Calculating Confidence Intervals on Cpks

Let’s look in on Patty, it’s been awhile.

Patty was looking forward to sleeping in.  Normally she was up very early, sometimes before 5:30 am, after usually getting to bed too late, so she was looking forward to an alarm set at 7:45 am. The kids were off from school and Rob was taking them skiing, so all agreed a 7:45 am wake up time was reasonable.  Since she had no early meetings, her scheduled 9 am arrival at her Ivy University office was also in the cards.

Patty was sleeping soundly when she heard her seven-year old twin sons shouting, “Mom! Dad! Come quickly.”   At the same time, their two-year old beagle, Duchess, started barking.

Her heart pounding, Patty raced to the racket now being produced by this energetic trio.  As she arrived she saw her sons and Duchess looking out of their back window to see a beautiful female deer eating from their bird feeder, just 30 feet away. The entire family was involved in a bird counting exercise and had noticed, several times, that the bird feeder was “wiped out” overnight. This mystery was now solved.

The entire family agreed that it was hard to be angry at the doe, as deer are such beautiful creatures.

Figure 1.  A Female Deer at the Bird Feeder at Patty’s House

 

It was 6:15 am and it didn’t seem to make sense to go back to bed.  So, Patty stayed up and was off to Ivy U in less than 30 minutes.

Patty had a rather light week as she had guest speakers for her two lectures.  However, she was sitting in for one of the engineering school’s senior professors later in the day.  This fellow prof had asked her to sub for him as he was called to an emergency meeting overseas.  Her topic was manufacturing processes; one with which she felt very comfortable.  But, she had to admit to being a bit nervous sitting in for one of Ivy U’s most famous professors.

As was her usual practice, Patty checked her email first.  After going through the first 5 or 6, she saw an email with the subject header, “Ivy U Professor Wins Prestigious Queen Elizabeth Prize for Engineering.”  As she opened the article, she was stunned as she saw a photo of the professor for whom she was substituting later in the day.  The article went on to explain that this prize was like the “Nobel Prize” for engineering.

As she finished her emails she was relishing the thought of having a less hectic day and week ahead.  Maybe she would even have time to read the Wall Street Journal during a relaxing lunch.  Suddenly, her phone rang, startling her a little.  She picked up the receiver to hear a familiar voice.

“Professor Coleman, this is your most faithful student Mike Madigan,” Madigan cheerfully said.

Madigan was CEO of ACME at large electronics assembly contractor. Patty worked at ACME before becoming a professor at Ivy U. Her husband, Rob, and sidekick, Pete, were also ACME employees, but were now all at Ivy U.  Pete was a research assistant and Rob was just becoming a research professor.  Although they all enjoyed their time at ACME, they were much happier at Ivy U.  All three had a part-time consulting contract with ACME and Madigan was typically their main contact at their former employer.

“Mike! What’s up?” Patty said cheerfully.

“We are evaluating a new solder paste and I’m concerned we might make a mistake if we switch,” Mike responded.

“How so?” Patty asked.

“Well, we agreed that consistency in the transfer efficiency (TE) of the stencil printed deposits was the most important criteria,” Madigan began.

“That sounds reasonable as most of our past work has shown that a consistent TE is a strong determinant of high first-pass yields,” Patty responded.

“Right! But the difference between the pastes is only two percent. The old paste has a Cpk of 0.98 and the new paste 1.00,” Mike went on.

“I sense there is more to the story,” Patty suggested.

“Yeah. The new paste has a poorer response to pause,” Madigan said.

“Yikes!” Patty almost shouted.

Patty had shown, time and time again, that poor response-to-pause in the stencil printing process can hurt productivity and lower profitability considerably.

“My sense is the two percent difference in Cpk, might not be significant,” Mike suggested.

“Mike, I think you are on to something. What printing specs were you using and how many samples did you test?” Patty asked.

“The lower TE spec was 50% and the upper 150%. We tested 1,000 prints,” Madigan answered.

“Let me do some homework and I’ll get back to you,” Patty said.

“One problem. Can you get back by 3 pm today? The new solder paste supplier is coming for a meeting at 4PM and is pressing us,” Mike pleaded.

“OK. Will do,” Patty said, sighing a bit.

“There goes my somewhat relaxing day,” she thought.

It was a good thing she had already prepared her lecture and that it was scheduled for 4:30PM.

For several hours Patty thought and searched through some textbooks on statistical process control.  Finally, she came upon the solution to the problem in Montgomery’s Introduction to Statistical Quality Control.

“Perfect!” she thought.

She did finish early enough that she could read the WSJ over lunch, marveling, as always, that she was the only person her age that enjoyed reading a real newspaper.

She called Madigan at 3 pm.

“Mike, I think I have your answer.  I found a formula to calculate the confidence intervals of Cpks,” Patty started.

“And the answer is?” Madigan asked expectantly.

“The Cpk 95% confidence interval on the new paste is 0.95 to 1.05, however the old paste is 0.93 to 1.03,” Patty began.

“So, even I can sense that they aren’t different,” Mike commented.

“Yes, since the confidence intervals overlap, they are not statistically different,” Patty agreed.

Figure 2. The Confidence Interval of the Cpk on the New Paste is 0.95 to 1.05.

 

They chatted for a while and Madigan asked if Patty could join the first 20 minutes of the meeting by teleconference.  It was a bit close to her lecture start time, but she agreed.

Patty had met Madigan’s son at West Point when she visited there to be an evaluator for a workshop two years ago.  She decided to ask how he was doing.

“Mike, how is your son doing at West Point?” she asked.

“Thanks for asking. He is now a Firstie and was in the running for First Captain, but he just missed it.  It’s a good thing he takes after his mom,” Madigan proudly responded.

“Wow! That’s great,” Patty replied.

“I have to admit though, my wife and I are a bit nervous. He has chosen armor as his branch and there is a good chance he will see combat sometime in his career,” Madigan responded with a bit of concern in his voice .

They chatted for a while more and Patty was touched to see so much humanity in Mike Madigan.  He seemed much changed from his gruffness of earlier years.

Cheers,

Dr. Ron

As always, some of this story is based on true events

 

PCs, Tablets, and Mobile Phones are not Dying (and Will Continue to Present Voiding Challenges)

Folks,

Looks like Patty and Rob are on another adventure.  Let’s look in ….

Patty had been driving the same 2001 Saab station wagon since college. It had been a great car, but, with almost 200,000 miles on it and its outdated safety features, perhaps it was time for a change. Both her and Rob’s parents had been bugging them about getting a new, safer vehicle for a while. Finally, for her birthday, both sets of parents chipped in to give her a significant down payment on a new car.  They even suggested which specific car she should get. It was a car with one of the best safety records, not an insignificant concern for doting grandparents.  The manufacturer has a goal of no deaths in its automobiles by 2020.

As Patty and Rob went shopping, they were overwhelmed by the features that 2016 autos have. Detections of cars in the “blind spot,” warnings when the car leaves the lane, warnings and prevention from backing in to something, reading the speed limit signs, pairing to smartphones, the internet, and on and on.

“Patty, these aren’t cars; they are computers that you can drive,” Rob commented.

“Actually this car has 13 computers,” the salesperson chuckled.

“What is the soonest we can take the car home?” Rob asked, expecting it to be 3 or 4 days.

“You can take it home in an hour,” the salesperson affirmed.

In an hour, Patty and Rob were driving home in their new car, amazed at its capabilities as a “computer on wheels.”

“Rob, look at this. As we pass the speed limit sign, the speed limit is shown on the speedometer,” Patty exclaimed in amazement.

They stopped in their driveway and played with the car’s features for 30 minutes, streaming music from their smartphones, connecting to the internet, and changing many modes on the dashboard display.  It was more fun than their first time playing with a tablet.

lasky1

Figure 1.  Patty and Rob’s new car has 13 computers

Two days later, it was Monday and Patty, Rob, and Pete had been asked to see the Professor for a brainstorming session.  Recently, as Patty’s career had skyrocketed, she had been working with the Professor less and less.  The trio agreed to meet in Patty’s office so they could head over to the Professor’s office together.

“Hey, this is just like old times!” Pete exclaimed.

“I agree,” added Patty, “I miss some of the adventures we used to have.”

The professor welcomed them in.

“I hope all of you had a chance to review the material on the many links that I sent you,” the Professor began.

They all murmured that they had.

They reason I asked you to come is that I am going to be interviewed on national television, The topic is, ‘The Death of PC, Tablets, and Smartphones.’ I thought you all might be able to help me prepare.

They all though in unison, “Us help the Professor prepare?!”

“What are your thoughts on the ‘Death of the PC,’” the Professor asked his humble mentees.

“One of the links you sent has shows PC sales declining,” Rob said.

Lasky2Figure 2. PC sales peaked around 2011 and have been declining since then.

“But, do you think it portends the end of PCs?” the Professor asked.

“This is something I have thought about ever since you sent us the links.  I think the ‘death of the PC’ people are missing some key points,” Pete replied.

“Such as?” the Professor encouraged.

“When I was a teenage we got an IBM PC XT. It had a 10MB hard drive. We replaced it in three years,” Pete began.

“Why did you replace it?” Patty asked.

“It didn’t have enough memory or processor speed for the new games.  The new PC had a 200MB hard drive. We kept that one for about 3 more years and the cycle repeated,” Pete answered.

“And what about today?” the Professor asked.

“My parents have a six-year-old computer. They recently complained they needed to upgrade it because the audio plug is worn out, some keys on the keyboard are intermittent, and it doesn’t have enough USB ports. No problem with the memory; it has 6GB of RAM and a 250GB hard drive,” Pete answered.

“So, it did not run out of memory or computer speed?” the Professor asked.

Patty interrupted, “I remember the Professor and I talking about ‘the constancy of memory metrics’. The argument was that a photo is about 1MB, a song 5MB and a movie about 5,000MB.  These metrics are approximately constant. Initially, the size of these metrics overwhelmed early computers, but now these memory metrics are small compared to the capability of current technology. The impact was that early computers had to be changed often, because people wanted to store more photos, songs, etc., but now, with computers having 1TB of memory, getting a new computer for this reason is not so compelling.”

“Maybe with the exception of some new video games, but admittedly this is a small part of the market,” Rob added.

“Well, is the PC market dying then?” the Professor prompted.

“No way!” Pete jumped in. All of us use our PCs for hours each day.  Am I the only one longing for my PC when I answer an email from my smartphone?” Pete asked.

They all chuckled.

“So, it seems that we are concluding that, today, the performance requirements for PCs, mostly laptops, have leveled off and upgrades are needed less frequently. These upgrades are often driven by mechanical failures such as connectors and keyboards, not necessarily the need for more memory or faster processor speed.  It is natural then to expect sales of PCs to level off and even go down some as, in addition to these points, the market has reached saturation.  Everyone who needs a PC has one,” the Professor summed up.

“Yeah, and the 238.5 million sold last year is not really small potatoes,” Rob added.

“What about tablets? Are they going away?” the Professor asked with a mischievous smile.

“Again, the data show a downward trend, but I’m not a believer that they are going away either,” Pete commented.

Lasky3

Figure 3.  Tablet sales are declining.

“I think a similar thing is happening here,” Patty mused. “Tablets are so powerful that there just isn’t an incentive to purchase one frequently. We have an iPad II that we bought in 2011 that we still use, although it doesn’t run some of the newer games.”

“And they sure are popular with our boys. We have to limit the time they spend on them,” Rob added.

“What about people using large smartphones instead of tablets?” Patty asked.

“That has definitely cut into tablet sales. Some of the new smartphones are so big that they are almost comical.  They are as big as some of the mini tablets,” Pete opined.

“Professor, I thought one of the links you sent was fascinating: 4.6 billion mobile phone users in a world of 7.3 billion people!” Rob exclaimed.

“I have a friend who works in humanitarian engineering in third world countries. He tells me that people in some places he visits, will go without food to have a cellphone. In the past, communicating with relatives 60 miles away was a one week commitment of time, because of the primitive transportation. Now, they can do it instantly,” the Professor shared.

“What about the fact that there are as many mobile phones as people on the earth,” Pete exclaimed.

“I guess some people have more than one,” Rob suggested.

“So are mobile phones dying?” the Professor asked.

“I think it is the same argument. When I was starting out at ACME, I had a mobile phone that could take photos, but the quality was really poor. By 2010 the photo quality was good, today it is excellent. I hardly ever take a camera with me, my smartphone photos are excellent,” Patty said.

“So, I’m guessing you don’t need to get a new smartphone as often because the technology has now stabilized, and improvements are only incremental?” the Professor asked.

“Precisely,” Patty responded.

“I think we agree; PCs, tablets, and mobile phones are here to stay, but their sales will be flat or slightly down due to market saturation and technology maturity.”

“Here, here,” Pete chuckled.

“Where do you see electronics growing?” the Professor asked.

Patty and Rob then shared their exciting experience in buying a new car and all of the electronics it has.

Pete then chimed in, “Don’t forget the internet of things (IoT).  I think this is the future of electronics growth, but it is not one device.  The number of devices is innumerable – and growing! And I think it will help electronics grow even faster than in the past.”

They discussed IoT for quite a while and then Rob had a thought.

“Bottom terminated components and especially QFNs will be with us for a long time as they are in all of these devices.  So the work we did for Mike Madigan on voiding should have a lasting impact,” Rob posited.

“Patty, you need to do something about Rob. He’s becoming too serious,” Pete teased.

Everyone laughed at that and got up to leave after what they all felt was a fruitful meeting.

Best wishes,

Ron

Using Solder Preforms to Reduce Voiding in BTCs

Folks,

Let’s see how Patty and the team are doing on their presentation on voiding for Mike Madigan …

Patty was kind of down. Like millions of others, she and Rob watched, in horror, as Jordan Spieth had his meltdown at the 2016 Masters Golf Tournament. Some newscasters considered it the biggest meltdown in golf history, but Patty considered Rory McIlroy’s 2011 and especially Greg Norman’s 1996 meltdowns to be worse. She felt the NY Daily News did the best job of comparing the five worst Masters meltdowns. She agreed that Spieth would surely recover, certainly better than Ken Venturi in his famous collapse in the 1956 Masters. She was surprised that so many newscasters often seemed to not put history in as strong a perspective as it deserved.

As she sat in her office, she was reminded that she needed to finish her part of the presentation that Mike Madigan needed on minimizing voiding. Her topic was, “Using Solder Preforms to Minimize Voiding.” To her, voiding appeared to be the hottest issue in electronics assembly.  Especially voiding under bottom-terminated components, or BTCs. Rob and Pete were coming by in a few minutes to review her progress. Just as she finished, they were at her door.

“Hey, Professor! What’s the scoop on using solder preforms to minimize voiding?” Pete asked, clearly teasing by calling her “Professor.”

They all chuckled a bit and Rob added, “Yes, Professor. Let’s hear it.”

Patty began, “Remember a few years ago the standard approach to using preforms, to minimize voiding under BTCs, was to use a flux-coated solder preform and place it on the thermal pad on the PWB after printing a minimum amount of solder paste?”

“Sure! A great paper was written on it, by some of the folks at Indium Corporation,” Rob said.

Then Pete added, “I gather there is a new approach?”

“Well, think about the motivation to find another technique,” Patty replied.

“A specialized preform needed to be made, it needed flux coating and placing it was a bit of a challenge,” she continued.

“So, what’s the new technique?” Rob asked.

“Well, I chatted with Tim Jensen. Although the original technique is still used, a preferred technique using 0201- or 0402-sized solder preforms has been developed.  The preforms are purposely placed off center so that the BTC is at an angle.  This angle allows the solder paste volatiles to escape.  Since these preforms are a standard size, and not flux-coated, they will typically be less expensive and easier to handle in the assembly process,” Patty elaborated.

“How well do they work?” Pete asked.

“They work quite well. Look at these data,” Patty replied. (see Figure 1).

Figure 1. Preforms of either 0201 or 0402 reduce voiding by up to 50%.  Note that the standard deviation is also tighter by using preforms.

Figure 1. Preforms of either 0201 or 0402 reduce voiding by up to 50%.  Note that the standard deviation is also tighter by using preforms.

“Looks like the 0402 preforms do a little better than 0201s,” Rob commented.

“Yeah! And using two of them instead of one seems to help a little,” Pete added.

“It’s also striking how the preforms tighten the data up. Look at how much the standard deviation is reduced by using them,” Rob added.

The trio spent the next several hours collating all their PowerPoint slides into one 45-minute presentation. Patty then scheduled a meeting with Mike Madigan to review the entire presentation.

Epilogue: Patty, Rob and Pete reviewed the presentation with Mike Madigan using WebEx.  Mike implemented the recommendations after reviewing them with his critical customers.  By using the best solder paste, making minor modifications to the SMT processes, and using solder preforms where appropriate, ACME was able to reduce voiding to less than 10% in all products and less than 5% in most.

Cheers,

Dr. Ron

 

 

To Minimize BTC Voiding, Start with the Right Solder Paste

Let’s see what’s up with Patty ….

Patty was just dropped off at O’Hare airport after finishing a 3 day workshop on Lean Six Sigma statistics, design of experiments, and statistical process control. Interestingly, the students were lawyers. In recent years more and more service-based organizations were adopting lean Six Sigma and it was a long time since Patty had taught such a workshop to engineers. She noted that although the lawyer’s math skills were a bit rusty, they were very good listeners and picked up the math behind lean Six Sigma topics very quickly.

After paying the cab driver, she entered the terminal and went to see an agent. She was early enough to get an early flight home, so she had called the people at the online ticket agency during the cab ride. They said the change fee would be over $300, she felt that was just too much to pay. She was delighted to see that it was only $75 at the terminal.

She looked at her paper boarding pass and saw that she had more than two hours, just enough time for a relaxed lunch at Wolfgang Puck while she read USA Today. Patty was the only person her age that she knew who enjoyed reading a paper newspaper, she guessed that she picked the habit up from her dad.

The two hours went by quickly and she was standing in line waiting to board the flight to Boston’s Logan Airport. She had now been at Ivy U for a few years and traveled much less than when she worked at ACME. She had forgotten how stressful and unpleasant traveling was. As she stood in line, the man in front of her put his smartphone on the scanner and the scanner could not read the QC code. He and the agent fumbled for a while before they got it to work. This was another place where, in her opinion, paper was still king.

Patty got on board and settled into her middle row seat. She groaned a little bit at how uncomfortable and cramped it was. Patty was reminded of what her dad used to say in situations like this; “I know it is a bit uncomfortable, but just think what the 49ers went through to get to California,” he would tease.

After takeoff, she turned on her laptop. She absolutely had to send some emails, so she signed on to the onboard WiFi. She got sticker shock when she saw that it cost $18.95!  Even though Ivy U would pay for it, the high price galled her.

After she finished the emails, a wave of fatigue swept over her and she needed a break.  She chuckled to herself when she thought of a recent event. She had taken two of her best teaching assistants (TAs) to lunch and the conversation somehow came to discussing people who hid Jews from the Nazi’s in World War II. Patty mentioned to her two young protégés about an excellent book and movie she read and saw as a teenager, The Hiding Place. The story is about Corrie Ten Boom and her family and how they hid, and hence saved, many Jews from the Nazis in Holland during WWII. Although the movie was made before she was born, it was shown at Patty’s church every few years, for the new sets of youngsters who came along. Patty mentioned to her two superstar TAs that the film was produced by Billy Graham’s organization.

“Who is Billy Graham?” they both asked in unison.

Patty struggled to keep her composure as she explained who he was. How could they not know this?  She decided to examine the situation a bit further.

“OK, you two. Who was Mickey Mantle?” Patty asked.

The youngster’s both looked at each other.

“We have no clue,” they chuckled.

Patty though she would try a few more, “Nikita Khrushchev?”

Nothing.

Roy Orbison?”

Nothing.

Patty started humming a few bars of Orbison’s most popular song.

“Oh, Pretty Woman,” the boys said in unison.

Patty thought to herself, “Each of these young lads are the best student in every class that they take and yet they don’t know these ‘celebrities’?”

The next day Patty arrived at her office early to meet with Rob and Pete to discuss how the presentations that they were making for Mike Madigan on voiding were coming. Patty had arrived so late the night before, that Rob was already asleep. She did not see him in the morning as it was her turn to get the boys ready for school and he was off early to get in his 90 minutes of exercising. So, they had no chance to discuss the progress of the presentation.

“Pete, your presentation of BGA voiding is terrific. How is my hubby doing on BTC voiding?” she chuckled as she looked at Rob.

“I feel like I’m going to get yelled at ’cause I didn’t do my homework,” Rob said sheepishly.

“Yikes! We only have a few days,” Patty responded. “And I have yet to do my part on using solder preforms to minimize voiding,” she went on.

“I’m only teasing. I have quite a bit of info,” Rob said.

“We have been out of the mainstream for a while and one thing is for sure, voiding is the number one issue among assemblers today.  So many people are assembling QFNs and are struggling with voiding. Voiding with some solder pastes can be over 50% of the area,” Rob went on.

“Wow! With 50% voids, think of how poorly the heat is being transfer away for the BTCs,” she looked at Rob and chuckled. “Remember, ‘BTC’ not ‘QFN,’ Patty went on.

“Yes ma’am,” Rob jokingly replied.

“Can you imagine the effect on reliability and field issues with so little heat being removed? The ICs inside the BTCs must be frying” Pete added.

“Voiding at this level has got to be really costly,” Patty mused.

“One of the things that really helped me was that I found quite a few experiments on voiding,” Rob added.

“What were some of the key points?” Pete asked.

“Well, as you might expect, the solder paste is typically the most critical part of the process. Some pastes have voiding lower than 10% with others above 50%,” Rob replied.

“What about the process?” Patty asked.

“Well, the reflow profile can be very important, as is controlling the PWBs and components. But, with the best pastes, it has been found that you can control the voiding content even if you can’t change the reflow profile and the PWBs and components have some issues,” Rob responded.

“Look at the x-rays of poor and good voiding between two pastes,” Rob said.

“What a difference,” Patty and Pete said in unison.

“What about the stencil design and venting?” Pete asked.

“Chris said that stencil design for venting is not as critical as once thought, although a window pane design is usually used,” Rob replied.

Figure 1.  The window pane design for the stencil is used to permit venting.

Figure 1.  The window pane design for the stencil is used to permit venting.

“So it sounds like starting with the best solder paste solves 90% of the problem and adjusting the process, say with the right reflow profile, helps refine the result,” Patty summed up.

With this Rob went off to put the finishing touches on his PowerPoint® slides for his part of the presentation, while Patty started working on her part of the presentation on using solder preforms to reduce voiding.

Two weeks later.

Patty’s mom and dad came for a visit on a Sunday. Her mom had graciously offered to bring a complete Sunday dinner. Patty, Rob and the boys were grateful for the delicious meal. As they began to eat, Patty shared the story of her best students not knowing Billy Graham, et al.

“But, what was even more surprising was that I ended up asking 10 or 20 more students and only one had ever heard of any of these four ‘famous’ people,” Patty sighed.

“It’s your age,” Patty’s mom replied.

Thirty years old was not that far in the rear view mirror for Patty and she really didn’t consider herself old.

“These youngsters were born in the late 1990s, a generation after these people were prominent,” her mom went on.

“Mom’s right.  Do you know Billy Sunday, Ty Cobb, Glenn Miller, and Trotsky?”  her dad asked.

“Who?” Patty asked.  And then she chuckled, getting the point.

After a brief pause, she said, “I do know who Trotsky was; tell me about the others.”

Cheers,

Dr. Ron

As always, this story is based on true events.

 

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?

Sincerely,

Disappointed

 

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

Folks,

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!

Cheers,

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.

Cheers,

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 rlasky@indium.com.

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…

Cheers,

Dr. Ron

Using the Coffin-Manson Equation to Calculate Thermal Cycles

Folks,

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.

 

DrRon1

 

“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.

Cheers,

Dr. Ron