value: The p-value is the probability that the means (the averages) of two probability distributions are the same. A p-value smaller than 0.05 indicates that the means are most likely not the same.
Equal Variance p-value: The p-value is the probability that the variances of two probability distributions are the same. A p-value smaller than 0.05 indicates that the variances are most likely not the same.
Comparable summaries
Matching units of measure: Comparison tests are only available if statistics summaries have the same units of measure.
In Figure 10, when the baseline for comparison is Statistics Summary – RH (%) the compatible statistics summaries are those in the second and third summaries. The results of comparison tests appear in the table. However, in this case the probabilities are small or zero, showing that the means and variances are not the same as in the Baseline Summary.
Non-matching units of measure: The fourth and fifth summaries cannot be compared because the units for Temperature and Wet Bulb are not the same as the units of the Relative Humidity signal.
Overlay view: When the overlay view is selected, the comparable summaries are overlaid pair-wise with the selected baseline summary, as shown in Figure 11.
Figure 10
Figure 11
Statistics Table
Overview
Figure 12
Descriptive statistics
Average: The mean value of the samples in the sample set
Count: The number of samples in the sample set
Maximum and Minimum: The largest and smallest values in the sample set
Standard Deviation: The sample standard deviation (equivalent to STDEV.S in Excel)
Distribution
Normal Distribution p-value: The probability value in a test for Normal distribution. A p-value smaller than 0.05 indicates that probability distribution of the sample set is most likely not Normal.
Quartiles
Quartile 1: Twenty five percent of the samples in the sample set have values smaller than or equal to Quartile 1 (Q1).
Median: Fifty percent of the samples in the sample set have values smaller than or equal to the median.
Quartile 3: Seventy five percent of the samples in the sample set have values smaller than or equal to Quartile 3 (Q3). Fifty percent of the samples have values between Q1 and Q3.
Capability and performance
The process performance metrics show how well an operating process consistently produces output that meets its specification limits.
Mathematical formulations
Figure 13
Figure 14
Performance indexes
Figure 13 shows mathematical expressions for the performance indexes. U and L represent the upper and lower specification limits, μ is the sample mean and σ is the sample standard deviation.
Pp: The overall capability of a process comparing the full six-sigma spread of the data to the range between the upper and lower specification limits.
Ppl and Ppu: The performance relative to the lower and upper specification limits individually.
Ppk: The actual performance when the mean is not perfectly centered.
A low value for any of the four indexes indicates too many samples in the data set are lying beyond one or both of the upper and lower specification limits. Rules of thumb for Ppk are:
Ppk >= 1.33 is acceptable,
Ppk >=1.67 is good,
Ppk >= 2.0 is world-class.
Probability calculations
Normality test: The Normality test uses the Shapiro-Wilk method with Royston approximation. The test is most reliable when the sample set has fewer than 5000 samples.
Comparison test for equal means: The test is the Student t-test. The test is most reliable when the two distributions being compared both have a Normal distribution.
Comparison test for equal valiance: The test is the F-test. The test is most reliable when the two distributions being compared both have a Normal distribution.
Box plot whiskers and outliers
Whiskers: The lower whisker WL on the Box Plot is located at the larger of xmin (the minimum sample value), or at the zero quartile Q0. The upper whisker WU is located at the smaller of xmax (the maximum sample value) or at the fourth quartile Q4. Figure 14 shows the mathematical expressions for these quantities
Outliers: If any sample values lie below Q0 or above Q4 they are displayed on the box plot as outliers.
Tutorial - Creating and Managing Statistics Summaries
A step-by-step tutorial is available here demonstrating the use of statistics summaries for a signal in order to track the behavior of the signal over time. The signal has high sampling rate and is noisy. A derived signal is created giving daily averages of the signal. The statistical analysis is executed on a monthly basis and the results inserted into Organizer.