Design of Experiments (DoE) in Automotive Industry Focusing on Design Augmentation

This document gives an overview of the workflow when doing a designed experiment with Cornerstone. The focus is a situation where a considerable number of runs already have been made and they have to be included in a final design that gives a wide enough picture.

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Workflow in Design of Experiments (DoE) using an example from the paints and coatings industry

This document gives an overview of the workflow when doing a designed experiment with Cornerstone. DoE features of Cornerstone creating designs and for analyzing data from DoEs using regression analysis are shown. As an example, a spray application process from the coatings industries is used.

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Wafermap: Wafermap-Designs Based on Zernike Polynomials

In Semiconductor industries, homogeneity of the results of many process steps across the wafer is an essential goal and tightly correlated with the final yield. It is important to make a judgement of homogeneity based on a sample of points that is efficient: Typical deviation from “flatness” have to be detected with an affordable (i. e. small) number of test points on the wafer. Easy to interpret deviations from flatness can be described by Zernike polynomials which are state of the art in describing optical deficiencies in the human eye or in adaptive optics.

This report describes Zernike Polynomials and shows how the measuring points are optimally placed on the wafer surface using the statistical software Cornerstone.

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Use Case Example: Balancing experimental designs having several block factors

How to get experiments that respect given lot sizes and other balancing requirement in more that than one process step?

Cornerstone experimental designs allow beside scaled and categorical factors also one block factor for which the number of runs per block is specified in advance by the user as a number bigger equal than 2. For most situations this functionality is totally sufficient. In case there is more than one factor for which the runs per level have to be balanced perfectly, a pathway to fulfill this requirement is given here.

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Big Data Access and Analysis with Cornerstone

What are common mistakes and which strategies work in analyzing Big Data in manufacturing?

As described in a previous research report: "Cornerstone Big Data Analysis through Apache Spark", the systematic analysis of ever-expanding data collections presents companies with ever-greater challenges. However, some of the know-how is simply missing in order to be able to carry out big data projects successfully. Therefore one simply follows the current trends and buzz words and adopts approaches which are currently en vogue. This approach often leads to less successful projects and several regularly reoccurring patterns of misconceptions can be identified.
This research report highlights some of these unsuccessful patterns and introduces some of the work done in the PRO-OPT SMART-DATA research project. The project experimented with various approaches for the modeling of production data of an automotive supplier. One objective was to be able to apply and compare statistically grounded analysis and classification procedures as well as new procedures from the AI eco-system. Different tool stacks were used. This report focuses on Cornerstone’s direct access to Big Data databases.

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Improved regression models by transforming factors and responses

How can you achieve a better fit of the polynomial approximation in Cornerstone regression models?

Cornerstone Regression covers polynomial models allowing for Box-Cox transformation with
an optional offset. In this work situations are handled where also the factors have to be casted
to a different scale to reach an appropriate model.

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The Multi-Category-Chart A Novel Tool for Exploratory Analysis of Categorical Data

How to find correlations in high amounts of categorical variables visually?

Logistical data from industrial production processes spanning across many process steps or intermediate products contain a wealth of categorical variables. Each step or intermediate product adds his own data about used tools, consumables, materials, suppliers and operators to the process history of a complex product.

If downstream test data show a relevant discrete structure such as stratification into multiple groups, the task of root cause analysis is to find the few – ideally just one - categorical upstream variables that explain this structure best. In the simplest case this can be phrased as the question: “What do the bad units have in common that the good units do not have?”

This research report introduces a novel visualization called Multi-Category-Chart. It explains the motivation, compares it with other common visualizations and describes the benefits of the new approach.

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Success story: How Cornerstone contributes to leading edge yield

How Cornerstone contributes to leading edge yield

At a leading edge semiconductor Integrated Device Manufacturer (IDM) the department of product engineering widely uses the Cornerstone statistical software from camLine. Cornerstone provides statistical techniques, including DoE, regression, and multivariate analysis. Implementing an internal tool based on the Cornerstone Extension Language (CEL), the manufacturer analyzes yield, performs yield learning and characterizes products.

In this success story we describe the major features helping the customer to work fast, consistent, efficient and to the highest quality standards.

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Non Linear

Use case example: Non linear constraints in Cornerstone Design of Experiments

How can non-linear constraints be used in Cornerstone experimental designs?

The constraint editor of Cornerstone Experimental Design only allows for linear constraints: the involved factors may get a pre factor (coefficient) and the resulting weighted sum can be constrained by a certain limit. General constraints involving nonlinear functions like log(), exp(), sin(), tan() and even simpler ones like the product of 2 factors are not supported by the editor.

This usage example builds a workmap with an example that shows the path to construct the design obeying general constraints and that also respects them for optimization and prediction.

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Research Report: Cornerstone Big Data Analysis through Apache Spark

How can different data buckets be integrated and flexibly analyzed using Big Data techniques?

The systematic analysis of ever-increasing data collection presents companies with ever-greater challenges. Many companies simply lack the know-how to handle big data projects. Following to the motto “Let’s do a Data Lake first”, they bring together all available data in one system. Because often they are subject to the misconception that you should put as much data as possible in the system in order to gain the maximum insight and the most flexible evaluations. Unfortunately this does not work, because we can expect performance problems here.

This research report summarizes a part of the work performed in the PRO-OPT SMART-DATA research project. In the project a wide variety of production data modeling approaches of an automotive supplier were tested out. One of the objectives was to be able to apply and compare statistically reliable analyses and classification procedures as well as new procedures from the upcoming AI instruments. The work is summarizes in this report.

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Variant Minimizing

Whitepaper: Variant minimizing Designs

How can the amount of experiment runs be reduced via minimizing the variants?

The cost for the runs of a design is dominated by a subset of factors. In this whitepaper an example with  7 factors is considered with 4 factors which account for most of the costs / efforts. Typical situations are factors which need to be made by prototype manufacturing whereas the other factors are different settings the hardware variants are used in.

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Whitepaper: Configurations for D-optimal Designs

How to determine the optimal settings for D-Optimal Designs in Cornerstone?

Designed experiments in Cornerstone are often based on D-optimal designs which are flexible enough to handle special situations. The criteria for the design, namely the determinant of the information matrix after rescaling the factors to standard range fits well to the embedding theory and its reciprocal is often called generalized variance. In addition, a maximized determinant minimizes the coefficient confidence intervals. The construction of D-optimal designs relies on a iterative algorithm which uses a list of settings and conditions from the planned experiment under consideration.

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Use Case example: Optimizing Factors in Experimental Design

How to use Cornerstone’s DoE module and regression to perform an optimization on a factor

In many designed experiments, factors with a known high influence on the response(s) are varied. As an example, the factor throughput of a combine harvester is used. The response considered are the loss of grain material or its quality. Other factors are adjustments to the machine and / or technical variants which usually have only a smaller effect on the response compared to the dominating factor throughput. In Cornerstone, regression models can be used to define targets for response variables that are to be achieved by varying the factors. In the example considered here, however, the factor throughput is to be maximized for a defined level of the response variable. Levers for this goal are the remaining factors.

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Product retrospective: Cornerstone Statistics for Engineers

A brief history and a summary of the most beneficial functionalities

Cornerstone is a proprietary software of the independent software vendor camLine GmbH. The software has a long tradition reaching back to the year 1991. It primarily is designed for engineers in research and development or in manufacturing who need a tool for applied statistics. Cornerstone has a special focus on the fields of Analyses by Regression, Exploratory Data Analysis (EDA), quality control (control charts, process capability), and Design of Experiments (DoE).

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