In Part I of this article, we introduced the concept of utilizing Deviation from Nominal (DNOM) control charts for short production runs.  These charts allow us to monitor process characteristics over time even when the units being controlled have varying nominal values.  DNOM charts assume that the process variability (i.e. standard deviation) does not vary significantly by part type.  However, often this assumption does not hold.  Characteristics with larger nominal values tend to have more variation than characteristics with smaller nominal values.  In Part II we discuss how to test whether or not significant differences in variability exist and if so, how to modify the DNOM methods and charts to handle this situation. [Read more…]

In the last Article, we explored the use of contour plots and other tools (such as a response optimizer) to help us quickly find solutions to our models.  In this article, we will look at the uncertainty in these predictions.  We will also discuss model validation to ensure that technical assumptions that are inherent in the modeling process is satisfied. [Read more…]

In the last Article, we learned how to work with predictive models to find solutions that solve for desired responses.  We used some basic algebra to solve for solutions and looked at the use of contour plots to quickly visualize many solutions at a glance.

In this article, we further explore the use of contour plots and other tools to help us quickly find solutions to our models.  We start by revisiting the battery life DOE example that was discussed in the previous article.  The statistical output below shows the coded model that contains only the statistically significant (main and interaction) effects. [Read more…]

Traditional SPC methods were developed to support high volume production and long production runs.  However, with the trend toward product specialization, product diversity, and flexible manufacturing, short production runs have become more common.  Applying SPC in the traditional manner presents challenges in short production runs, because by the time enough data is collected to establish valid control charts, the production run may be over! [Read more…]

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…]