In Electronics Manufacturing, Does Cpk =1 Yield 66,800 DPM?

As Patty was walking past the Professor’s office on her way to see Pete and Rob, she decided to drop in.

“Professor, I got the strangest phone call. A man claimed he had invented a machine that could create energy,” Patty began.

“Tell me about it,” the Professor chuckled.

“Well, he correctly noted that, when he took his kids to the beach, a submerged beach ball pushed up with a lot of force. So, he developed a technique to extract the energy produced when the ball is released,” Patty explained.

“Let me guess,” the Professor offered. “He then developed a technique to continuously extract energy; an energy producer of sorts.”

“Exactly! How did you know?” Patty responded.

“Well, I have been here about 40 years, and I have had forty such calls,” the Professor said.

“Tell me the details of your call,” he continued.

“There would be a box of small mass with a generator and pump inside; the generator and pump occupying little of the volume of the box. The box would be filled with water at the top of a lake and would then would sink to the bottom. Once the box was at the bottom, the water would be pumped out and the buoyancy would cause the box to rise. A rope would guide the box on its up and down journey and the generator would spin as it travels up the rope, hence generating electricity. The cycle would be repeated over and over and, in a sense, become a power plant,” Patty explained.

“And the problems are?” the Professor asked.

“I told him that it violates the laws of thermodynamics, and that I could make some calculations that would show that it would not work. Basically, the amount of energy required to pump the water out is greater than what the buoyancy would generate, considering friction, etc.,” Patty replied.

“His response?” the Professor led.

“My sense is that he thought he could make it work, in spite of the physics,” Patty answered.

“In my experience, that is always the response. Probably my most troubling experience was a chap who convinced a small venture capital firm to advance him about $3 million. He had a machine that, he claimed, continuously extracted energy out of the earth’s magnetic field. The biggest shock to me was that the leader of the venture capital firm was a graduate engineer who had retired as COO of a Fortune 50 company. I still haven’t figured out how such an accomplished person could not see that an energy-producing machine is not possible,” the Professor expounded.

“What was the upshot of all of this?” Patty asked.

“Well, they didn’t pay my consulting fee when I explained how it couldn’t work,” he chuckled. I checked a few months ago and the company’s website is down,” the Professor replied.

“The people that are into this folly don’t even realize that, if an energy-creating machine could be made, it would be the greatest discovery in history,” the Professor went on.

After a few more minutes of this discussion, Patty resumed her short walk to Pete’s office. Rob was already there.

“Looks like Mike Madigan needs us again. Did you see the email he sent us?” Pete asked.

“No, what’s up?” Patty and Rob said in unison.

“Something about Cpk,” Pete answered.

Patty reached for the phone to set up a conference call to Mike.

As she dialed, Patty admonished, “Now remember you two, good manners. No laughing at any of Mike’s questions.”

“Yes, ma’am,” Pete and Rob said in unison.

Mike’s secretary answered and said she would put them right through.

After a few pleasantries, Mike got to the point.

“Remember the tolerance analysis and specification that you did for passive resistor and capacitor length?”  Mike began.

“Yes. We were all involved in that project,” Patty answered.

“So, it is a Cpk = 1, or a Three Sigma spec, right?” Mike asked.

“Sure,” Patty, Rob, and Pete answered in unison.

“So, what percent of parts should be out of spec?” Mike asked.

“Let’s see … Three Sigma is 99.73% of parts in spec … so that would be 0.27% out of spec,” Pete calculated.

“Well, they are shipping us 5% out of spec parts and claiming they are better than Three Sigma, or a Cpk of 1, because they used a recently published graph, that said a Three Sigma, or Cpk = 1, process was 6.68% of parts out ot spec. I just sent it to all of you,” Mike said.

Pete opened the email and showed it to Patty and Rob.

“I’ll be darned! It does say that a Cpk = 1, or Three Sigma, has a defect rate of 66,800 defects per million or 6.68%,” Rob groaned.

“I’ll bet it has to do with the definition of ‘Six Sigma,’” Patty opined.

A look of recognition came over Pete and Robs eyes.

“What do you mean by the definition of ‘Six Sigma?’” Mike asked.

“We have all heard people claim that ‘Six Sigma’ is 3.4 ppm out of spec. Actually that’s a 4.5 sigma process. This definition allows a drift in the average of 1.5 Sigma that knocks the Cpk down to 1.5.  True Six Sigma is a Cpk = 2 and is 0.002 ppm parts out of spec,” Patty replied.

“I’m a bit confused. But, let me show you some of the length data for 0402 passives,” Mike said.

“We measured them metrically so the length should be 1mm +/-0.1, Three Sigma.  Instead, it is more like 1mm +/-0.1, Two Sigma. That’s a little more than 5% outside of the spec,” Mike continued.

A Minitab Analysis of the 0402 Length Data.

“Give us some time to sort it out,” Patty suggested.

Is a Cpk of 1, or a Three Sigma, process really 66,800 ppm (6.68%) out of spec?  Will Patty and the crew figure out what’s going on?

Stay tuned…


Dr. Ron

Implementing 5S Workplace Organization Methodology Programs in Manufacturing Facilities

Many manufacturing facilities have opted to follow the path towards a “5S” workplace organizational and housekeeping methodology as part of continuous improvement or Lean manufacturing processes.

5S is a system to reduce waste and optimize productivity through maintaining an orderly workplace and using visual cues to achieve more consistent operational results. The term refers to five steps – sort, set in order, shine, standardize, and sustain – that are also sometimes known as the 5 pillars of a visual workplace. 5S programs are usually implemented by small teams working together to get materials closer to operations, right at workers’ fingertips and organized and labeled to facilitate operations with the smallest amount of wasted time and materials.

The 5S system is a good starting point for all improvement efforts aiming to drive out waste from the manufacturing process, and ultimately improve a company’s bottom line by improving products and services, and lowering costs. Many companies are seeking to make operations more efficient, and the concept is especially attractive to older manufacturing facilities looking to improve the bottom line by reducing their costs.

“A place for everything, and everything in its place” is the mantra of the 5S method.  The result is an improved manufacturing process and the lowest overall cost for goods produced.  Implementing the 5S method means cleaning up and organizing the workplace in its existing configuration. It is typically the first lean method that organizations implement. This lean method encourages workers to improve their working conditions and helps them to learn to reduce waste, unplanned downtime, and in-process inventory.
A typical 5S implementation would result in significant reductions in the square footage of space needed for existing operations. It also would result in the organization of tools and materials into labeled and color coded storage locations, as well as “kits” that contain just what is needed to perform a task.

The 5S methodology is a simple and universal approach that works in companies all over the world. It is essentially a support to such other manufacturing improvements as just-in-time (JIT) production, cellular manufacturing, total quality management (TQM), or Six Sigma initiatives, and is also a great contributor to making the workplace a better place to spend time.

Benefits to the company from using the 5S methodology include raising quality, lowering costs, promoting safety, building customer confidence, increasing factory uptime, and lowering repair costs.

The Leaning Tower of Six Sigma

Whatever happened to Six Sigma? It was so intently-discussed in years past — then faded from the conference table. Well, it’s back. From the Obama administration’s Oval Office to siloed enterprise facilities in rural areas of America, Six Sigma is a hot topic — again.

What is Lean Six Sigma? Lean emphasizes removing waste from organizations and processes while focusing on and delivering more value to customers. Six Sigma focuses on variation reduction in processes, products, and services. Lean Six Sigma is basically streamlined processes but faster, simpler. (And yes, there’s an app for that.)

Lean Six Sigma has been back in the spotlight recently as several U.S. presidential candidates have pledged to use the management tool, if elected. Also, the Obama administration is reportedly studying how Lean Six Sigma could help eliminate federal government waste.

Lean Six Sigma online survey  More than 2,500 quality improvement professionals participated in a recent survey around the subject of Lean Six Sigma. A group called ASQ conducted the survey, ASQ being a “leading global network of quality experts,” and in all fairness is a reputable organization. It was conducted using online technology, across disparate geographies.

Lean Six Sigma could help reduce the soaring national debt, decided the survey respondents, but it faces some key challenges in government implementations. The biggest obstacle, survey respondents said, is a U.S. federal government structure that can be a barrier to comprehensive evaluation and accountability.

In addition to noting challenges with the federal government’s structure, survey participants noted other obstacles to implementing Lean Six Sigma in government agencies:

  1.     An environment faced with conflicting strategies, goals, and priorities
  2.     Creating a sense of urgency to deploy a comprehensive improvement methodology across all government agencies
  3.     The personnel management model currently used by many government agencies
  4.     A lack of familiarity with Lean Six Sigma and how it can benefit the organization
  5.     Ongoing political partisanship

Lean Six Sigma in Action  “In business, some process improvements are obvious,” said Russell McCann, national speaker on Six Sigma and President and CEO of Actio. “For instance, if a scientist is creating a new product, and the product contains a chemical that is banned or is restricted in some countries, then it’s best to identify the issues at the request stage.  This averts a scenario where the enterprise spends millions of dollars developing an unusable product.

“While these sorts of process improvements can be done manually – with traditional paper-based systems – process efficiency and accuracy are compromised,” said McCann.  “Critical information is inevitably ‘siloed’ at individual locations rather than being shared across an enterprise; in some cases data is not even shared within a single facility.  This type of scenario presents an ideal environment for a Six Sigma program.

“A Six Sigma initiative that includes Six Sigma software such as Actio modules will reduce cost, improve control processes, and rationalize materials management,” McCann said.

Survey says…  Many participants in the ASQ survey said there are benefits to using Lean Six Sigma. More than 75% of participants surveyed said they have implemented Lean Six Sigma in their organizations and an impressive 79% said the tool is very effective in improving efficiency and productivity.

The respondents found that Lean Six Sigma has also been effective in the following areas:

  1. Raised levels of quality in their organization (74%)
  2. Reduced costs (73%)
  3. Helped individuals in their organization be competitive in the marketplace or to pursue the organization’s core mission (68%)
  4. Had a positive impact on employee safety (56%)
  5. Improved innovation (46%)

Kudos to ASQ for pulling this data together, certainly an interesting study.  ASQ is headquartered in Milwaukee, Wisconsin, with national service centers in China, India, and Mexico.  Learn more about ASQ’s survey, their members, mission, technologies and training at

The Obvious and Not So Obvious About Yields

It was Charles Talbert’s first major assignment after graduating from Tech top in his Industrial Engineering class. He was excited and didn’t want to blow it, but how hard could it be? All he had to do was select the contract manufacturer with the best yields. His company, Excalibur, has rapidly become a leader in designing premier laptops and mobile phones. Excalibur’s exciting and highly functional designs have made it the envy of the industry and a great place to work. So Charles wanted to add value by helping Excalibur find the best EMS firm. To make his job even easier, senior management performed preliminary screening, limiting the candidates to two: ACME and AJAX. Charles visited both and found they both had excellent quality systems in place including an effective continuous improvement program founded on statistical process control. It looks like it would come down to the yield numbers.

ACME argued that it was clearly the best choice as it had superior yield in both laptop and mobile phone manufacturing. AJAX argued that, while that was true, AJAX’s overall yield beat ACME’s 96.6 to 95.4% (table). How is this possible? And which vendor would you choose?

No. Built Yield (%)
ACME 90,000 95
AJAX 10,000 93

Mobile Phones

No. Built Yield (%)
ACME 10,000 99
AJAX 90,000 97

Overall Yield (%)

ACME 95.4

When Six Is Really 4.5


In teaching Six Sigma workshops at Dartmouth, we ensure that everyone understands that “Six Sigma,” as presented in the industry, is in fact mathematically 4.5 sigma. So when folks say Six Sigma is 3.4 defects per million (dpm), they are in fact not referring to plus-and-minus six standard deviations from the mean (even though they may not know it), as 3.4 dpm is only 4.5 sigma.

The true six sigma defect rate is 2 defects per billion. The figure shows this error.

Where does this confusion come from? When Six Sigma was developed, it was defined as a Cp of 2 and a Cpk of 1.5. These process capability indices are where the confusion lies. A Cpk of 1.5 permits a shifting of the process mean of 1.5 sigma, hence the true statistical measure of Cpk = 1.5 is 4.5 sigma (or 3.4 ppm). True statistical six sigma (Cpk = 2) is elusive indeed at 2 dpb!

Dr. Ron