# The Variety of Statistical Tools to Support Your Decision Making

My wife and I moved to a new home last year. We have yet to organize our tools.

The bedroom and kitchen are now organized. We, for the most part, can find the sweater or pan that we’re seeking.

No so for our tools in the shop. We have an assortment of hand tools for painting, home maintenance, yard work, and woodworking. In our previous home, we had the tools on pegboards, on shelves, in cabinets. We could find the right tool for the job at hand quickly. We’ve avoided the tool aisle at the hardware store recently, as we were sure we had the tool we need in the jumbled mess in our garage already. Still haven’t found it, though.

Have you noticed the number of statistical tools available? It’s like visiting a well-stocked tool store. There are basic tools like trend charting and advanced tools like proportional hazard models. Let’s explore the available tools a little so you can quickly find the right tool for the question or problem you are facing today.

## The Questions Statistical Tools Help Resolve

In business and as engineers, we ask questions. We ask questions out of curiosity as we explore the next marvelous invention. We ask questions to guide our decisions. We ask questions to seek insights and guidance.

The statistics toolbox has the tools to help answer questions. Questions of all sorts. Here are a few that you may have already encountered:

- What should we work on next?
- Are we making progress toward a goal?
- What does this dataset tell us?
- What tolerance should we specify?
- Are the items within specification?
- Is the vendor’s assembly process stable? Is it capable?
- Have the changes actually made an improvement?
- How long will this product last once placed into use?
- Is there a relationship between our line speed and production yield?
- Can we make that assumption?

For each of these questions did a specific tool come to mind? Having a range of options, different tools, allows you to not only solve a wider range of problems, it also allows you to use the specific tool that best supports your work.I’ve met a few folks that believe duct tape and WD-40 are the only tools one really needs for

I’ve met a few folks that believe duct tape and WD-40 are the only tools one really needs for car or home maintenance. Just as there are a few reliability engineers that believe the formula to calculate MTBF is the only necessary tool for reliability work.

Just as not every trip to my (pile of) tools is to find a hammer, every time I work with a new dataset I don’t only use a Weibull analysis. The tool I use is in large part dependent on the task or question.

Just as not every trip to my (pile of) tools is to find a hammer, every time I work with a new dataset I don’t only use a Weibull analysis. The tool I use is in large part dependent on the task or question.

## Exploratory Tools

When there are more unknowns than knows, when you examine the nature of a data set, or when you are simply looking for patterns, you are exploring. Exploratory data analysis (EDA) is a set of tools to

- Provide insight into a data set
- Reveal patterns or structure
- Identify the critical variables
- Spot elements not like the others (outliers or anomalies)
- Summarize the data with a model

A few of the common and not so common EDA tools include:

- Histogram
- Autocorrelation Plot
- Box Plot
- Probability Plot
- Scatter Plot
- Lag Plot
- Grubb’s Test for Outliers
- Measures of Skewness and Kurtosis
- Confidence Limits
- ANOVA

Read more about EDA and the approach for exploring your data with these references:

- Exploratory Data Analysis
- Visualizing Data
- Applications, Basics, and Computing of Exploratory Data Analysis

## Measurement Tools

Beyond which specific gauge you use to gather information about the physical world, you also want to make sure the measurements minimize errors.

The ability to trust your readings or measurements is an essential step is creating meaningful decisions. Measurement tools do not only include calibration, it includes:

- Calibration
- Uncertainty analysis
- Control or short and long term stability
- Gauge Repeatability and Reproducibility

Here are a few references that may be useful.

- Churchill Eisenhart (1962). Realistic Evaluation of the Precision and Accuracy of Instrument Calibration SystemsJ Research National Bureau of Standards-C. Engineering and Instrumentation, Vol. 67C, No.2, p. 161-187.
- ASTM Method E691-92, Standard Practice for Conducting an Interlaboratory Study to Determine the Precision of a Test Method. Annual Book of ASTM Standards, 10.05, West Conshohocken, PA 19428.
- ISO/IEC Guide 98-3:2008, Uncertainty of measurement – Part 3: Guide to the expression of uncertainty in measurement (GUM:1995)
- Measurement Systems Analysis (MSA)

## Characterize Your Process

If you have a process to create more than one of an item, you need to ensure the process variability does not contribute unwanted (unnecessary) product variability. The common tool we think of is control charts. Keep in mind there are dozens of types of control charts each best suited for specific situations. The goal is not to have a control chart, it is to understand process capability.

Here are few references to help you understand, monitor, and control your processes.

- Statistical Quality Control Handbook: Second Edition
- Quality Control (8th Edition)
- Statistics for Experimenters: An Introduction to Design, Data Analysis, and Model Building
- Visualizing Data

## Modeling for Understanding

Regression analysis is a technic to fit a line, curve, or surface (a formula) to a set of data. It provides a means to describe the data, to summarize. It also permits us to use the data and resulting model for predictions, calibration, or optimization work.

Modeling is a mathematical endeavor and a few of the tools are:

- Least Squares
- Rank Regression
- Maximum Likelihood Estimators
- Goodness-of-fit measures
- Graphical methods
- Residual analysis
- Data Transformations

Here are few references describing modeling tools:

- Transformation and Weighting in Regression (Chapman & Hall/CRC Monographs on Statistics & Applied Probability)
- Design and Analysis of Experiments
- Applied Linear Regression Models- 4th Edition with Student CD (McGraw Hill/Irwin Series: Operations and Decision Sciences)

## Improvement of Your Process

In design or process development this is often many potential opportunities for improvement. Which change make the biggest impact of performance? At times this can be a difficult question to resolve.Designs and processes also have many influencing factors that collectively produce an output. Which of these factors should you control and which really do not matter much?

Designs and processes also have many influencing factors that collectively produce an output. Which of these factors should you control and which really do not matter much?The ability to employ the full array of

The ability to employ the full array of design of experiments tools allows you to bring the full power of statistical analysis to your experimentation and design work.

The assortment of tools include:

- Taguchi Analysis
- Randomized designs
- Full and fractional factorial design
- Response surface designs

A few references to get started are:

- Statistics for Experimenters: An Introduction to Design, Data Analysis, and Model Building
- Empirical Model-Building and Response Surfaces (Wiley Series in Probability and Statistics)
- Reliability Improvement with Design of Experiment, Second Edition, (Quality and Reliability)

## Monitor Your Process

A bit of an overlap with the section on characterization, as control charts are in both sections. Both graphical and mathematical approaches apply as you gather data and try to make sense of it over time.

The basic groups of tools include

- Control charts
- Acceptance or Lot Sampling
- Time series models

Of course, there are many tools within each of those groups. A few references that describe the tools in detail include:

- Time Series Analysis: Forecasting and Control (Wiley Series in Probability and Statistics)
- Statistical Quality Control
- Acceptance Sampling in Quality Control, Second Edition (Statistics: Textbooks and Monographs)

## Making Comparisons

Ever have to make a decision between two vendors based on some data? The hypothesis test is likely the right tool. Comparing means, variances and other parameters allows us to find the best, most improved, or stable option for our decision making.

The tools here include graphical and analytical approaches, and a mix of both approaches should be your regular practice. Tools include:

- Box plots
- Dot plots
- Parametric and Non-parametric tests
- Confidence intervals
- Hypothesis tests
- ANOVA
- MANOVA

A few references that you should add to your library.

- Statistical Intervals: A Guide for Practitioners and Researchers (Wiley Series in Probability and Statistics)
- Nonparametric Statistical Methods
- An Introduction to Statistical Methods and Data Analysis

## Reliability Analysis Tools

The ability to understand the durability of your product includes the use of a range of tools. Given today’s short product development times we often use acceleration techniques to ‘cheat’ time. The tools concerning reliability analysis include:

- Physics of failure modeling
- Accelerated life testing and analysis
- Degradation life testing and analysis
- Reliability growth modeling
- Prognostic health management

These tools include measurements, careful experimental design, and regression tools.

A few references you may find useful include:

- Statistical Methods for Reliability Data
- Accelerated Testing: Statistical Models, Test Plans, and Data Analysis (Wiley Series in Probability and Statistics)
- Applied Reliability, Third Edition

## In Summary

There is a lot to know and a lot tools to help us improve our understanding and decision making. With all these references available, you may need a nice way to organize your bookshelves and files.

Certainly, do not want the jumbled mess that is my shop at the moment.What are your favorite tools and why? Add you comments and recommendations below.

What are your favorite tools and why? Add you comments and recommendations below.

Note: many of the links are affiliate links to the books mentioned.