Multiple Authors
By: Michelle Paret, Eston Martz

Story update 8/27/2009: An error was spotted and corrected by author in paragraph starting with "The population mean for a six-sided die..."

Mark Twain famously quipped that there were three ways to avoid telling the truth: lies, damned lies, and statistics. The joke works because statistics frequently seem like a black box—it can be difficult to understand how statistical theorems make it possible to draw conclusions from data that, on their face, defy easy analysis.

But because data analysis plays a critical role in everything from jet engine reliability to determining the shows we see on television, it’s important to acquire at least a basic understanding of statistics. One of the most important concepts to understand is the central limit theorem.

In this article, we will explain the central limit theorem and show how to demonstrate it using common examples, including the roll of a die and the birthdays of Major League Baseball players.

Defining the central limit theorem

A typical textbook definition of the central limit theorem goes something like this:

As the sample size increases, the sampling distribution of the mean, X-bar, can be approximated by a normal distribution with mean µ and standard deviation σ/√n where:

Miriam Boudreaux’s picture

By: Miriam Boudreaux

Even after many years of hearing the words ISO 9000 and seeing many organizations achieve registration to ISO 9001, there are still companies who are skeptical when it comes to going for ISO 9001 registration. For some, a misconception about the objectives of the ISO 9001 standard or a lack of knowledge may steer them off this path. For others, it may be financing this goal plus the long-term costs associated with maintaining compliance. Whatever your fears may be, allow me to explain the fundamental benefits and try to demonstrate the reason why ISO 9001 is the best management tool that was ever created.

ISO 9001 as a foundation

When we look at how houses are built all over the world, you will find various construction techniques. Whatever the architectural preference may be, there is one thing that most houses built to code have and that is a foundation. The better the foundation, the better the house will stand the test of time, regardless of how many families pass through its doors.

International Electrotechnical Commission IEC’s picture

By: International Electrotechnical Commission IEC

To come to the brow of a hill and see on the horizon a line of giant wind turbines, their arms turning majestically, never fails to take one’s breath away. These are awesome structures, imposing in their size, their grandeur—and their simplicity.

World wind power capacity

Wind turbines are becoming ever more familiar as environmental concerns drive forward the agenda for renewable energy policies. In terms of world wind power capacity, 2009 figures quoted by the World Wind Energy Association (WWEA) show that China is currently the fourth-largest wind power producer after the United States, Germany, and Spain.

In terms of world wind power capacity, 2009 figures show that China is currently the fourth-largest wind power producer after the United States, Germany, and Spain as quoted by the World Wind Energy Association (WWEA).

Brenda Bence’s picture

By: Brenda Bence

All you have to do is look around you to know that brands are powerful. In fact, most people are so loyal to certain brands that they stick with them for life. If brand-name products can evoke that kind of loyalty, why can't people? Well, they can!

The truth is that we all have a personal brand whether we like it or not. Simply by being ourselves in the workplace, others perceive, think, and feel about us in a certain way. The question is whether we have created the personal brand we want.

This is especially important for those who hold leadership positions. If you lead others, the way they perceive, think, and feel about you as a leader, in relation to other leaders, can make or break your short-term and long-term success. These "others" might consist of your subordinates, colleagues, superiors, or even entire divisions or corporations.

Your leadership personal brand affects your image, your reputation, your relationships, and your performance. As a result, it will also affect your overall career and your finances. So, unless you create your desired leadership personal brand consciously, negative perceptions can undermine your best efforts.

Belinda Jones’s picture

By: Belinda Jones

Robert James had what it takes to start a manufacturing company focused on oil-free air and gas compressors—history, expertise, and the willingness to take a second chance on a business he knows well. Nearly 40 years ago, his father William James, began producing oil-free air compressors under the trade name Aeroflow Industries. Aeroflow compressors quickly gained a reputation for longevity and dependability, and soon oil-free gas compressors were introduced to their product line. The company was sold by the James family in 1990 and the name changed to Hycomp.

In 1997, Robert James purchased Hycomp back. As a young boy, he worked on the shop floor of the family business and had a “feel” for the business. James began to reassess the marketplace, and moved to expand the business to include the production of air boosters. The company teamed up with key manufacturers of onsite nitrogen generation systems, and began a hard push to develop and add nitrogen boosters to their product line. Today, Hycomp has a global clientele, and serves a wide range of industries such as pharmaceuticals, oil and natural gas production, laser cutting, and food and beverage

Miriam Boudreaux’s picture

By: Miriam Boudreaux

Story update 8/21/2009: We corrected an error regarding the function of the accreditation body.

 

I’ve worked with several companies over the years and dealt with different individuals, different processes, and different levels of ISO 9001 understanding. However, when an organization is getting ready to apply for ISO 9001 certification, the question most often asked is: “Are we going to pass the audit?" Similar questions I've been asked are:

"How many of your clients have passed the audit?"

"How many of your clients failed the audit?"

And after I have conducted an internal audit, the usual question is, of course, “Did we pass?”

Those seem to be very simple questions and a yes or no should suffice, however the truth of the matter is that ISO 9001 audits don't have a grade, there is no pass or fail status or there is no pass or fail grade. 

Please visit our blog on the ISO Audit Results and Nonconformities for a detail explanation on what constitute an audit finding, or nonconformity.

David C. Crosby’s picture

By: David C. Crosby

If you are not actively selling quality, you’re missing the boat. Quality (both goodness and conformance), should be sold inside and outside of your company. A song from an old Broadway musical says, “How are you going to conquer the world if nobody knows you’re there?” Good question.

Selling quality outside

I have two definitions of quality and it’s important to understand the difference.

If you’re making a product or providing a service, the first definition is “free of defects” or “conformance to the requirement.” That means the product is exactly what you promised your customer. There are several highfalutin’ definitions of quality, but they are all nonsense. Don’t bother with them.

The second definition of quality is “Goodness.” It’s how good your product is in the marketplace. Lincoln is “gooder” than Mercury. Mercury is “gooder” than Ford, a Rolls Royce is “gooder” than all of them. How do I know Rolls is “gooder?” Rolls told me so.

IBS America’s picture

By: IBS America

Madico, the world’s preeminent manufacturer of metalized, coated, and laminated films, has been producing high quality manufactured film systems since 1903. Located in Woburn, Massachusetts, the hi-tech ISO 9001-certified firm has more than 170 employees.

A quality and compliance management system was hardly a priority for Madico in its first 96 years of existence. Company documentation had been handled in much the same way as it  had in the past—in paper systems stored in a selection of binders distributed to multiple departments at its various locations. With hundreds of different products, each with its own specification, the inherent problem with this particular system was ensuring that all employees were using the most current revision of each specification, a situation that was not always the case.

Currently, with three distribution sites, sales offices in California, Florida, and Arizona, as well as their main manufacturing and corporate offices in Massachusetts, there was a need for everyone to have access to the most up-to-date documentation. As the system was setup, that was almost impossible, as paper documentation was stored in 34 locations within the Woburn plant in up to five three-inch binders at each location.

Stewart Anderson’s picture

By: Stewart Anderson

Today, more than ever, the quest for productivity, quality, and speed has spawned a significant number of techniques and tools: lean manufacturing or service, business process improvement; Six Sigma, total quality management, and so forth. Although the operational improvements resulting from these practices have often been dramatic and impressive, many companies remain frustrated by their inability to translate those gains into superior profitability and growth.

“Determine value from the perspective of the customer,” is the oft-heard mantra from adherents of lean, Six Sigma, and other quality improvement programs. Yet, how often do we really do this? Many times, when we start drawing our value stream or process maps, after we place that customer box in the top right corner of the map, we then go right to the process flow, begin mapping the system, and then start applying tools to it. But, the system serves the customer—indeed it must include the customer—and is the reason why the system exists in the first place.

Geoff Bilau’s picture

By: Geoff Bilau

Mario Angeles was stuck. His family-operated machine shop, Angeles Precision Engineering LLC, was busy enough with work farmed out to it by larger shops, but Angeles had been repeatedly rebuffed in his attempts to secure a long-term contract on his own; especially one from the “Big Four” aerospace firms.

“We used to meet people from the four big ones—Boeing, Northrop Grumman, Lockheed Martin, and Raytheon—and ask them what we could do to earn their business,” Angeles says. “The first question they would ask is ‘Are you ISO 9001 certified?’ ” When Angeles told them he was not, he understood the uphill battle he was fighting.

“They would say, ‘If I have 100 shops I give work to and they’re all certified, why should I take work from them to give you?” he says. “ ‘What assurance can you give me that you’ll deliver higher quality work than the others?’ ” Angeles quickly discovered his word alone wasn’t worth much to the “Big Four.”

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