The Integral Concepts article series

In the last article, we learned how to determine the coefficients of a predictive model for 2-level screening designs.  It is more complex to determine model coefficients for multi-level experiments so for those, we rely on statistical methods software.

In this article, we look at using the model to develop solutions.  So that we learn the basics, we first use some simple algebra to find a solution.  Then, in the next article, we will explore some common tools that are found in DOE software programs to help uncover solutions. [Read more…]

When processes trend naturally due to tool wear, traditional control charting methods fail.  The trend (which is expected) results in inappropriate “out-of-control” signals.  Control charts should detect unexpected changes in the process.  If the trend is expected, we do not want to be alerted to this trend.  If no accommodation is made for this trend, the chart will incorrectly produce “out-of-control” signals.   [Read more…]

In the last article, we learned how to determine which effects are statistically significant.  This is an important step to develop the predictive model(s) because only the statistically significant factors and interactions belong in the model.  If we include insignificant terms in the model, the predictive ability of the model will appear to be better than it really is and we will overstate the ability of our model to predict the response(s). [Read more…]

Introduction

In previous articles, we discussed the advantages that Xbar charts have over Individuals charts in detecting process shifts.  (See “How Should the Subgroup Size be Selected for an Xbar Chart (Part I)”)  We saw that charts of Individuals are ineffective at quickly detecting small process shifts (and detecting these small process changes may be critical!).

Charts of averages (Xbar) are superior because averaging the subgroup data gives us greater certainty as to where the process is actually running at a point in time.  Selecting an appropriate sample size on an Xbar chart allows us to align the statistical performance of the control chart with the desired practical process changes we’d like to detect.  That is, the sensitivity (ability to detect change) may be adjusted based on the sample size utilized.   [Read more…]

In the last article, we learned how to compute and graphically interpret both main effects and interaction effects.  Eventually, the statistically significant effects will be used to develop a predictive model.  But how do we determine which effects are statistically significant?

Conceptually, we first develop an “error” distribution that represents the distribution of Insignificant Effects.  If we have an idea of what the Insignificant Effects look like, we can determine which of the effects we compute look significant by comparison.   [Read more…]

Statistical Process Control (SPC) charts allow timely detection of assignable causes of process changes (e.g. shifts, trends, variation) so that root causes may be determined and corrective actions taken before product performance is adversely impacted.  Proper use of SPC identifies and eliminates “special cause” sources of variation.  To achieve desired process capability, sources of “common cause” variation may need to be identified as well, using tools such as Design of Experiments to develop process understanding and predictive models that explain the source of the unwanted variability.   [Read more…]

We are ready to learn how to analyze the data collected during the experiment.  This is the most exciting part of DOE!  We will cover the analysis in this article as well as the next several articles.

The following are the main steps to perform during the analysis:

• Calculate the Main Effects and Interaction Effects
• Test the Effects for Statistical Significance
• Interpret the Significant Effects (Often with Plots)
• Develop Predictive Model(s)
• Perform Model Validation (Residual Analysis)
• Find Solutions and Perform Optimization to find Best Solution(s)
• Validate the Solutions
• Determine if Follow-up Experimentation is Necessary

[Read more…]

When applied properly, SPC provides manufacturers a proven method to increase profitability and achieve a deeper understanding of their processes..  Additionally, SPC can prevent problems—saving companies money that would have been lost in scrap, rework, warranty, litigation, and market share decline.  A key factor in obtaining these SPC benefits is the proper deployment of control charts.  Correctly designed control charts identify significant changes to a process.  These can be changes that are still within specification, but are statistically different than where the process was previously running.  By identifying the changes, personnel can determine what caused the change and potentially improve the process or prevent the production of inferior products.   [Read more…]

In this week’s article entry, we discuss some guidelines for conducting an experiment.  As we discussed in an earlier post, planning the study is critical for a successful outcome.  A good plan makes the conduct of the study straightforward.

Below are some key aspects of conducting the study: [Read more…]

In this article post, we discuss several important techniques to consider when conducting and analyzing an experiment.  They are summarized in the table below and next we discuss each one in a bit more detail.  Some of these techniques are bit more advanced (e.g. Blocking, Covariates), but they are introduced here.    [Read more…]

An earlier article focused on the conceptual application of appropriate sample sizes for X-bar charts.  As we discussed, the purpose of control charts is to detect significant process changes when they occur.  When the proper sample size is selected, X-bar charts will detect process shifts (that have practical significance) in a timely manner. [Read more…]

In this article post, we discuss the suggested steps for planning a Designed Experiment.

Step #1 – Clearly Define the Problem and Objectives

It is critical to clearly define the problem before beginning experimentation.  When the problem is not clearly defined and described, there will be confusion in designing and executing effective studies.  To define appropriate responses to measure requires that the problem be understood and agreed on.  Also, it is key to define the objectives of the actual experiment.  If the problem is to reduce scrap rate, how much of a reduction is targeted? [Read more…]

The purpose of control charts is to detect significant process changes when they occur.  In general, charts that display averages of data/measurements (X-bar charts) are more useful than charts of individual data points or measurements.  Charts of individuals are not nearly as sensitive as charts of averages at detecting process changes quickly.  X-bar charts are far superior at detecting process shifts in a timely manner, and the sample size is a crucial element in ensuring that appropriate chart signals are produced. [Read more…]

While the construction of control charts is relatively straight-forward, often a more difficult question is “how do I know what process characteristic to control in the first place?”  Clearly, controlling “everything” is not feasible or a smart use of limited resources.   [Read more…]

In this article post, we formally define or describe the basic terminology that is commonly used in Design of Experiments.  Some of the terms we have already been using in prior posts, but they will also be presented here for completeness.  This is Part I of a two part article covering DOE Terminology.  [Read more…]