BGA Voiding in Electronics Assembly

Patty had to admit that the last few weeks were exciting.  Her talk to US Army Rangers and Navy Seals on critical thinking went really well.  Now, the local newspaper was asking her to comment on political polling in the current presidential primaries.  Patty was just finishing her response to the paper before a meeting with Pete to discuss the voiding presentation that they were working on for Mike Madigan.  Her response follows:

Dear Editor:

My favorite candidate was trailing in the polls by only 1% in my state, but on primary day he lost by 5%.  Why isn’t polling more accurate?




Dear Disappointed,

Pity the pollsters. They have to predict what will happen by sampling a manageable number of people, say 1,000. This situation creates several challenges. The first is that their sample should represent the population as a whole. This challenge is not easy. They need to assure that the 1,000 people represent the population of the entire state. If they get an inappropriate number of old, young, wealthy, lower income, educated, less educated, etc., in these 1,000 people then their prediction will be off. As an example, let’s say that 45% of a state’s residents have a bachelor’s degree or higher, yet their sample has 60% with a bachelor’s degree or more. This difference will likely make their sample non-representative of the population as a whole and will skew the results.

Let’s go back to your candidate, whom we will call candidate A. It ends up that candidate A was supported by only 47.5% of the total population and his opponent, candidate B, by 52.5%, giving the difference of 5% that you mentioned. Let’s assume that the pollsters establish a good sample of 1,000 people that is very close to representing the state as a whole. It is unreasonable to expect that the 1,000 people polled would exactly have 47.5% or 475 supporting candidate A, due to statistical variation.  To show the likelihood of a number different than 475, we have to use the binomial distribution as seen in  Figure 1 below. Note that there is about a 10% (0.1085 in the figure) chance that a population of 1,000 will have 495 or greater supporting candidate A. This uncertainty, added to the difficulty of establishing a perfect sample, makes polling error of 5% or so not uncommon.

Figure 1.  Note that, even though 475/1,000 is the most likely, if the larger population has 47.5% supporting candidate A, there is a 10% chance a sample of 1,000 could have 495 or greater favoring candidate A.

Figure 1. Note that, even though 475/1,000 is the most likely, if the larger population has 47.5% supporting candidate A, there is a 10% chance a sample of 1,000 could have 495 or greater favoring candidate A.


Just as Patty finished her response, Pete came to her office door.

“Hey kiddo! Can we go over my thoughts on the voiding in BGA balls section on voiding for Mike Madigan?” Pete asked cheerfully.

“Sure. What do you have so far?” Patty asked.

“I’m focusing on the importance of the reflow profile.  Have you seen this graph,” Pete began.

Figure 2. The hot soak profile produces the fewest voids in CSP and BGA balls.

Figure 2. The hot soak profile produces the fewest voids in CSP and BGA balls.

“Wow! That really shows the benefit of a hot soak profile over a cool soak profile. But, I am most surprised at how much benefit a hot soak profile has over a ramp-to-peak profile (RTP),” Patty commented.

“Isn’t the timing of the higher temperatures important, too?” Patty asked.

“My next point precisely. Look at this graph,” Pete said enthusiastically.

Figure 3.  The combination of the reflow profile and flux characteristics that produces outgassing before the solder becomes liquid (the red curve) will minimize voiding.

Figure 3.  The combination of the reflow profile and flux characteristics that produces outgassing before the solder becomes liquid (the red curve) will minimize voiding.

“The process engineer needs to assure that most of the flux is volatilized before the solder melts, as in the red curve, not as in the black curve where almost all of the flux is outgassing during the melting it the solder (Tm). This situation is assured by the correct combination of flux and reflow profile,” Pete said confidently.

“Anything else, Professor Pete?” Patty asked.

“It is really helpful to work with your solder paste supplier to obtain the red curve. They should be able to tell you what type of reflow profile and solder paste will most likely provide this kind of result,” Pete finished with a chuckle.

And he added drolly. “Right … Professor Pete.”

“Rob’s working on voiding on thermal pads for BTCs right?” Patty asked.

“Yep. He said he will be ready in two days,” Pete answered.

What will Robs plan be for minimizing voiding with BTCs?  Will Patty be happy with it?  Stayed tuned for the details.

Best Wishes,

Dr. Ron

Voiding: A Critical Issue in Electronics Assembly


Looks like Patty and the team have a new assignment from Mike Madigan. Let’s look in ….

Patty had just waved to her twin boys as they got on the school bus when her mobile phone rang.  The voice was unfamiliar.

“Professor Coleman, this is Mel Ott.  I’m doing some classroom trading for a bunch of Navy Seals and Army Rangers at a location about an hour from Ivy U. I wondered if you could conduct a workshop on critical thinking for these folks?” Ott asked.

Before Patty knew it, she had agreed to do it. As she drove to the university, she kept on thinking,

“Me teaching Army Rangers and Navy Seals!?”

However, a few moments later, an outline for a workshop was forming in her mind. One topic would be: Which animal is implicated in more human fatalities in the US each year?

  1. Bears
  2. Mountain Lions
  3. Horses
  4. Deer
  5. Sharks

A few moments later, Patty was in the Engineering building complex and was rounding the corner to her office. She saw Pete and Rob waiting outside the door.

“By the looks on your faces, I can tell that we must have another assignment from Mike Madigan,” she said with a chuckle.

“This one is a little strange, even for him,” Pete began.

“Yeah! Look at this note he sent us,” Rob chimed in.

Ever since the three of them left ACME to join the ranks of Ivy University, ACME CEO Mike Madigan continued to use their services. They were paid a fair consulting fee, which all agreed more than paid for Christmas presents and vacations. In addition, Madigan convinced the board of directors at ACME to generously contribute to Ivy U’s general fund. In the three times Patty had met Ivy U’s president, he pointed this out to her with his appreciation. So, the bottom line was that the three of them were quite responsive to Mike’s requests.

Together they read his note:

“Team, our biggest customer is concerned with voiding. They claim it to be their number one concern. Since the three of you left, we have drifted a bit in keeping on top of these things. I am away for a week in Eastern Europe and my wife and daughter are joining me after that for a bit of a vacation in Slovakia. My wife’s heritage is from there, steeped in the traditions of the Rusyn peoples. So, she wants to visit the hometown of her great grandfather. Bottom line is that I will be gone for more than two weeks, without reliable Internet access, so I will be out of touch.

I need you to prepare a presentation on voiding that I (with you) will give to the customer’s president the day I get back. The presentation should have recommended actions. The pitch is at 2PM, 20 days from today. Come at 11AM and join us for lunch.”  Mike

“It’s just like Mike to give us an assignment with no details and we can’t ask him any questions and he schedules the meeting without asking if we are available,” grumbled Pete.

“I, for one, think it is great he is going on vacation,” Patty said brightly.

“Good point,” Rob added.  “I can’t recall him ever taking time off.”

“Well, what is our plan?” Patty asked.

“I’m almost certain that they are not interested in champagne voids, Rob pointed out.

“I agree, since they are mostly associated with immersion sliver finish while ACME’s customers mostly use OSP finish,” Pete added.

“I think the big issue today is voiding in quad flat pack no leads (QFN) thermal pads, BGA voiding is sort of passé,” Rob suggested.

A BGA void image, taken by CALCE.

A BGA void image, taken by CALCE.

“Oops! We are supposed to call them bottom-terminated components (BTCs), right?” Patty asked.

“OK. You’re right on that one,” Rob chuckled.

“So, let’s focus on BTC thermal pad voids. But, I think, for completeness, we should cover BGA voids, too,” Patty said.

“Pete, if you can cover BGA voids Rob and I will pull together something on BTC voids.  Let’s put it on our calendars to meet one week from today to review our material,” Patty sort of commanded.

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

Patty was about ready to get annoyed, but they all burst into laughter as they got up to leave her office.  Even though Patty was now a prof, she still had a lot of manager in her!


Dr. Ron

Your ‘Common Cause Floor’ will Help Define a Reasonable DPMO Target

Let’s look in on Patty; it has been a very long time …

Patty left her house in Woodstock VT very early on her way to Ivy University. She chuckled at the darkness of the early morning; it reminded her of a book she was reading.  In the book, Gray Girl, Jan Wishart is a young woman in her first year at West Point. The cadets use military time, so, for example, 9:00AM is referred to as 0900 hrs. When it is so early that it is still very dark, the cadets simply call it, “0 dark thirty.”

She had to admit that, even though she occasionally had to leave at “0 dark thirty,” she loved being a professor at Ivy University. She had just finished teaching a statistics class and had submitted the grades – she was ready for the holiday break.  As she drove past the Woodstock Green, she noticed that Christmas ornaments decorated Woodstock’s covered bridge. The entire town was getting ready for Wassail Weekend.

“What a great place to raise a family,” Patty thought.  She, her husband Rob, and their twin 7-year-old sons just loved it there.  It was a very wholesome place for the boys (all three), with many outdoor activities.

She was going in early to meet with The Professor, but, before that, she had to hit the gym for her daily workout.  As she approached the Taftsville Bridge she decided to venture across and take the back road. This route was a mile longer, but crossing the bridge and riding on the back road was more uplifting to the soul.  The back road went along the river and was more picturesque and peaceful than the bustling Vermont Route 4.

The bridge in Taftsville, VT, is a pleasant sight on the way to Ivy University.

Wild turkeys near Taftsville, VT.

After crossing the bridge and driving a few miles, she suddenly had to hit the brakes as a flock of wild turkeys crossed the road – just another reason to like living in Vermont.


Before she knew it, she was in the faculty parking lot.  As with almost all universities, parking was a challenge. But, the sun was just rising on this late November day and the lot was mostly empty – except for Dean Howard’s car.

After her workout and shower, she was in The Professor’s office with her long-term sidekick, Pete.  Her husband Rob would join them soon after getting the boys off to school.  The four of them spoke Spanish and, when together, agreed to converse in this romance language to keep their skill sharp.  If Pete wasn’t there, the three would speak Mandarin Chinese, a language he didn’t know.  No one knew for sure how many languages The Professor spoke, but it was rumored to be about 18.  His parents were missionaries for Wycliffe Bible Translators, so he lived in many countries as a youth.

“Hola a mis amigos, la razón por la que les invité aquí fue a discutir DPMO,” The Professor began.

(The remainder of the text will be in English for our non-Spanish speakers.)

“Gee, I haven’t heard people talk about DPMO in years,” Pete responded.

“Remind us how it is tallied,” The Professor requested.

“Well, in electronics assembly, each lead that is assembled is counted as a possible soldering defect ‘opportunity,’ so you count the end of line defects and divide by the opportunities,” Pete began.

“Don’t forget that you normalize to parts per million,” Patty added.

“That’s where DPMO (defects per million opportunities) comes from,” Rob chimed in as he stuck his head in the door.

“And don’t forget to add one defect opportunity for the component itself,” The Professor added.

“Why the concern for DPMO?” Patty asked.

“One of my clients asked if a DPMO of 20 was good enough.” The Professor answered.

“With continuous improvement, shouldn’t they be striving to improve?” Pete asked.

“Well, to a point. But does anyone have a counter-thought?” The Professor answered, always trying to make a learning experience.

“Well if all special cause defects have been addressed and only common cause variation is left, it may be too expensive to improve significantly,” Patty commented.

Pete opined, ”I remember about 20 years ago, I worked for a large OEM and they were at a DPMO of 20.  They tried to get to 5, but it cost a fortune in engineering expense.  A DPMO of 20 hit their ‘common cause floor.’ It costs much more in engineering expense to try to get below the 20 DPMO than the small amount they would be saving in rework costs.”

“Hitting your ‘Common Cause Floor’ sounds like a new expression that you just created Pete— congrats,” Patty said.

Rob had been busy on his laptop and he suddenly chimed in, “I found an article that suggests that 20 to 50 DPMO is a reasonable goal.”

“Let’s do a shirt-sleeve calculation,” the Professor suggested.

“My client has a DPMO of 20. Each product has about 2500 leads and components. It costs $2 to repair a defective device. And, they make 1 million devices with a value of $100 each and a net profit margin of 5%,” The Professor went on.

“So, 20 DPMO times 2500 equals 50,000 or 5% defects in the 1 million units,” Patty started.

“That means 50,000 reworked devices out of the million manufactured for a cost of $100,000 or 2% of the $5 million net profit,” Rob added.

“Getting the DPMO to much less than 20 will cost millions a year in engineering expense,” Pete stated.

“So, let’s sum it all up,” the Professor suggested. “The ‘Common Cause Floor’ will be different for different manufacturers, but hoping to get a DPMO near 0 will likely be too expensive in engineering costs.”

“And, Pete will become famous for inventing the term, ‘The Common Cause Floor,” Patty joked.

They all ended the meeting with a laugh and a slap on Pete’s back.


Dr. Ron

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

Patty, Rob, and Pete were quite sure they understood the confusion in the Cpk = 1 issue, but wanted to make sure they discussed it with the Professor.  After a brief chat with him, they called ACME CEO Mike Madigan from The Professor’s office.

“Professor, it’s great to speak with you again,” Madigan began.

The all exchanged pleasantries, with the Professor thanking Madigan for his financial support of Ivy U through the ACME Corporation.  In a few moments the discussion turned to the Cpk = 1 issue.

“Tell me what you amazing intellectuals have figured out,” Mike chuckled.

“We all thought the article that the vendor referred to had a great discussion on statistical process control (SPC)”, Patty began.

“We especially liked the discussion on the difference between a process being in ‘control’ and ‘capable,’” Rob added.

“But, what about 66,800 ppm equals a Three Sigma process?” Mike implored.

“As we know, Motorola started the ‘Six Sigma’ movement,” the Professor began.  “They defined ‘Six Sigma’ quality has having a Cp of 2 and a Cpk of 1.5.  True mathematical Six Sigma is Cp=Cpk=2.  Their definition, with a Cpk = 1.5, allows for a shift in the mean of 1.5 Sigma.  The adage that ‘Six Sigma’ equals 3.4 ppm defects comes from this definition.  Because of this shift, most of the defects are on one side of the distribution.  By the way, true mathematical Six Sigma is about 2 defects per billion,” he went on.

“It seems a little like cheating to me,” Madigan added.

“Me too. I think they wanted something sexy sounding, like ‘Six Sigma,’ but knew they couldn’t really achieve less than 2 ppb defects, so they created the 1.5 sigma shift of the mean,” Pete chimed in.

“I’m sure that others agree with Pete, but that is where the world of ‘Six Sigma’ is.  Unfortunately, it can create confusion – as in the case at hand,” the Professor responded.

“So how does it relate to the 66,800 defects per million equaling a Cpk of 1 and a Three Sigma process?” Mike asked.

“Pete has done the most work on this. Let’s let him answer,” the Professor suggested.

“If you apply the 1.5 Sigma shift of the mean to process capabilities, we get the table below,” Pete said.

lasky table





Note that the Cpk level for 66,800 dpm is 0.5 not 1 and the true process level is not Three Sigma, but 1.5 Sigma.  Admittedly the Cp level could be 1, but Cpk is a precise calculation and the graph from the paper in question (reprinted below) has it wrong.  The values they list for Cpk are the Cp values.  This is the mistake your vendor made by using this chart. ” Pete said.

lasky figure










“The graph below shows the situation for the vendor.  Distribution A has a Cp and Cpk =1, where as distribution B has a Cp = 1, but a Cpk of only 0.5.  The 1.5 Sigma shift for B is also shown.  The vendor’s data are similar to B, with its the 66,800 dpm..  It is improtant to note that Cp alone tells nothing about the defect level,” Pete went on.

lasky figure 2

“Pete, please tell Mike about the spread sheet you made,” Patty suggested.

They had signed onto Webex, so Pete gave a limit demo.

“By entering the spec limits, as well as the mean and sigma of the data, it will calculate Cp, Cpk, the sigma limit of the process, and the process dpm,” Pete said.


“Oh, and you can enter the dpm and it will estimate the Cpk and process sigma level,” Pete went on.

“Quite impressive,” Madigan summed up. “I assume it is OK if my team uses it?” he went on.

“Sure,” Pete said, beaming a little.

Math was never Pete’s strong suit. But, being at Ivy U, he had recently taken a statistics and calculus class. He had a strong sense of accomplishment after creating this useful spreadsheet.

For those who would like a copy of Pete’s spreadsheet, send me an email at

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

Using the Coffin-Manson Equation to Calculate Thermal Cycles


Let’s look in on Patty and friends ….

Patty, Rob and Pete were headed to their regular monthly meeting where they, along with the Professor, discussed a book they were all reading.  This month’s book was about General Leslie R. GrovesRacing for the Bomb

“This was one of the most interesting books we have read,” Pete said starting the meeting.  “I think most people are aware of the technical genius of the scientists involved in the Manhattan Project, such as J. Robert Oppenhiemer and Richard Feynman, but few appreciate the contributions of Gen. Groves,” Pete continued.

“I agree,” Rob said.  “Without Grove’s orchestrating of the overwhelming number of small and large details of the program, it would have taken three times as long,” he went on.

“Right!” the Professor chimed in. “He set up a $20 billion enterprise to produce the components of the bomb in less than three years.  Who else could have done that?”

“One of the things that I found almost comical was that he was so good at the secrecy of the project that his family had no idea he was working on the bomb until it came out in the newspapers,” Patty exclaimed.

The four book club members chatted about the book for about 20 more minutes.  Patty felt her cellphone vibrate.  It was a text from Mike Madigan.

“Rob, Pete, it looks like we may have another assignment from Mike. He wants us to call, so let’s go to my office,” Patty suggested.

Even though the three of them were all at the engineering school at Ivy U, Mike Madigan, the CEO of ACME, established a blank contract with them to do part-time consulting.  Part-time consulting is quite a common thing in the academic world as it helps the profs and technical staff keep current and also earn a little money.

Patty called Mike’s number and activated the speakerphone.

“We have a customer who we assemble TVs for.  Each TV goes through 10,000 on/off cycles in its field life.  The temperature change from these on/off cycles is from 20°C to 50°C.  We are performing thermal cycle testing of the PCBs from 0°C to 100°C.  How many thermal cycles will we need to perform to equal the 10,000 field cycles?” Madigan asked.

Patty chuckled to herself as she had just solved a problem like this for a reliability workshop that she was developing. So, the technique was fresh in her mind.

“You need to use the Coffin-Manson equation,” Patty explained.

“Whoa!” Mike chuckled, “Is the problem so serious that we need to worry about coffins?”

“Coffin-Manson is used to relate strain to temperature changes. It will help us to calculate the right number of cycles,” Rob chimed in.

Rob, Patty, and Pete all got calculators out to see who could get the answer first.  Pete won the contest.

“I get an acceleration factor (AF) of 25,” Pete announced victoriously.

“Agreed,” Patty and Rob sighed in unison.

“The equation is quite simple,” Patty shared.  See the figure below.




“The Coffin-Manson acceleration factor for lead-free solder, m, is about 2.7,” Patty finished.

“So, you need to perform about 400 (10,000/25) cycles in the test chamber,” Pete said.

“Wow! I’m really relieved,” Mike said, “I thought it might take 2,500 thermal cycles or more.”

“There is no way we had enough time for that number of cycles, but 400 is easily doable,” Mike concluded as he sighed a breath of relief.

The four of them chatted for a while more and then went their ways after having mastered another electronics assembly problem.


Dr. Ron

In SMT Assembly, Even 1 Second of Cycle Time Can Affect Profitability


Patty had just returned from SMTAI 2015. It was a sentimental meeting with the retirement of longtime executive administrator JoAnn Stromberg. At one of the technical sessions, Patty was especially interested in epoxy flux being used as an underfill. She couldn’t wait to discuss it with The Professor.

As she drove up to Ivy University’s campus, she was struck by the many hundreds of students walking to class. No one was overweight and no one was smoking. She reminded herself to discuss this topic in her statistics class. Surely Ivy U did not represent the typical 18-22 year-olds in this regard.

Soon, she arrived at her office. After clearing her laptop of emails, she headed to The Professor’s office.

Patty had been working to improve her French. Since French was one of the 18 languages in The Professor’s repertoire, they often spoke it to improve (for Patty) and keep sharp (for The Professor). Patty chuckled to herself that her French was now good enough to hear The Professor’s Quebecois accent. He learned French as a pre-teen, as his parents were missionaries for Wycliffe Bible Translators and worked with some remote Indian tribes in northern Quebec.

Bonjour Professeur, comment allez-vous?Patty dit gaiement.

“Je suis bon Patty, comment étais SMTAI?” Le professeur a répondu.

The remainder of the discussion will be translated into English for our non-Francophone readers.

“It’s too bad that you couldn’t make it this year. The retirement dinner for JoAnn was touching,” Patty began.

“It will be hard to replace her, indeed. Her commitment was extraordinary,” The Professor responded.

After discussing this topic for a few minutes, The Professor changed the subject.

“Were there any interesting papers presented at the SMTAI tech sessions?” he asked.

“That’s why I’m here,” Patty replied. “There was a paper on epoxy flux as an underfill material. It was a great talk comparing epoxy fluxes to standard underfills. The speaker mentioned how using epoxy flux allows the operator to avoid using a separate dispensing process and curing oven that standard underfills require. His point was that the epoxy underfill approach would save a lot of money, as long as the epoxy process only added one second or less to the cycle time. This one second was the time it took to dip the flip chip or BGA into the flux.”

Patty immediately saw the troubled look on The Professor’s face.

“Professor, I sense you are thinking the same thing that I was,” Patty said.

“Yes, one second is a long time,” The Professor replied. “One second is 5% of a 20-second cycle time, so your production is reduced by 5%. Not a trivial amount.”

“My sense is that this one second would be a greater cost than paying for the dispenser and curing oven in a standard underfill process that keeps the cycle time at 20 seconds,” Patty said.

The Professor nodded his head in agreement and then went to his laptop. In just 3 or 4 minutes, he had calculated four different scenarios using ProfitPro software.

“Well, in most cases, the cost of that 1 second/cycle lost by the epoxy flux process costs the operator somewhere between a few hundreds of thousands of dollars to more than one million dollars per line per year,” The Professor explained. “This estimate even considers the fact that the standard process already needs a dispenser and curing oven.”

“You know what I always say.” The Professor started.

“It never pays to reduce productivity,” Patty chimed in, always the faithful student.

“Take a look at this one example. A large ESM manufactures a product with a 3-shift, 5-day/week operation on a state-of-the-art SMT line. The default, as shown in the figure, is the financial result for one year of production, using a typical underfill, assuming $200K for a dispenser and curing oven and a 28 second cycle time.


“The second run shows the financial results using an epoxy flux that requires a one second longer cycle time (29 seconds), but saves capital cost in that the line does not need a dispenser or reflow oven.”

“Wow, the company loses over $100,000 per year with the epoxy flux!” Patty exclaimed.

“Precisely,” The Professor responded.

“But, this doesn’t mean that people shouldn’t use epoxy flux as an underfill,” Patty stated.

“Right, they just need to avoid losing the one second.” The Professor agreed. “Where do you think the one second can be found?”

“Probably in line balancing,” Patty responded. “About the closest you can balance a line is within a second or two. It could be as simple as having the epoxy-fluxed part placed by the fastest placement machine.”

“And if there are many components that use epoxy flux?” The Professor asked.

“It would likely pay to get another placement machine,” Patty answered quickly.

“As always, there is never one right or wrong way to address a problem like this,” The Professor pointed out. “But, we should always perform the calculations to determine which approach makes the most sense.”

“Yes, and always remember that it never pays to reduce productivity,” Patty joked.

They both smiled as Patty left The Professor’s office.


Dr. Ron

Failure Rate Calculation


Let’s see how Patty, Rob, and Pete are doing helping Mike Madigan establish his Zero Defects program.

“So let me see if I got this straight: if I want to establish that the defect rate is 1 per million or less, I need to have 3 million in the field with no fails?” Mike asked.

“That’s correct,” Rob responded. “Patty and I developed an Excel spreadsheet that will calculate the number of samples needed, with no fails, to verify a given defect rate. I sent a copy to your email account. Open it.”

“Select the sheet titled,  ‘Calculate Number of Samples.’ Now enter ‘95’ in the blue cell after ‘Percent Confidence Desired’ and 1E-6 in the blue cell after ‘Failure Rate to Verify.’ The number of samples needed to verify this defect rate is in the gray cell. Note that it is a little short of 3 million.”

From a different perspective,” Patty added, “if you have a certain number of samples in the field and want to verify the defect rate they can support, if none fail, the sheet ‘Calculate Failure Rate’ will make that calculation.”

Lasky“Let me see if I can use it,” Mike replied.

Mike entered 95% and a desired defect rate of 1E-6.

“Wow! It works!” Mike exclaimed, “It says I need a little less than 3 million samples.”

“So how many samples do you need to demonstrate 0 defects?” Pete teased.

Mike thought for a while and then responded, “Three times infinity! Yikes!”

“I think three times infinity is infinity,” Pete teased again.

Patty glared at Pete.

The group ended by discussing the nobility of a zero defects plan, but the futility of demonstrating it by field sampling.

After they hung up, Patty looked a little agitated.

“Sometimes you two act like 12-year-olds,” she scolded.

Both Rob and Pete had a “Who? Me?” look.

“Why do you say that?” Rob asked sheepishly.

“Both of you laughed when Mike proposed a sample size of 20 to demonstrate zero defects, and then Pete teased about 3 times infinity equals infinity,” Patty responded. “Mike deserves to be treated with respect. We shouldn’t laugh at people when they don’t know or understand something that we do. Especially now that we are all at Ivy U, we are here to help people learn.”

“But he was so annoying when we worked at ACME,” Pete shot back.

“That doesn’t matter. And besides, for whatever reason, we all agree he is much nicer now.”

Both Pete and Rob murmured in agreement.

“Ma’am, we will be better in the future,” Rob and Pete teased in unison.

“Hey, Patty. Remember your concern that almost 50% of Ivy U students did not know who wrote A Christmas Carol?” Rob asked.

“Sure,” Patty responded.

“I asked Pete and he said J. K. Rowling,’” Rob said.

“Well at least I got the right country,” Pete replied.

Patty couldn’t help herself; she burst out laughing with the other two.


Dr. Ron

  1. If you would like a copy of the Excel Spreadsheet that performs the defect rate calculations discussed in this post, send me an email at



The Rule of 3/N for Estimating Field Failure Rates


It looks like Patty is a bit troubled….

When she was younger, Patty was always annoyed by cranky old people, and now she was worrying that she might become one. The trigger making her cranky was what students know and don’t know. It all started when a colleague showed her the “Texas Tech Politically Challenged Video.” 

“How could so many students not know who won the American Civil War, who the Vice President is, or who the United States won its freedom from?” she thought.

Some of her colleagues felt the video was staged, but the producers came up with a response video that strongly suggested that it was not. What was even more unsettling was the fact that all the students knew who Snooki was and who Brad Pitt’s wife was.

Some of Patty’s statistics students got wind of this video and decided to make a similar video at Ivy University. The results were mostly comforting: 49 out of 50 students knew who won the Civil War, and the one student who didn’t was from India. They also did well with some other questions, 85% knowing that Joseph Stalin was the leader of the Soviet Union in World War II, and a high number knew that Joe Biden was the VP.

But Patty was most troubled that almost 50% did not know who wrote A Christmas Carol. She had discussed the topic with Rob and was further annoyed that he didn’t seem as troubled as she was. Rob pointed out that some international students might not have had English literature in their studies, and being a story about Christmas, it could be a cultural thing. Patty was unconvinced by his arguments. It still seemed troubling to her.

Charles Dickens

Charles Dickens in 1867, 24 years after he authored “A Christmas Carol”

As she was mulling over these thoughts, the phone rang. It was Mike Madigan, CEO of her former employer, ACME.

“Hey, Patty, it’s Mike,” Madigan said cheerfully. “I need your help with a statistic problem. It might be good if Rob and Pete were involved, so could we do a teleconference?”

Patty scheduled the teleconference for later in the day. When the time came, Pete and Rob were in Patty’s office and she called Madigan. After exchanging pleasantries, Madigan got to the point.

“We have a demanding customer from the military,” Mike started. “They have a Zero Defects program and want to know how we can guarantee it after field exposure.”

“To clarify, you mean guarantee zero defects for units in the field?” Pete asked.

“Yeah,” Mike replied.

“The way I figure it, if we have 20 units in the field and none fail, we can say with 95% confidence that we have zero defects, because one unit is 5% of 20, and if none fail, that means we can be 100%-5% or 95% confident,” Mike said.

Patty instinctively reached for the mute button, as Rob and Pete went into hysterics. She glared at both of them.

“Hello, hello, are you there?” Mike asked as he heard no response.

Finally, with Patty continuing to glare, Pete and Rob had stopped laughing. So she unmuted the phone.

“Sorry Mike, the failure rate in the situation you described is that you can be 95% confident that is it less than or equal to 15%” Patty replied.

The other end of the conference call was quiet for a while and finally Mike answered,

“Yikes! OK, can you explain?”

“Patty and I have developed the math to explain how to calculate confidence limits on field failure rates,” Rob responded. “For 95% confidence we have developed what we call The Rule of 3/N.”

“How does it work?” Mike asked.

“If you have N samples in the field, and none have failed, you can say with 95% confidence that your failure rate is 3/N or less. As an example, let’s say you have 300 units in the field and none fail. You can then say with 95% confidence that the failure rate is less than or equal to 3/300 = 1/100 = 0.01 = 1%.”

“If we have 300 units with no fails, we can only have confidence in a 1% failure rate?” Mike groaned.

“One percent or less, with 95% confidence,” Patty chimed in.

Is demonstrating a 0% failure rate possible?  Will Patty and the team find a way to help Mike? Stay tuned for more details.


Dr. Ron


Phil Zarrow Weighs in on Productivity


I ran into good friend Phil Zarrow the other day. Phil, Jim Hall, and I developed the SMTA Certification Program. We ended up chatting a bit about productivity, one of my favorite topics.

Ron: Phil, you have likely visited more assembly factories than anyone I know, hundreds for sure. What are some of your observations on how folks address or don’t address productivity?

Phil: Ron, there are so many bad practices that result in low productivity. More often than not, when we enter the manufacturing floor (for a process audit or other reason) we see a sea of red and/or orange light towers – rather than PCBAs in process. Most managers have no concept of the capacity they are operating at and usually feel that adding another line (with faster equipment) will increase capacity. However, there are three top “sins” that should be addressed – immediately!

The first is setup time. Unless you’re an OEM building the same PCBA day in and day out, this is something you have to master. And the higher the product mix, the more line changeovers prevail, and the more this impacts throughput. There are a number of things that can be done to “expedite” setup and they all add up. Any facility with more than one active line can benefit from a systematic approach toward setup. I tend to favor (and have had excellent luck with) the “Pit-Crew” approach. Note that the operators and setup crew are working together. Sequential changeover goes a long way: as soon as the last PCBA in a run passes through a machine center the crew commences changing over that machine (stencil, feeders, programs, etc.) rather than waiting for that last PCBA to clear the reflow oven.

Usually, hand-in-hand with this situation is a lack of adequate feeders for the different components that need to be changed over. Having a feeder already loaded with the component and “popping” it in rather than having to remove a reel and replace the component reel goes a long way. Feeder carts go even further. But this costs money and management usually doesn’t “get it.” In fact, we’ve encountered situations where there is such a shortage of extra feeders that, when the tech or engineer discovers that a feeder is malfunctioning, they don’t have a “spare” and are forced to continue using it, continuing to produce defects that have to be attended to (more time, expense, etc.).

Ron: Phil, I have observed similar practices as, noted in my book “The Adventures of Patty and the Professor.” What is the second sin?

Phil: Another common situation is a lack of balance in the line. Particularly predominant in the placement machines, if one machine is waiting a disproportionate time for another machine, the line is unbalanced. Components can and should be shifted from one machine to the other. While most of the placement machines come with software for calculating this, it is very simple math – single variable algebra (like we learned in 8th grade). But the “math phobia” we seem to suffer from is a subject for a different day….

Ron: I agree. The engineers will tell me that the line is balanced, but when I go out to the shop floor and check with my watch, the lines are almost never balanced, even though, in theory, the placement machines will easily handle it.

Now, we are holding our breath, what is number 3?

Phil: I’d finally like to comment on, to use a term you originated, “floundering time.” This is where the operator or tech comes across a problem or situation and has no idea what to do. She is not sure of the reporting system or “who to call.” It could be a machine problem, a tooling problem, a component outage, or a variety of other things. But, they all result in unscheduled downtime and severely impact productivity.

That’s just the tip of the iceberg, Ron. But just addressing these areas can improve productivity and cost a lot less than adding another line.

By the way Ron, I know you have thoughts on how materials can affect productivity. What’s a top example?

Ron: Obviously the main consideration for materials is that they perform their material function well. As an example, you would want your solder paste to form a reliable solder joint. However, solder pastes can affect productivity. I have seen cases where the poor response to pause of a solder paste was so bad that, if the line was idle for more than 20 minutes, the paste would stiffen up and have to be wiped off the stencil and replaced with fresh paste. These types of issues are discussed in “The Adventures of Patty and the Professor” in Chapters 9, 10 and 21 and can affect productivity and profitability more than you might expect.

Phil, thanks for the nice chat!

Dr. Ron