The JMP® Advantage

Lee Creighton

Bradley Jones

John Sall

Annie Zangi

Executive Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

User Interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

Integrated Graphics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2Interactivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3Problem-centric vs. Tool-centric Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4Data Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4Scripting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Six Sigma® Quality Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

Design of Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6Control Charts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7Attribute Gage Charts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8Gage R&R And Variability Charts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

Statistical Modeling Capabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

Fitting Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10Mean-dispersion Models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12Nonlinear Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13Neural Nets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13Recursive Partitioning (Trees) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

Table of Contents

The JMP® Advantage

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Executive Summary

JMP® provides comprehensive statistics and an interactive environment for designing experiments, analyzing and exploring data, and uncovering trends that might otherwise go unnoticed. JMP can be customized and tailored to fit the varied needs and levels of practitio-ners in your organization, and its graphical interactivity enables everyone to make a contribution to the productivity gains promised by Six Sigma. JMP is ideally suited for those needing a desk-top statistics package that is suited for all users, including every level of Six Sigma practitioners from Master Black Belts on down.

This paper highlights the distinctive aspects of JMP, its user interface, Six Sigma tools and advanced statistical modeling capabilities.

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User Interface

Integrated GraphicsEvery JMP® analysis has a graph as its central element and often has a graph for every sta-tistical test. JMP fluidly scrolls the graphs and reports together as a single document in single window. JMP has innovative graphs for some analyses that help you interpret the analysis, find patterns, find points that don’t fit patterns, and follow up on any pattern, outlier, or analyti-cal insight you have. JMP automatically gives graphs, rather than you having to ask for them.

JMP interactive profilers promote exploring opportunity spaces. In fitting equations to data, the fitting is only half the job. Interpreting the fit, understanding the fitted response surface, and finding factor values to optimize the responses is desirable.

Prediction and optimization are integrated into JMP’s fitting platforms through the use of three platforms: the prediction profiler, which shows response surface slices through each factor; the contour profiler, which shows horizontal response surface slices with respect to two factors at a time, and the surface profiler, which shows a 3-D rendered surface. All of these are completely interactive.

In the case of the Prediction Profiler, not only can you interactively explore the different slices of the response surface, but you can specify the desirability of levels of each factor and have JMP find optimal factor settings.

Most platforms support commands to save predicted values or prediction formulas. You therefore have easy access to the mathematical model.

JMP displays graphs that help users interpret analyses and discover patterns in data..

Prediction, contour, and surface profilers help users interpret the fit and find factor values to optimize the response.

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InteractivityJMP’s analyses are interactive, not static. In JMP, commands are available interactively to extend an analysis or provide more details. As an analysis unfolds, further opportunities appear. You don’t have to think ahead and specify everything you want before you launch the analysis.

JMP encourages active exploration. Because each analysis is interactive, you are naturally encouraged to follow clues to dig deeper into the analysis. You don’t have to relaunch the analy-sis to find available options. If you turn on an option that doesn’t contribute to your understand-ing, you can turn it back off, uncluttering the report.

JMP features dynamic linking. It is common to identify a point in one graph and want to see where that point falls in other graphs. This is easy in JMP—just click on the point.

The rows in JMP data tables are dynamically linked. Click on a histogram bar, and all the rows for that bar become highlighted, leading to highlighting the points in any open graph or analysis. Once highlighted, you can adjust color, marker, and label styles, as well as exclude them from future analyses—all by shifting your finger from the left mouse button used to high-light, to the right mouse button to access a con-textual command.

JMP reports are interactive. You see a report table and want to sort it by the p-value? Easy—just right click to the sort by column command. You want to make that table into a data table? Again, just right click. You want to rearrange the columns of the table? Just drag with the hand cursor. Want to see more (or fewer) decimal places in a report column? Just double click and enter the number you want.

In addition, all graphs can be dragged to any size. Related graphs resize. Drag axes to change them, expand them, contract them. Right click to do many other customizations.

Click on data point, and all the rows for that point become highlighted in any open graph or analysis.

JMP lets you select analyses that are appropriate to the situation.

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Problem-centric vs. Tool-centric DesignJMP’s interface is problem-centric. JMP’s analyses are organized into platforms. Each plat-form is a launch point for the analysis of a statistical situation. The applicable statistical tools are automatically applied and new analysis options are revealed based on the types of variables in the analysis. This allows for a short menu organization that can be mastered quickly. In addition, novice users are not burdened with having to know the appropriate tool for every special case in every statistical problem. By arranging menus as simply a list of tools, other software packages can place this burden squarely on the shoulders of the user.

With JMP, the launching process is often just specifying the variables you want, rather than all of the details of the analysis. In addition, analysis dialogs are non-modal. You are free to work on other windows and check details in deciding what you want before you commit or dismiss a dialog.

Data TableJMP data is richer. JMP’s data tables support a rich set of metadata, including table name-value pairs, scripts that you can store with the data, many types of property data, including coding, value labels, models, and so on. In JMP, you identify a variable as continuous or categorical once, and the setting is remembered and doesn’t need to be respecified in each analysis.

JMP supports active and persistent formulas. JMP has column formulas which stay with the data, and are evaluated as data is changed or added. Using a formula, you can easily fill a col-umn with data.

With JMP, you select the data table and the type of analysis you want, drag and drop variables, specify parameters, and run the analyses.

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ScriptingEarly JMP adopters wanted to use extend their use of JMP in three ways. They wanted to

• Automate common analysis tasks

• Extend JMP’s capabilities by adding their own statistical analyses

• Create animations to demonstrate statistical points.

To answer these requests, JMP now includes a complete scripting language. In fact, JMP can produce scripts itself that mirror actions you perform interactively, allowing you to quickly use JMP to monitor frequently updated processes.

JMP captures your analyses as a script you can replay or edit. In this script to demonstrate how Kernel densities work, a handle allows users to interactively change the bandwidth while the script is running.

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Six Sigma® Quality Tools

Design of ExperimentsThe majority of experiments done in industry today use two-level fractional factorial designs. Using these designs often involves changing the problem to fit the requirements of the design. For instance, many real-world systems have categorical factors with more than two levels. To use a traditional two-level factorial design involves ignoring all but two of the possible settings.

By contrast, JMP’s Custom designer builds a design to match the requirements of the problem. The Custom designer is a general-purpose tool supporting screening, RSM, and mixture experi-ments. By supporting these objectives with a single designer, JMP returns the work to being problem-centered, rather than tool-centered.

The Custom designer is also flexible, allowing

• Any number of factors

• Any number of levels of categorical factors

• Blocking factors with any number of runs per block

• Arbitrary constraints on the settings of factors

• Fixed covariate factors

• Mixture factors

• Any combination of the above factor types

Pre-formulated designs require specific sample sizes. For example, two-level factorial designs have sample sizes that are powers of two. The Custom designer can build designs for any sample size greater than or equal to the number of estimated parameters. This can result in substantial savings of resources and time.

Optimal experiments involving dozens of factors are infeasible for older algorithms that required a candidate set (that grows exponentially with the number of factors). The Custom designer generates either D-optimal or I-optimal designs using the coordinate exchange algorithm. Because the coordinate exchange algorithm does not require a candidate set, the Custom designer can quickly produce designs for these large problems.

There are situations where there are dozens of factors, but resource constraints limit the number of runs to be fewer than the number of factors. The Custom designer can generate supersaturated designs using an extension of Bayesian D-optimality that allows these situations to be analyzed.

Before running the experiment, the JMP prediction variance profiler lets you see the prediction variance relative to the noise variance to determine if the experiment has enough predictive specificity.

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Augmenting existing designs. The Augment designer can add a specified number of runs either D- or I-optimally to any existing experiment. This addition can occur simultaneously with new factor ranges and a more complex model specification. Thus, the Augment designer sup-ports a process of sequential experimentation that speeds the discovery of optimal settings.

Space-filling designs. Many leading-edge companies employ computer models to prototype design ideas, saving the expense of building physical prototypes. These computer models are typically complex and involve many variable parameters. Space-filling designs are useful for building simpler empirical approximations to the computer models. An engineer can then use JMP’s graphical profilers to visualize the results, quickly determine the dominant variable rela-tionships, relative sensitivities, and optimal settings within the parameter ranges.

Control ChartsJMP produces all common control charts. In addi-tion, it can capture data in real time (for an instrument attached to a serial port) and augment a chart instantly. Tests for out-of-control points (Western Electric rules and Westgard Rules) can trigger an email, speak a warning, or execute a script.

Before running an experiment, you can use the prediction variance profiler to help determine if the experiment has enough predictive specificity.

Control charts offer a variety of ways to analyze and monitor process data that has been captured in real time or stored in data tables.

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Attribute Gage ChartsAttribute gage charts in JMP have live graphs. JMP gives summary graphs on both the parts, or any variety of x variables given and a summary graph showing the average agreement on the raters. Because the graphs are live, you can click on points for further exploratory analysis. Below you see the data from the AIAG MSA 3rd edition on Attribute Gage charts. You can easily see the problem parts.

Agreement counts. In addition to Kappa statistics, JMP gives agreement reports with counts showing the number correct with each level of the response for each rater, by name.

JMP Attribute Gage Charts are live llinked for additional exploration of variables.

For some companies, parts arriving off an assembly line which are incorrectly labeled as “Working” by the inspector are more of a problem than those labeled “Not Working”

Effectiveness summary reports show total correct/total possible responses, each summarized by rater to provide an overall summary together with confidence intervals.

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The Misclassification table. The Misclassification table is particularly useful when you have more than two possible responses and you’d like to track the misclassifications.

Gage R&R And Variability ChartsJMP’s variability charts are not limited to only two x variables, but can handle several. For exam-ple, the graph shown here is from data that has variables for Part, Operator and Instrument.

REML available in variability charts. When data is unbalanced, JMP automatically computes variance components using REML.

In the call data, you can see that 8 calls were incorrectly sent to the DR group, when they should have been routed to the DT group.

The platform gives output including graphs and variance components. JMP is only limited by the total number of levels (232-1).

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Statistical Modeling Capabilities

Fitting ModelsJMP uses a general problem-solving approach rather than employing a larger collection of more specific tools. When you have a combination of specific needs, the toolbox approach, used in other statistical software programs, may not have an entry corresponding to your need. For example, some packages claim to support random effects and variance components estimation but that support is for categorical effects and balanced data. Some packages limit you to using a simple method of moments on expected mean squares. JMP, on the other hand, implements random effects in the general case, allowing unbalanced data, continuous regressors, random regressors, and uses the REML method.

In JMP there is one main linear fitting facility that has almost all the features available with any model. The same facility that supports random effects supports cube plots and multiple com-parisons and dozens of other features upon request. Learn this single dialog to launch stepwise, MANOVA, log-variance, nominal logistic, ordinal logistic, parametric survival, and proportional hazards survival models. You do not have to learn different dialogs to launch models with differ-ent features.

JMP fits models using the REML method and implements random effects in the general case to allow for any type of effects, unbalanced data, continuous regressors and random regressors.

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Suppose that you have five hard-to-change factors in a fractional factorial whole plot design, subdivided by two other factors in the split plots. In JMP, you simply specify a high-order interaction of the whole plot factors as a random effect to absorb the whole plot error, and everything else is automatic. JMP treats random effect interactions sparsely, making this a rea-sonable model, matching SAS PROC MIXED.

JMP lets you include fractional factorial whole plots in a split plot analysis.

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Mean-dispersion ModelsSometimes, different factor settings lead to changes in both the mean and variance of the response. JMP supports a way to model this situation. JMP does a series of EM alternations of two linear models, one for the mean response, the other for the log of the variance of the response, and produces maximum likelihood estimates of the models.

Setting Htime = -1 leads to dramatically reduced variability. JMP supports mean dispersion models with its other model diagnostic tools, like the prediction profiler.

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Nonlinear Regression JMP has a platform for nonlinear modeling that allows you to build your model by entering a formula or choosing from a model library. It is a general-purpose facility that is interactive, produces its own analytic derivatives, use loss functions to do maximum likelihood, calculate profile-likelihood confidence limits, and more. In fact, in most platforms that offer likelihood-based estimates, JMP offers profile-likelihood confidence limits, which are much more reliable than the normal-asymptotic limits. In addition to nonlinear regression, you see these limits in logistic regression, ordinal logistic regression, parametric survival models, and survival regression models.

Neural NetsOften, quadratic models are not adequate to capture the curvature in a response surface. JMP offers neural nets, a more flexible tool for modeling curvature. This is especially valuable when there are multiple responses, since neural net models are more parsimonious. JMP pro-vides controls to tune the behavior of the neural net algorithm, allowing you to match the fit to your problem.

As with other modeling platforms, Neural Nets have a complete set of tools to explore and optimize the model.

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Recursive Partitioning (Trees)The key to a Six Sigma® discovery may be to find the important relationships in a set of data. Exploring for relationships is the idea behind a Multi-vari study. Ordinary statistics and graphs can find these relationships if you already know where to look. If you don’t know where to look, and you have a lot of places to look, you need something with more power in finding relation-ships—a data mining tool. Recursive partitioning (trees) is the preeminent tool that can look through hundreds of columns, and for each column hundreds of cut points or classification arrangements, and report on what is most strongly associated with the response. For each split, other relationships become apparent, just suggesting a recursive splitting of the data at many steps until you have characterized which conditions are associated with good and with bad results.

These are the clues that can lead to breakthrough discoveries and changes. JMP has a particu-larly interactive and graphical implementation of recursive partitioning that is easy to use, fast and powerful up to hundreds of columns, and hundreds of thousands of rows.

JMP presents recursive trees in an interactive, graphical report that gives you control over splitting and pruning the tree’s nodes.

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Conclusion

JMP was written from scratch with modern graphical interactivity in mind. JMP has made huge investments in features that matter to engineers and researchers: DOE, modeling, surface exploration, data exploration, statistical discovery. We have kept our product focused, friendly, and engaging for the user.

SAS, JMP, and all other SAS Institute Inc. product or service names are registered trademarks or trademarks of SAS Institute Inc. in the USA and other countries. ® indicates USA registration. Other brand and product names are trademarks of their respective companies. Copyright © 2005, All rights reserved. Six Sigma is a registered trademark of Motorola, Inc. 349306US_0805

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