Cornerstone (statistics software)

In computer application software, Cornerstone is statistics software of the independent software vendor camLine GmbH. The software has a long tradition reaching back to the year 1991. Since then, the owners of the software have changed several times. Since 2010, it is owned and maintained by camLine. It is proprietary software.

Cornerstone is designed mainly for engineers in research and development or manufacturing who need a tool for applied statistics. It has a special focus on the fields of regression analysis, exploratory data analysis (EDA), quality control (control charts, process capability), and design of experiments (DoE).

Analyses are presented and recorded graphically in the form of a calculation graph (termed Workmaps). The structures can be saved in conjunction with the data, and thus are reusable with similar data to perform the same analyses with refreshed or new data in the same structure. The software interactively combines all created objects in a logical execution sequence (live linking). That allows connecting the results actively and affecting selections in all corresponding visualizations, and changes in data get propagated to all dependent analyses and graphics.

Cornerstone is available in 32-bit and 64-bit versions. The later can handle very large data sets above the 4 GB limit, which is a typical restriction of the older 32-bit architecture. Otherwise, the functions are identical. Until Cornerstone 7.0, the 64-bit version was named Cornerstone++. With version 7.0, the ++ extension is deprecated, and the 64-bit version is the default and named simply Cornerstone. Starting with that release, both versions are shipped and the user can decide which version to install.

History

Cornerstone version 1.0 was developed by BBN Software Products (since 1995, BBN Domain Corporation or rather Domain Manufacturing Corporation) as a follower to RS/1 since 1991. In 1999 Brooks Automation took over Domain Manufacturing including the Cornerstone software. The software business unit (including Cornerstone) of Brooks Automation was transferred to Applied Materials in 2007. camLine acquired the Cornerstone software in 2010 and continues the development since then.

The original main feature in Cornerstone was exploratory data analysis (EDA). This is a means to analyze data with visual methods to identify the main traits. It is used for seeing what the data can tell beyond formal modeling. Afterward, Cornerstone was expanded with more key features. Design of experiments (DoE) is used to explore a small subset of experiments within all possibilities that provide initially defined questions. Linear regression models are used as analysis and mathematical optimization modeling method.

Cornerstone was available initially for Unix based systems (SunOS, HP-UX) only. Since its version 1.5, introduced in March 1995, Microsoft Windows is supported too. camLine extended the DoE support and the analysis of large data sets above the 4 GB limit. Due to low demand, maintenance of Unix based systems ended in 2009, with version 5.0. The table below shows the version history, with supported platforms, publication date, and main innovations.

Versions

Application and availability

Cornerstone is applied in an industrial environment to analyze manufacturing and process data. The software is leveraged in research and development (R&D) to design experiments and analyze the results. This results currently in a focus on semiconductor and automotive production. Other users are in other industrial areas with similar analysis tasks like photovoltaics, chemistry, paper, paint, optics, pharmaceutics, electronics and white goods. Cornerstone is used in industry-oriented academic sectors.

Recently, the ability of Cornerstone to analyze data efficiently is used ever more directly in manufacturing environments. Most use cases involve condensing the high amount of production data in cyclic analysis. The results are reported automatically on the intranet, for example. In this application, a workmap is seen as an analysis template. Application engineers can develop these templates on the basis of well established workmaps. Thus, it is possible to choose an individual and intuitive analysis depth. Improvements can be implemented and tested separately from the subject process to ensure reliable continued optimizing.

Cornerstone is distributed directly by the software maker.

Scope of operation

Cornerstone is a statistical software which provides the essential analysis functions for engineering and natural sciences, in a few modules. For example, the analysis of variance and group comparisons are summarized in the regression module. This lean approach supports engineers in doing appropriate statistical analysis.

Design of experiments

Design of experiments (DoE) is used by engineers or applied scientist in physical or simulated experiments to reduce the number of runs. Each experiment is defined by a number of factors, for example, the oven temperature or the heating time. One run is defined by specific values of each factor. Hence, a huge number of runs occurs which increase exponentially with the number of factors. The main question in DoE is to figure out a reliable small subset of runs to answer initially defined questions. These questions vary from the significance of a factor to predictions of unobserved areas in the experiment. Cornerstone focuses on D-optimal designs to select the subset of runs. They can be adjusted flexibly to practical requirements like constraints in the design space, integrating extant experiments, and model approaches in any order. The analysis of DoEs use regression methods for both categorical and continuous factors (incl. compositions). Cornerstone supports a standard evaluation procedure for regression analysis.

Further, this list outlines supported types of experimental designs in Cornerstone:

1. Full factorial
2. Fractional factorial
3. Plackett–Burman
4. Box–Behnken
5. Centrel-Composit
6. D-optimal
7. L9, L18, L28, L36 as 3-level
8. Spacefilling
9. Optional user-defined

2-field Taguchi methods (designs) are available for a robust parameter design. They can be replaced by D-optimal designs with a corresponding interaction structure. Mixture designs involve the slack variable approach via D-optimal designs with constraint design space.

Exploratory data analysis

Exploratory data analysis (EDA) is a means to analyze data with visual methods to identify the main traits. It is used for seeing what the data can tell beyond formal modeling. Fahrmeir describes EDA as a method that goes further than descriptive statistics. It does not use stochastic or other methods based on probability theory, but some of their methods are influenced by inductive statistics. Beyond the description and presentation of data, EDA is designed to identify structures and special traits in the data, which often can lead to new questions or hypothesis in the corresponding application. Fahrmeir states that it is typically applied if the problem is unspecified in detail, or the choice of a suitable model is unclear yet.

Cornerstone includes graphical methods of EDA along with contemporary, continuous implemented interactive features like brushing and linking. These interactive methods operate meaningfully across all linked objects. For example, highlighting a date in a histogram (brush) causes the residuum belonging dataset from a regression to also be highlighted in corresponding graphics. The datasets are connected comprehensively and are highlighted in all related objects, they are linked to. Its purpose is to reveal multivariate relations in small and especially in huge and complex datasets. For that matter, Cornerstone uses an exploratory rather than a confirmatory approach. Many parameters (resp. variables) can be analyzed by matrix graphics and the ability to create many different graphic types in parallel. Statistical values and the corresponding confidence interval are listed or displayed wherever reasonable. All results are available as tables or graphics. It is possible to export them in standard file types or via clipboard to arbitrary programs.

Regression

A regression analyses the relationship between dependent variables (response) and independent variables (factors, predictors). The linear regression in Cornerstone is the main tool of statistical analysis and uses quantitative and qualitative predictors. An evaluation of qualitative predictors is often done by an analysis of variance instead of a regression. The term linear relates to the power of the regression coefficients, not the predictors. The order of a regression model is described as the highest power of a predictor. Cornerstone can fit models of arbitrary order.

The focus is on a compact and fast analysis of many responses, versus many predictors (multiple multivariate regression), even if models of higher order are used. Missing values of a response influence only the corresponding regression.

A regression analysis provides statistical values of the linear models in tables. Graphical methods (Q–Q plot, interaction plot, different plots of residuals) are available in the regression module.

Selection of the power for a power transform (Box–Cox transformation) of a response is done on the basis of a Box-Cox plot. The result of each regression analysis is a prediction with confidence intervals for each predictor with respect to each response. It is charted in an interactive prediction graph on the original (untransformed) scale for an optimal use of the statistical model.

Multivariate statistics

General linear models (regression), principal component analysis (PCA), and multivariate analysis of variance (MANOVA) are supported. The key aspect is on regression methods which summarize analysis of variance methods. It is described in section regression and can analyze many responses versus many predictors efficiently. A MANOVA provides the ability to determine whether two or more groups are different based on their relationship with multiple continuous responses. The well-known iris dataset by Anderson wants to evaluate the difference between three iris flower species related to their sepal and petal length and width. The MANOVA, which use a PCA, reveal the rules to classify a new flower with respect to its measurements. Furthermore, a PCA can be leveraged, for example, to reduce the number of variables in a correlated dataset with the ability to control information loss.

Quality methods

The software can perform process capability and control chart analyses for well established distribution types. A process capability analysis describes a process matching to predefined specification limits. The match is measured by different process capability indexes (Cp indexes) and illustrated by a histogram with an overlay of the used distribution. Control charts are used to analyze manufacturing data off-line. It has the goals to identify unexpected statistical dispersion (variability) and optimize the corresponding process afterward. Using two different rule sets, control charts provide a tool to determine unforeseen variation or changes in a process from the variability inherited by the process. Occasionally, sample size determination is used in this range which is dedicated to the DoE module.

Included extension language

Cornerstone Extension Language (CEL) is used to develop supplements and automate analysis work-flows. For example, preparing a loaded dataset and its following analysis can be automated. Hence, CEL provides the ability to develop added work-flows inside Cornerstone which are tailored to user needs.

The internal class library is exposed and accessible via an adapted C++ development environment. It contains classes for nearly every object (e.g., dataset, regression, xyscatterplot) and its methods. The DoE module is inaccessible via CEL. Functions in CEL can be triggered by notify events, like the startup, a reread of a dataset, or when dragging a reference line. This ability is used when acting with Cornerstone externally.

See also

• Comparison of statistical packages
• Data mining
• Data processing
• Online analytical processing (OLAP)
• SQL

Literature

• Box, George E. P., and Draper, Norman R.: Empirical Model Building and Response Surfaces. Wiley 1987, New York, NY,
• John A. Cornell: A Primer on Experiments with Mixtures. Wiley 2011,
• Norman Draper & Harry Smith: Applied Regression Analysis, 3rd Edition. Wiley 1998,
• John Fox: Applied Regression Analysis and Generalized Linear Models. Sage Publications 2008,
• Peter Goos, Bradley Jones: Optimal Design of Experiments: A Case Study Approach. Wiley 2011,
• Hinkelmann, K., and Kempthorne, O: Design and Analysis of Experiments. Volume 2, „Advanced Experimental Design". Wiley 2005,
• Wilhelm Kleppmann: Versuchsplanung. Produkte und Prozesse optimieren. 7. aktualisierte und erweiterte Auflage, „Praxisreihe Qualitätswissen", Hanser München u. a. 2011,

External links

• , Applied Materials, Inc.

• , Brooks Automation, Inc.

• , Raytheon BBN Technologies