Monthly Archives: January 2013

2013 Data Mining Survey


Rexer Analytics, a data mining consulting firm, is conducting its every-two-year survey of analytics professionals—analysts, modelers, and scientists—covering data mining techniques, tools, behaviors, views, preferences, and challenges. You are invited to participate in this year’s survey.

STATISTICA has consistently ranked very high in the Rexer surveys, and we appreciate the support from our users that has brought us this recognition. If you would like to see a summary of StatSoft’s position in last year’s survey, visit our StatSoft Reviews page.
To participate, visit the Rexer Survey page and click the ‘Start Survey’ link found there. The survey should take approximately 15 minutes to complete.






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How To Create Random Subset of Your Data

A customer asked recently how to create a random subset. And I thought this would be a good topic for a blog.

Let us pretend…

We want to develop a credit scoring model that can be used to determine if a new applicant is a good credit risk or a bad credit risk. But I want to use a random subset of data.

Start by opening STATISTICA’s example dataset, CreditScore.sta. It has 1000 rows of data.

You don’t know where the example datasets are located? Select the Open Example menu under the File menu (or Home tab / Open). See the Datasets folder? Select it and browse for CreditScore.sta.

Select the Data menu or Data tab. If you are using the classic menus, then look for Random Sampling menu.If you are using the Ribbonbar, then look for Sampling on the far right.

On the Simple Sampling tab, select the Exact checkbox. Type 25 in to the Approximate % field. Click OK.

You now have a random subset with 250 rows of data.

How To Create Random Subset of Your Data

A customer asked recently how to create a random subset. And I thought this would be a good topic for a blog.

Let us pretend…

We want to develop a credit scoring model that can be used to determine if a new applicant is a good credit risk or a bad credit risk. But I want to use a random subset of data.

Start by opening STATISTICA’s example dataset, CreditScore.sta. It has 1000 rows of data.

You don’t know where the example datasets are located? Select the Open Example menu under the File menu (or Home tab / Open). See the Datasets folder? Select it and browse for CreditScore.sta.

Select the Data menu or Data tab. If you are using the classic menus, then look for Random Sampling menu.If you are using the Ribbonbar, then look for Sampling on the far right.

On the Simple Sampling tab, select the Exact checkbox. Type 25 in to the Approximate % field. Click OK.

You now have a random subset with 250 rows of data.

Lottery Statistics

Written by: Jennifer Thompson

I read an article about some proposed legislation in North Carolina which would restrict some residents from being able to purchase lottery tickets. These restricted residents include those involved in bankruptcy proceedings and those receiving public assistance. I am going to stay far away from the discussion of whether this proposed law is a good idea and sound legislation or a gross overreach of government power. Feel free to carry out that discussion without me. But I will take the opportunity to talk about the statistics of the lottery.

Let’s talk Powerball. They are nice enough to publish the probabilities of the prizes available to their customers. Let’s use the annuity payout number for the jackpot since it is higher and forget about the taxes. It’s only nearly half your winnings for the larger prizes. So for the Powerball drawing on Saturday, January 26, the jackpot is $130 million. What is your expected return on a $2 lottery ticket?

Powerball table

The above chart gives the odds and prize amount for each of the possible ways to win regular Powerball as well as Powerplay. (Powerplay costs an additional dollar and increases all prizes except the jackpot.) The prize amount and odds of winning are taken from the Powerball website. The two columns of returns are calculated by taking the prize value and subtracting off the cost of the ticket. This is $2 for a regular ticket and $3 for a Powerplay ticket. Then divide that difference by the odds of winning that prize. When we sum the expected return columns, we get the overall expected return for a lottery ticket purchase. The expected value of a regular Powerball ticket for the Saturday drawing with a $130,000,000 jackpot is $1.04 (for a $2 ticket purchase and a loss of $0.96) and for Powerplay, the expected return is $1.51 (on a $3 purchase, a loss of $1.49). (Note that the return column is rounded to the cent. The sum is performed on the raw data before rounding.)

Expected returns are generalized over the whole population of lottery customers. Any statistician knows that rare events do happen. A 1 in 175,223,510 chance means that with enough players, someone is getting lucky. The census claims the US population is 315,218,311. So if everyone in the US plays 1 ticket, 1.8 people should win jackpots. Wait, you have to be 18 to play. So it’s a little less than that. But thinking of it that way actually makes it seem more likely to me that someone would actually win.

An interesting side note, the folks at Powerball actually advocate buying 35 tickets, each with a different Powerball number so you are guaranteed a win of at least $4 on your $70 purchase. Doesn’t sound like smart money to me, even with this method of beating the system. (See their FAQ section. There is no anchor on the page to link to the exact spot, sorry.)

Innovation Knows No Boundaries

We live in an exciting time in the world of data because data can be collected from innumerable sources and can be used in innumerable ways to improve our daily lives.

As an analytics software development company, StatSoft is all about innovative data analysis. Data and analysis are central to our business. We analyze data for our own benefit, such as customer behavior on our website and marketing initiatives. We also enable our customers to analyze data with our products, as we provide the means for them to harness the power of the data that they collect.
So, for instance, this helps a power plant generate more electricity while producing fewer pollutants. This helps a hospital reduce re-admittance rates, which lowers costs and at the same time improves quality of care. This helps a bank extend credit to maximize its profits. This helps an insurance company determine what rates it should offer for an insurance policy to be competitively priced while maintaining a profitable offering.
Data analysis helps pharmaceutical companies develop and manufacture safe and effective drugs. It helps high tech manufacturing companies produce high-quality products at the lowest cost. Data analysis can be used to increase productivity, reduce scrap, predict who your best customers are, and help a company know which market segments to target and how to grow and develop its business.
The biggest challenge that data analysts face is how to communicate to others what the data tells us. What does that data tell us to do? There is so much data, how do you know what results should be “paid attention to,” and which results really matter?
That is where data analysis tools like STATISTICA come into play. With graphics and dashboards that help us to visualize results, we can instantly grasp what we should do as a result of the analysis that has been performed.
As we celebrate Data Innovation Day, we must never forget that it is not the data itself that matters, but it is the innovation that matters. And having tools that make it possible for us to communicate the results from that innovation makes everyone a winner.
[Image credit: Username ilco, image id#1042388 at stock.xchng®]

STATISTICA – Variance Estimation and Precision (VEPAC)

Variance Estimation and Precision (VEPAC) software provides a comprehensive set of
techniques for analyzing data from experiments that include both fixed and random effects.
With VEPAC, you can obtain estimates of variance components and use them to make
precision statements while at the same time comparing fixed effects in the presence of
multiple sources of variation. In the VEPAC module, an alternative to ANOVA estimation is
provided by restricted maximum likelihood estimation (REML). The REML method is based on
quadratic forms and requires iteration to find a solution for the variance components.

VEPAC is an augmentation of the award-winning and widely adopted STATISTICA software
suite, enhancing the set of comprehensive STATISTICA products currently available for
analysis of variance, including General Linear Models, Generalized Linear/Nonlinear Models,
Design of Experiments (DOE), and Variance Components.

VEPAC is currently used by companies in Pharmaceutical, Chemical, Petrochemical, Consumer
Products, Semiconductor, and other industries for specific applications of analysis of variance,

˜ valuating method transfer between two labs of manufacturing facilities

˜ Evaluating the differences between treatment groups in a study that includes both fixed
and random effects

˜ Evaluating the factors that contribute to product variability in manufacturing

˜ Evaluating the contributions of variation attributed to instruments, operators, raw
materials, and other factors

Integrated in the VEPAC product, is a new graph type: the Variability Plot. The Variability Plot
is a display of data where the underlying organization of the data collection is represented by a
series of hierarchical or nested rectangles enclosing the data. This type of graph is useful to
evaluate the variability of one factor within several other organizing factors…

The VEPAC design specification dialog enables users to specify effects in the model and save
the design. Users have several options for displaying means as seen above, while the
variability plot helps to visualize the data.

STATISTICA – User Interface

I’m a visual person. Does STATISTICA have a Ribbon like Office 2007 does?

Yes. Application navigation is simpler and more intuitive with the addition of an Office 2007-style ribbon bar. Frequently used functionality is quickly visible, and related functionality is easily found.

user interface ribbon bar

Note that the classic menus/toolbars will continue to be available, and you can switch between the two interfaces at any time.

  • To display the classic menus/toolbars, click Menus on the Quick Access toolbar in the upper-left corner of the ribbon bar.
  • To display the STATISTICA ribbon bar, select Ribbon Bar from the View menu.

How do I access help for a specific dialog?

Quick access to the STATISTICA Electronic Manual (Help) is provided via the question mark button at the right side of the caption bar of most dialog boxes.

user interface help

Click the question mark button or press F1 to display a Help window containing the description of that dialog. Note that when you highlight a menu command, you can press F1 to display its Help window.

Help doesn’t work after I installed Windows Server 2003 SP1 and security updates 896358 and 840315. What can I do?

This Microsoft Windows security update (MS05-026) was intended to reduce security vulnerabilities in HTML Help. However, it interferes with the Help system for network versions of many applications (including the regular network and concurrent network installations of STATISTICA).

Fortunately, Microsoft has also issued instructions on how to correct the problem:

  • Simple solution: Most users can download the file HTMLHelp.reg, just click here to start downloading. This will fix the problem by modifying your Windows registry to allow your PC to access the local intranet.
  • More complex solution: Users with sophisticated security issues should read Microsoft’s article that describes this problem in detail and provides solutions for different situations:

What are microscrolls?

Numerical values in dialogs can be changed by using the microscrolls controls on text boxes. Click the microscrolls to either increment or decrement the last digit. Right-click them to either increment or decrement the next-to-last digit (e.g., clicking the up microscroll increments .15 to .16, then .17, .18, etc., right-clicking the up microscroll increments 0.15 to 0.25, then .35, .45, etc.).

The following example illustrates how the microscrolls can be controlled with the left and right mouse buttons.

user interface microscroll

What are ToolTips?

ToolTips are small “balloon help tips” that are displayed when the mouse pointer is on a toolbar button. ToolTips help you quickly learn the functions of toolbar buttons.

user interface tooltips

You can control the display of the ToolTips for graph objects by toggling the ToolTips on Graph Objects command on the View menu. You can toggle the display of all other types of ToolTips on the Options tab of the Customize dialog (available by selecting Customize from the Tools menu).

Can I automate commonly used procedures or repeat similar tasks in STATISTICA?

Automation facilities in STATISTICA are available via STATISTICA Visual Basic. When you run an analytic procedure (from the Statistics or Data Mining menus) or create a graph (from the Graphs menu), the Visual Basic code corresponding to all design specifications as well as output options that you select are recorded. To display that code, select Create Macro from the Options button drop-down list (available on any analysis or graph dialog), or click the Create Macro toolbar button, or select the particular analysis or graph from the Tools – Macro – Create Analysis/Graph Macro submenu. The code can later be executed repeatedly or edited by changing options, variables, or data files and optionally adding user interfaces, etc.

Programs can also be written using the STATISTICA Visual Basic professional development environment featuring a convenient program editor with a powerful debugger (with breakpoints, etc.), an intuitive dialog painter, and many facilities that aid in efficient code building. To display the SVB editor, select New from the File menu to display the Create New Document dialog, and select the Macro tab.

user interface svb visual basic

Note that Master Macros (logs of multiple analyses) and Keyboard Macros (context sensitive recordings of sequences of keystrokes) are also available.

Also, many procedures and graphs allow you to automatically repeat the same analysis for each of a series of variables (e.g., Design of Experiments uses multiple dependent variables) or each level of a grouping variable (e.g., categorized graphs).

How can I break, stop, or interrupt the current action?

The following facilities are available to stop, break, or interrupt the current action (depending on the operation being performed by STATISTICA):

  • Analysis. Click the Cancel button on the Progress bar to interrupt the task in progress.
  • Brushing (in a graph). Deactivate the brushing tool by clicking the Selection Tool  toolbar button.
  • Printing. Interrupt the printing of spreadsheets, graphs, reports, etc., by clicking the Cancel button in the Print dialog.
  • STATISTICA Visual Basic. You can interrupt SVB programs in several ways. Click the Pause  toolbar button to pause the currently running macro, or click the Reset  toolbar button to stop running (i.e., reset) the current macro. You can also press the ESC key or CTRL+BREAK in order to interrupt the execution of the STATISTICA Visual Basic program.

How can I learn what information is necessary to start an analysis (variables, grouping, codes, options, etc.)?

Click the Help  button or press the F1 key to display the relevant section of the STATISTICA Electronic Manual containing a comprehensive explanation of all options in the current dialog. However, all analysis definition screens in STATISTICA follow the “self-prompting” dialog conventions: The OK button is never dimmed; whenever you are not sure what to select next, simply click OK and STATISTICA proceeds to the next logical step and prompts you for specific input if it is necessary.

How can I find a particular statistical procedure?

If you are not certain where to find a particular procedure within STATISTICA, consult the Statistical Advisor by selecting Statistical Advisor from the Help menu. The Statistical Advisor lists a set of questions about the nature of the research problem and the type of your data. Click the link for the most appropriate answer, and the next topic will be displayed, which will either list more questions or list suggestions of the statistical procedures that appear most relevant and where they are located in the STATISTICA application.

user interface advisor

You can also search for topics in the STATISTICA Electronic Manual (Help) using the Index or Search facilities. Help is always available by pressing the F1 key.

How can I copy/print result summaries?

Located at the top of some results dialogs is a summary box. This box contains relevant summary information for the type of analysis (e.g., descriptive statistics, design attributes, regression results, etc.). Additionally, two buttons are provided with the summary box: a copy button that is used to copy the summary results to the Clipboard and an expand/collapse button that is used to expand (show) or collapse (don’t show) the summary box.

You can copy a portion of the summary results to the Clipboard by selecting the desired text and clicking the copy button. To copy all of the text, click the copy button without selecting any text. You can then paste the text into a STATISTICA Spreadsheet, Report, Graph, or any word processing document (e.g., Microsoft Notepad or Word) for printing.

user interface analysis results<br />
summary” src=”<a href=; />

Note that the copied text retains formatting information (such as font, color, etc.).


How do I select items from multiple-selection lists?

Select items in a multiple-selection list in the following manner:

1. Click on an item to select (highlight) it. Click the OK button in the dialog to accept the selection.

2. Double-click on an item to select it and accept the selection (i.e., close the dialog).

3. In order to select a continuous list of items, (1) hold down the mouse button and drag the cursor over the items that you want to select or (2) select the first item and then while holding down the SHIFT key, click on the last item that you want to select.

In order to select a discontinuous list of items, hold down the CTRL key and click on the desired items.

How do I select items in the workbook tree?

You can select one or more items in the workbook tree using the standard Windows SHIFT+click and CTRL+click conventions to select ranges and discontinuous lists of variables, respectively. Additionally, you can select or deselect tree items using the keyboard navigation keys (e.g., HOME, END, PAGE UP, PAGE DOWN, and arrow keys). You can delete an entire selection by pressing the DELETE key. Pressing the INSERT key will display the Insert Workbook Item dialog for the currently selected item.

Note that only visible items can be selected; therefore, to select the contents of a particular node, you will need to expand the node (by clicking on the plus sign adjacent to the node).

How is the mouse used in other operations?

Besides the standard Windows SHIFT+click and CTRL+click conventions, you can perform the following actions using the mouse:

  • Drag-and-drop. Provides mouse shortcuts for moving, copying, deleting, inserting, and/or extrapolating a block of values in the spreadsheet.

user interface mouse drag

  • Increase/decrease column width. Adjusts the spreadsheet column width by dragging the right column border to the desired width. The variable header automatically expands, and the new width of the column is indicated by a dashed line.

user interface increase decrease<br />
 mouse column width” src=”<a href=; />

  • Split scrolling (in spreadsheets). Splits the spreadsheet (i.e., split scrolling) by dragging the split box (the small rectangle at the top of the vertical scrollbar or to the left of the horizontal scrollbar).

user interface mouse split<br />
scroll” src=”<a href=; />

  • Variable speed scrolling. Controls the speed at which you scroll (1 line at a time by moving the cursor a short distance away or one page at a time by moving the cursor further away) when you extend a block outside the spreadsheet.
  • Microscrolls. Enable you to increase or decrease the value in a numeric edit field incrementally, by either the last digit (click the up microscroll, e.g., 1.11, 1.12, 1.13, …), or the last digit by a factor of 10 (right-click the up microscroll).

user interface microscrolls

  • Toolbar configuration. Double-click on the space between the buttons of the toolbar to undock the toolbar, allowing you to place it wherever you want. To return the toolbar to a docked setting, double-click in the title bar of the floating toolbar.
  • Reordering items in a list. You can reorder items in a list by selecting one or more items (in a continuous or discontinuous list) and then moving the cursor, which changes to a Vertical Resize, to the desired position.

user interface reorder list

Clicking the mouse will then move the highlighted item(s) to the insertion point.

Reduce Journal Research from Weeks to Hours…

Researchers find it difficult to keep up with the ever-increasing number of journal articles in their fields of research. For instance, a PubMed search for “Breast Cancer Genetics” returns over 45,000 hits alone. Refining search strings only goes so far to reduce this number, so experts still must sift through many abstracts—a cumbersome and laborious process—perhaps only eventually to find that very few are relevant.

Can a recommender service be created to identify relevant articles and, if so, could such a service be automated? The answer to this question is yes, with tools such as STATISTICA Data Miner and Text Miner.

Furthermore, since XML is becoming a standard means of storing and sharing information, this presentation may have additional cross-appeal, as importing XML with a STATISTICA Visual Basic (SVB) macro is discussed.

Join us Tuesday, Feb. 19, as Toby Barrus, Sr. Quality Engineer at Myriad Genetics, presents a case study for a PubMed recommender service using STATISTICA Data Miner and Text Miner. He based this successful implementation on an example from the textbook, “Practical Text Mining,” by Dr. Gary Miner, et al. Toby will cover the following topics:

* Brief overview of PubMed search results and the “Send to” feature to export data in XML format
* Import XML data into STATISTICA using a SVB macro
* Text Miner to convert free-form text into usable format for data mining
* Data Miner to create and compare predictive models
* Rapid Deployment of best model to new search results

FREE registration at

Advanced Quality Control in a Manufacturing Company

One of our consultants at StatSoft CR, Miloš Uldrich, recently penned an article for IT Systems magazine, a Czech publication.

In his article, Uldrich provides a broad overview of business intelligence as it relates to quality processes:

“The term business intelligence (BI) can be interpreted in at least two different ways,” he writes. “In one sense, it is a platform for advanced analysis and reporting; in another, it is a comprehensive business system that consolidates accounting, management and other systems.”

Uldrich focuses his attention on the common understanding of BI as a system that can analyze corporate data and transmit results in a useful form to relevant personnel.

As he explains it: “The question today is not why we have such systems. Every production company stores, measures, and evaluates data in some fashion. What differs are their methods for processing data. Some businesses store their measurements in databases, and others store their production data in Excel spreadsheets, which are rewritten from paper sheets. BI solutions are intended to improve business processes.”

In his article, Uldrich provides specific examples to illustrate the practical, cost-saving benefits of analytics in the pursuit of quality initiatives.

“One interesting, concrete example is the application of neural networks, which generally includes advanced data mining, in industrial environments…Based on dozens of input parameters (e.g., temperature, flow rate, composition, etc.), the neural network system evaluates product composition…If evaluation yields negative findings, the company has the option to respond immediately with action to remedy the technological process. As a result, it is possible to reduce the cost and frequency of sample collection while significantly contributing to the stabilization of production quality.”

Uldrich also addresses:

  • data storage and conversion from disparate repositories
  • parameters to consider when selecting a BI solution
  • the popularity of Six Sigma

Read the complete, original Czech article here.

SOURCE: SystemOnLine. Pokročilá kontrola kvality ve výrobním podniku. Miloš Uldrich. July-August issue, 2012. Excerpts and image retrieved and translated November 29, 2012, from

STATISTICA Advanced with Industrial Modules

Advanced with Industrial Modules

STATISTICA Advanced Modules:-


STATISTICA Base features all the graphics tools in STATISTICA and the following modules:

  • Descriptive Statistics, Breakdowns, and Exploratory Data Analysis
  • Correlations
  • Basic Statistics from Results Spreadsheets (Tables)
  • Interactive Probability Calculator
  • T-Tests (and other tests of group differences)
  • Frequency Tables, Crosstabulation Tables, Stub-and-Banner Tables, Multiple Response Analysis
  • Multiple Regression Methods
  • Nonparametric Statistics

§ Distribution Fitting

Multivariate Exploratory Techniques

STATISTICA Multivariate Exploratory Techniques offers a broad selection of exploratory techniques, from cluster analysis to advanced classification trees methods, with an endless array of interactive visualization tools for exploring relationships and patterns; built-in complete Visual Basic scripting.

  • Cluster Analysis Techniques
  • Factor Analysis
  • Principal Components & Classification Analysis
  • Canonical Correlation Analysis
  • Reliability/Item Analysis
  • Classification Trees
  • Correspondence Analysis
  • Multidimensional Scaling
  • Discriminant Analysis

§ General Discriminant Analysis Models (GDA)

Advanced Linear/Non-Linear Models

STATISTICA Advanced Linear/Non-Linear Modelsoffers a wide array of the most advanced linear and nonlinear modeling tools on the market, supports continuous and categorical predictors, interactions, hierarchical models; automatic model selection facilities; also, variance components, time series, and many other methods; all analyses with extensive, interactive graphical support and built-in complete Visual Basic scripting

It features the following modules:

§ Variance Components and Mixed Model ANOVA/ANCOVA

  • Survival/Failure Time Analysis
  • General Nonlinear Estimation (and Quick Logit/Probit Regression)
  • Log-Linear Analysis of Frequency Tables
  • Time Series Analysis/Forecasting
  • Structural Equation Modeling/Path Analysis (SEPATH)
  • General Linear Models (GLM)
  • General Regression Models (GRM)

§ Generalized Linear Models (GLZ)

Power Analysis and Interval Estimation

Using STATISTICA Power Analysis and Interval Estimation in planning and analyzing your research, you can always be confident that you are using your resources most efficiently. Nothing is more disappointing than realizing that your research findings lack precision because your sample size was too small. On the other hand, using a sample size that is too large could be a significant waste of time and resources.

STATISTICA Power Analysis and Interval Estimation will help you find the ideal sample size and enrich your research with a variety of tools for estimating confidence intervals.

Read more about STATISTICA Power Analysis and Interval Estimation:

§ Advantages

  • Power Calculation
  • Sample Size Calculation
  • Interval Estimation
  • Probability Distributions
  • List of Tests

§ Example Application

Quality Control Charts

STATISTICA Quality Control Charts features a wide selection of quality control analysis techniques with presentation-quality charts of unmatched versatility and comprehensiveness. It is uniquely ideal for both automated shop-floor quality control systems of all types and levels of complexity (see also STATISTICA Enterprise-wide Systems, as well as sophisticated analytic and quality improvement research. A selection of automation options and user-interface shortcuts simplify routine work and practically all of the numerous graph layout options and specifications can be permanently modified (saved as system default settings or as reusable templates). Finally, STATISTICA Quality Control Charts includes powerful and easy to use facilities to custom design entirely new analytic procedures and add them permanently to the application, and those options are particularly useful when quality control analyses need to be integrated into existing data collection/monitoring systems.

It features the following features:

§ Standard quality control charts

  • Multivariate charts
  • Interactive, analytic brushing and labeling of points
  • Assigning causes and actions
  • Flexible, customizable alarm notification system
  • Supervisor and operator mode; password protection
  • Organization of data
  • Short run charts
  • Chart options and statistics
  • Non-normal control limits and process capability and performance indices
  • Other plots and Spreadsheets

§ Real-time QC systems; external data sources

Design of Experiments

STATISTICA Design of Experiments offers one of the most comprehensive selection of procedures to design and analyze the experimental designs used in industrial (quality) research.

Technical notes:

§ General features

  • Residual analyses and transformations

§ Optimization of single or multiple response variables

Types of designs:

§ Standard two-level 2**(k-p) fractional factorial designs with blocks

  • Minimum aberration and maximum unconfounding 2**(k-p) fractional factorial designs with blocks
  • Screening (Plackett-Burman) designs
  • Mixed-level factorial designs
  • Three-level 3**(k-p) fractional factorial designs with blocks and Box-Behnken designs
  • Central composite (response surface) designs
  • Latin squares
  • Taguchi robust design experiments
  • Designs for mixtures and triangular graphs
  • Designs for constrained surfaces and mixtures
  • D- and A-optimal designs
  • D-optimal split plot design

§ D-optimal split plot analysis

Alternative procedures:

§ Designs can also be analyzed via alternative modules such as General Linear Models, General Regression Models, or Generalized Linear/Nonlinear Models.

Process Analysis

STATISTICA Process Analysis is a comprehensive implementation of Process Capability analysis, Gage Repeatability and Reproducibility analysis, Weibull analysis, sampling plans, and variance components for random


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