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Many statistical tests and procedures assume that data follows a normal (bell-shaped) distribution.
For example, all of the following statistical tests, statistics, or methods assume that data is normally distributed:
Most manufacturers would rate product quality as a key driver of their overall ability to satisfy customers and compete in a global market. Poor quality is simply not tolerated. It follows that manufacturers require objective measures of their product quality. While many companies still think of quality as “being in specification,” progressive companies focus on reducing variation to minimize waste and produce products that perform consistently well over time. Quality may be thought of as inversely proportional to variation–that is, as variation increases, product quality decreases. [Read more…]
Most quality professionals are familiar with basic hypothesis tests such as the 2-sample t test. However, depending on the goals of the study, another type of test, called an equivalence test, may be utilized instead of traditional hypothesis tests. This article will review statistical hypothesis testing in general and then introduce equivalence testing and its application. To illustrate the differences between traditional hypothesis tests and equivalence tests, we will focus on the case of comparing 2 independent samples. The concepts may be easily extended to other situations (such a comparing a sample to a target or paired comparisons). [Read more…]
We often think of Statistical Process Control as a tool to help drive product quality by informing us when process changes occur. By systematically detecting (and rectifying) sources of special cause variation upstream in the process, the important process outcomes become predictable. Furthermore, a focus on reducing common cause variation drives higher levels of process capability and more consistent product performance. [Read more…]
In order to maximize profitability while complying with government regulations regarding net package contents, food manufacturers and packagers must achieve an optimal balance. Consistent overfilling to minimize risk is inefficient and sacrifices profitability, while aggressive filling practices result in significant risks of non-compliance with net contents regulations leading to potential penalties, loss of reputation, and impaired customer relations. Statistical process control and process capability methods may be utilized to determine optimal targets for product fill weights or volumes for a given process. Subsequent focused efforts to minimize variation will allow the target to be further optimized, resulting in less waste without compromising risk. [Read more…]
The purpose of control charting is to regularly monitor a process so that significant process changes may be detected. These process changes may be a shift in the process average (Xbar) or a change in the amount of variation in the process. The variation observed when the process is operating normally is called common cause variation. When a process change occurs, then special cause variation occurs. [Read more…]
Effective use of data to drive decision making requires adequate measurement systems. For example, when implementing statistical process control charts, we assume that a signal represents a significant change in the process and we react as such. However, inadequate measurement systems may result in inappropriate signals or even worse, charts that fail to detect important process changes. Thus, it is incumbent upon us to ensure that measurement systems are adequate for their intended use via proper assessments prior to their use. Only capable measurement systems should be utilized in data based methods such as Statistical Process Control, Design of Experiments, Inspection activities, etc. [Read more…]
More companies are leveraging high speed vision systems to inspect multiple quality characteristics on their products.
For example, in a high volume baking operation, a vision system can test for bun height, bun length, slice thickness, topping distribution, surface color, and more. This happens automatically on the line at high speeds. In bottling or other plastic manufacturing, a vision system may inspect multiple dimensions and surface properties. [Read more…]
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…]