# Statistics Article

By: Ryan E. Day

Current business conversation often focuses on data and big data. Data are the raw information from which statistics are created and provide an interpretation and summary of data. Statistics make it possible to analyze real-world business problems and measure key performance indicators that enable us to set quantifiable goals. Control charts and capability analysis are key tools in these endeavors.

### Control charts

Developed in the 1920s by Walter A. Shewhart, control charts are used to monitor industrial or business processes over time. Control charts are invaluable for determining if a process is in a state of control. But what does that mean?

By: William A. Levinson

Anthony Chirico1 describes how narrow-limit gauging (NLG, aka compressed limit plans) can reduce enormously the required sample size, and therefore the inspection cost, of a traditional attribute sampling plan. The procedure consists of moving acceptance limits t standard deviations inside the engineering specifications, which increases the acceptable quality level (AQL) and therefore reduces the sample size necessary to detect an increase in the nonconforming fraction.

By: Teofilo Cortizo

Within maintenance management, the term MTBF (mean time between failures) is the most important key performance indicator after physical availability.

Unlike MTTF (mean time to failure), which relates directly to available equipment time, MTBF also adds up the time spent inside a repair. That is, it starts its count from a certain failure and only stops when the fault is remedied, and the equipment restarted and performing again. According to ISO 12489, this indicator can only be used for repairable equipment, and MTTF is the equivalent of nonrepairable equipment.

The graphic below illustrates these occurrences:

 Figure 1: Mean time between failures

To calculate the MTBF in figure 1, we add the times T1 and T2 and divide by two. That is, the average of all times between one failure and another, as well as its return, is calculated. It is, therefore, a simple mathematical calculation. But what does MTBF mean?

By: Scott A. Hindle

‘Process Capability: What It Is and How It Helps,” parts one, two, three, and four, discussed Alan’s development in the field of process capability1 He’d learned about the mistakes that can be made and how to avoid them in practice to become better at his job. Alan had since passed on his learning to colleagues, one of whom, Owen, had led some successful assessments of process capability.

By: Tom Siegfried, Knowable Magazine

If Fyodor Dostoyevsky had been a mathematician, he might have written a book called Crime and Statistics. However, since “statistics” doesn’t have quite the same ring as “punishment,” it wouldn’t have sold as well.

But such a book would make a better guide for formulating crime-fighting policy. Analyzing criminal behavior scientifically, using proper statistical methods, could enhance the ability of criminologists to better understand crime and what to do about it.

“The field needs broader and deeper scientific examination,” writes statistician-criminologist Greg Ridgeway in an upcoming Annual Review of Statistics and Its Application.

By: David Currie

This is part three of a three-part series. Read about good metrics in part one and bad metrics in part two.

Have you ever had occasion to dread a metric reviewed month after month, where the metric defies logic, and any action taken does not seem to reflect in the metric? It is most likely a bad metric in so many respects that it has turned ugly. Let’s look at a sample ugly metric.

By: Quality Digest

Annalise Suzuki, director of technology and engagement at software provider Elysium Inc., spoke to Quality Digest about the importance of model-based definitions (MBD) for data quality, validation, and engineering change management. With the increase of digital 3D models in the manufacturing workflow, companies are appreciating their value for speeding product development, improving quality and performance, and allowing for greater automation. Here, Suzuki answers seven questions about the model-based enterprise (MDE)’s current and future role in industry.

By: Anthony Chirico

Everybody wants to design and conduct a great experiment! To find enlightenment by the discovery of the big red X and perhaps a few smaller pink x’s along the way. Thoughtful selection of the best experiment factors, the right levels, the most efficient design, the best plan for randomization, and creative ways to quantify the response variable consume our thoughts and imagination. The list of considerations and trade-offs is quite impressive. Then, finally, after optimizing all these considerations, and successfully running the experiment, and then performing the analysis... there is the question of “statistical significance.” Can we claim victory and success?

The answer lies in-part on the critical value provided by a table of critical values—or by a computer program. If our calculated test statistic exceeds the critical value, we will reject the null hypothesis and claim there is a difference among the treatment averages. If our calculated test statistic does not exceed the critical value, we will fail to reject the null hypothesis. This is the moment of truth at the end of all our hard work. This is a moment of anticipation and excitement.

By: Scott A. Hindle

Walter Shewhart, father of statistical process control and creator of the control chart, put a premium on the time order sequence of data. Since many statistics and graphs are unaffected by this, you might wonder what the fuss is about. Read on to see why.

Figure 1 shows a series of measurements over 11 months. Each measurement value is from one production batch, with the date of each production given. The date is formatted as day first, and month second, meaning that “06.01”—the first measurement of 69.4—is from January 6.

 Figure 1: Measurement data in time order of production.

By: Minitab LLC

Machine learning as a tool in your analytical toolkit can help accelerate the discovery of insights in data that can create a more efficient manufacturing process and drive innovation.

### Machine learning in the spotlight

The growth in availability of technologies that give us the ability to monitor, collect, exchange, analyze, and deliver information will only continue to expand. With this network of growing devices creating a loop between the physical and digital worlds, we now have access to high volumes of data about manufacturing operations like never before. Leveraging these data to drive actionable insights will be the key to prioritizing improvements and driving innovation for overall competitiveness.