Tag Archives: Ron Lasky

Wave Soldering is Here to Stay

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Patty was just getting ready to leave her office for a bi-weekly luncheon with the Professor, Pete, and Rob. They had regular meetings like this to discuss new technical topics or to review books. It was Patty’s turn to take the lead in discussing the new book, Rust: The Longest War.

As Patty arrived at the faculty dining room, everyone else was already seated. After ordering, she began the discussion.

“I thought that, overall, the book rated 4 out of 5 stars,” Patty stated.

“It had many interesting stories and brought home that fighting rust is the ‘longest war,’” she went on.

“But shouldn’t the book really be called ‘Corrosion’?” Pete interjected.

“I agree. After all, the best story was about the work that was done to refurbish the statue of liberty, and most of that is copper.  By definition, only iron rusts; copper corrodes. We try to be very specific about the differences in our undergraduate materials classes,” Rob chimed in.

“Rob, I remember you telling us that one student wrote a paper that referred to wood corroding,” the Professor said.

At that comment everyone chuckled.

“We can all agree that corrosion is a big challenge to civilization. But, can anyone think of a big downside if iron didn’t rust?” the Professor asked.

Patty, Rob, and Pete looked at each other and then the Professor as they shrugged their shoulders.

“Think biological processes,” the Professor encouraged.

It hit them all at once, but Pete was the first to comment.

Figure 1. Rust: The Longest War

“Blood!” he cried out.

“Precisely! Without ‘rust’ we wouldn’t be here.  Iron’s unique ability to combine with oxygen in the hemoglobin of our blood makes ‘rust’ a requirement for human life,” the Professor explained.

None of them recalled seeing this point in the book.

“So, the conclusion is that rust costs the US over $400 billion per year. But, without it we wouldn’t be here,” Pete summarized as he chuckled.

“Patty, I understand that you had to fill in for Professor Croft as he recovers from a broken leg. The course was Everyday Technology as I recall. How did it work out?” the professor asked.

“Well, first of all, Pete agreed to help. And, it was only for the last two weeks of the term.  The final assignment for the students was to perform a teardown analysis on some electronic product, such as a DVD player, blender, hair dryer, etc.  They had to write a report and give a presentation on their findings.  They worked in teams of 2 or 3,” Patty summarized.

“It’s important to remember that the students that take this course are not engineering or science majors.  The course fulfills a technology requirement for non-technical students.  Most of them had never taken anything apart before,” Pete chimed in.

“Hey! Don’t forget that Patty made me sit in on all of the presentations,” Rob added teasingly.

“So, what were your impressions?” the Professor asked.

“I was impressed by how professional their presentations were and what a thorough job they did,” Pete responded.

Their work was especially impressive considering that almost all of them had never done anything like this this before,” Rob added.

“Anything else?” the Professor asked.

“I was surprised that all of the photos that the students took were taken with a smartphone, even macro shots of small components.  I remember photos from smartphones of 6 or 7 years ago were almost unusable. Those that the students took this semester looked high definition to my eyes,” Patty added.

There was a little more discussion and, finally, the Professor had one last question.

“You all had a chance to see many teardowns. How did it impact your understanding of the state of technology?” the Professor asked.

Patty began, “Pete, Rob, and I discussed this topic quite a bit.  We had to admit that the thing that surprised us the most was that, of the 18 devices that the students analyzed, almost all had a wave soldered PCB with through-hole technology.”

“I agree, we noticed that every power supply board was a through-hole wave soldered board.  I think we only saw a PCB or two that was all SMT.  If the boards weren’t pure through hole, they were mixed technology.  Through-hole and wave soldering are here to stay,” Pete added.

Figure 2. A typical wave-soldered through-hole power supply board.

“We have to consider that most of the devices were lower tech: blenders, toasters, and one hair dryer,” Rob pointed out.

“But, the DVD player struck me the most. It had a mixed technology board in which one side was wave soldered, and a power supply board that was all through hole and wave soldered,” Pete added.

“I think those of us in the electronics assembly field become so enamored with smart phones and other high tech devices that have SMT-only PCBs that we forget that there are billions of lower tech devices that still use wave soldered through-hole boards.  The technology is cheap and it works, so why change?” the Professor summarized.

“So, wave soldering will likely be around for my grandkids!” Patty chuckled.

Pin-in-Paste Aperture Calculations Using Solder Preforms

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Folks,

The pin-in-paste (PIP) process is often the best choice when the PCBA is a mixed SMT and through-hole board with a small number of through-hole components. However, ensuring that the correct volume of solder paste is printed to ensure an adequate amount of solder for a reliable thorough-hole solder joint can be a challenge. One tool to help in this regard is the Pin-in-Paste Aperture Calculator. This calculator is now online at http://software.indium.com/. The solder volume equations were developed by good friend Jim McLenaghan of Creyr Innovation.

To estimate the right amount of solder paste, we need to calculate the volume of the plated though-hole, subtract the volume of the component pin, and add the volume of the solder fillet. See Figure 1.

Figure 1. Solder volumes in the pin-in-paste process.

Let’s assume we have the PCB and component pin metrics, as seen in the left hand column of Figure 2, under the header “Input.” Blue cells are inputs, green cells are calculations by StencilCoach. Notice that, if you have a rectangular pin, the software will calculate the equivalent pin diameter for entry into the “Input” cells. The “paste reduction factor” is the fraction of the paste volume that is solder. Most pastes are about 50% by volume flux, so, typically, this metric would be about 50% or 0.50.

Figure 2. PIP metrics.

The “Output” calculations are not really necessary for the task at hand, which is determining the stencil aperture dimensions, but may be of interest. The important stencil dimensions are shown in the “Stencil Metrics” section. Note that in our example, even though we have a 7-mil thick stencil, we would need a square aperture with a side dimension of 93-mils to get enough solder paste. With a circular aperture the radius must be >50-mils, if the pin spacings were 100-mils, there would not be enough spacing between the printed deposits, they would overlap. So we must use square apertures.

As in this case, it is a common problem with the PIP process to deliver adequate solder volume. If the PCB and component metrics are such that obtaining enough solder paste is an issue, it can be helpful to use solder preforms to increase the solder volume. The next post will cover this topic.

Cheers,

Dr. Ron

Is the PC (or Tablet or Smartphone) Dead or Dying?

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Folks,

We hear, on a regular basis, that the PC is dead or dying and will be replaced by the tablet. More recently, there is news that the tablet is starting to fade and even, most recently, that the smartphone is on the wane.

What is the truth? Many articles skirt around the issues, but few discuss them in detail. I believe that the driving forces behind the slowdown in sales of all of these electronic marvels can be understood by five factors:

  1. Memory Constants
  2. The asymptotic improvement of features
  3. Feature fatigue
  4. Device changeover hassle
  5. Cost

Let’s discuss them one at a time.

Figure 1. According to some, tablets are replacing PCs.

Memory Constants

My family purchased our first computer in 1986, an IBM PC XT. It was one of the early PCs that even had a hard drive. We opted for the biggest hard drive available, 20MB. The PC also had 512 KB of RAM. The Lenovo X230 PC that I am writing this post on has a 250GB solid state hard drive and 18GB of RAM, over 10,000 times as much of both types of memory as the XT. By 1989, the XT could not run the latest software, especially games like Where in the World is Carmen Sandiego? It didn’t have enough memory, so my kids were protesting. As a result, our family upgraded about every three years as games, operating systems, and office software demanded it. However, this trend has slowed dramatically. One of the reasons for this is what I call Memory Constants. One Memory Constant is that a photo is about 1 to 2MB of memory, as is a book. A song is about 5 MB. A movie is about 5,000MB or maybe as much as 15,000MB in high definition. Certainly a photo can be more than 2MB, but most of us shoot photos with a smartphone and these excellent photos are in this memory range. My 1986 PC XT could only store 10 photos or books and only 4 songs; my current PC, 10s of thousands of photos, books, or songs. With video streaming, very few people store movies on their PCs or tablets. So, with the tremendous amount of memory that PCs and tablets have, and with the advent of low cost USB memory sticks and external hard drives, upgrading a PC or tablet for lack of memory is uncommon.

The Asymptotic Improvement of Features

In 2005, I went to a blogging workshop with my good friend, Rick Short. At the workshop, Rick took a few photos with his smartphone. The photos were of so poor quality as to be unusable. Today, smartphone photos are of such good quality that many people have retired their cameras. Almost all features on PCs, smartphones, and tablets have asymptotically approached an excellent level of performance, such that a newer version just doesn’t have a striking benefit. In addition to a slightly better camera, the latest smartphone screens are a little sharper, but hardly enough better to justify getting a new unit. Admittedly, some new features, like Amazon’s 3D Mobile Phone might tempt someone to take the plunge. But, with so many features already on devices, additional new features just aren’t as compelling.

Feature Fatigue

Most of our devices have so many features that a new device isn’t as compelling as it was when smartphones, for example, did not have cameras or could not readily access the internet. In addition, many new features are added by software upgrades to an old unit. Combining this with the fact that people are increasingly reluctant to learn the myriad new command and sequence nuances for all the software on their devices and we have a general reluctance to upgrade. Of course, there will always be those that want the latest features, but they are becoming more and more like statistical outliers. So feature fatigue can limit sales of new units.

Device Changeover Hassle

It is a big deal to changeover a PC, smartphone, or tablet to a new one. It’s a lot of work, and if you are switching from say an iPhone to an Android, with unfamiliar software, it is a real hassle.

Cost

Many people now own a PC, smartphone, tablet, and e-reader. Not too many years ago it was just a PC and a mobile phone. Considering cost alone, it would be unreasonable to expect many people to constantly upgrade three or four devices.

Summary

To me, some of the headlines are almost comical, such as “The PC is Dying.” All of the personal electronic marvels that we depend on are alive and well; we are just starting to keep all of them a lot longer. One other thing to note: the PC and the tablet do not compete as much as a large smartphone competes with a tablet.

Cheers,

Dr. Ron

The False Positive Paradox

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Folks,

Let’s check in on Patty…

Patty was intensely preparing a lecture on Bayes’ Theorem. She always felt that this theorem was the most profound in probability and statistics. She remembered a real application, when her best friend took the Tine test for tuberculosis before she got married – and tested positive. The test claimed to be 99.9% accurate in identifying someone with TB. Her friend was devastated to find out that she apparently had this ancient, dreaded disease. Further investigation uncovered that the 99.9% number was more accurately stated as, “if you have the disease, this test will pick it up 99.9% of the time.” There was an important number not told: false positives. This rate was 5%. With so few people having TB, a 5% false positive rate would indicate that almost everyone that tested positive for TB, would be a false positive, hence not have TB. So it was, much to the relief of many, with her friend. This situation is an example of the false positive paradox.

While Patty was deep in thought, she was startled by the sound of her phone ringing. She looked at the area code and exchange and knew it was from her old company, ACME. She picked up the phone.

“Professor Coleman,” Patty answered. She liked the sound of that.

“Hey, Patty! It’s Reggie Pierpont!” the cheery voice declared.

Patty’s heart sank. Reggie was an OK guy, but he always got involved in things he didn’t understand and often convinced management to pursue expensive and ineffective strategies. He was that persuasive.

“Reggie, what’s up?” Patty said half-heartedly.

“Well, Madigan insisted I call you before we order some new testers. I think it is a waste of your time, but I’m following orders,” Pierpont said.

“What are the details?” Patty asked.

“We have a contract to produce one hundred thousand Druid mobile phones a week. We are confident our first pass yield is greater than 99%,” he began.

“Impressive,” Patty said with sincerity.

“I want to order some testers that identify a defective phone in a rapid functional test with 99.9% certainly. The testers are very expensive, so Madigan wants a sanity check before buying them. The other important info is that we get a huge penalty from the customer for any defected phone we ship,” Reggie continued.

“Well, with a large penalty, 99.9% is the right number. What do you do with the units the tester determines are defective?” Patty asked.

“Well, it is a good thing yields are high. The phones are so complex that we have quite a drawn out process to find the defect and fix it. Just finding a defect can cost $5 to $10 dollars in burdened labor, but, considering the value of a phone, it’s worth it. Like I said, it’s a good thing yields are high so we don’t have too many units needing this procedure,” Pierpont continued.

“What about false positives by the tester?” Patty asked.

“Shouldn’t be a problem, remember the tester is 99.9% accurate,” Pierpont answered.

Patty knew that Pierpont was missing her point, but she didn’t want to embarrass him……too much.

“Reggie, from what you told me, if a unit is defective the tester will catch it 99.9% of the time. What I am asking is, if a unit is good, how often does the tester say it is bad? This situation is usually called a ‘false positive’,” Patty responded.

“Well, it would be 100 – 99.9 or 0.1%,” Pierpont replied.

“That’s the percentage of bad units that would be called good. These units are often called ‘escapes.’ The only way to determine false positive rate is by a test, you can’t determine it from the 99.9% number,” Patty went on.

There was silence at the other end of the phone.

“What do I need to do to get the false positive number?” Reggie asked.

“You need to test about a 1,000 known good units and see how many the tester says are bad,” Patty said.

“I’ll do that with the loaner tester the tester company is letting us use and get back to you,” Pierpont replied.

Patty hung up the phone. She thought it interesting that Pierpont’s problem was so closely related to both Bayes’ Theorem and her friend’s false positive with the Tine test.

Two days went by and Patty, Rob, and Pete had just returned from lunch with the Professor. They would all meet with him quite often to discuss technical problems they were having. So, they offered to treat him to lunch.

As she walked into her office, Pete spoke up.

“Did Reggie Pierpont ever get back to you?” Pete asked.

“No, maybe I’m off the hook,” Patty chuckled.

At that instant, her phone rang. It was Pierpont.

“Hey, Reggie! What’s up?” Patty asked with more enthusiasm than she felt.

“Well, the tester says 5% of the good units are bad, I think you are going to tell me this is a problem,” Peirpont began.

“What if you run them through the tester again?” Patty asked.

“That IS running them through two or more times! If we run them through just once, it was 7%,” Reggie sighed.

“Well, let’s look at the numbers. You are making 100,000 units a week, with a 5% false positive rate that’s 5,000 units. Your yield loss is 1% or 1,000 units. So, you will have about 6,000 units the tester will declare as bad when only 1,000 really are. These numbers are off a little bit. Bayes’ Theorem would give us the precise numbers, but these are very close. Since your process to analyze fails after the tester costs at least $5 per unit, you will be losing $25K per week due to false positives,” Patty elaborated.

“Time for a new strategy,” Pierpont sighed.

Patty and Pete agreed to help Pierpont work with the tester vendors to develop a better strategy.

Epilogue

Patty and Pete helped Pierpont develop an effective test strategy working with a tester vendor. Neither Patty nor Pete had known Reggie well before… but, after this joint effort, they grew quite close. Reggie became quite engaged in the process and seemed to learn quite a bit. Patty was able to use some of the data in her classes.

A few weeks later she got a beautiful card in the mail. She opened it. It read, “Dear Patty, Thanks for all of your help. We wouldn’t have made it without you and Pete helping us with our testing strategy. Best Regards, Your faithful student, Mike Madigan.”

Patty got a little choked up.

Cheers,

Dr. Ron

Demonstrating Zero Defects In SMT Production?

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Folks, let’s see how Patty is doing at Ivy U …

Patty had to admit that she really liked being a professor at Ivy University. No, that wasn’t strong enough; she was ecstatic. The combination of the stimulating and collegial environment and the flexible schedule was terrific. She was able to play a little more golf and spend more time with Rob and the boys. 

In addition to developing a course on manufacturing processes, she was asked to teach an additional offering on statistics. Engineering enrollments had increased so much that another stats class was needed. Teaching stats gave her an opportunity to delve into topics she was interesting in learning more about, such as non-parametric analysis, cluster analysis, and numerous other statistical concepts.

She was also happy for Pete. As much as he enjoyed working with her at ACME, he, too, was thrilled to be at Ivy U. As a research associate, he spent a lot of time working with students on projects for their classes. He was surprised at how grateful the students were for his practical experience.

As Patty was thinking these pleasant thoughts in her office, suddenly Pete was at the door.

“Hey, Professor Coleman! The folks we left behind at ACME are being asked, forced really, to guarantee zero defects by examining a small sample size, say 20 samples,” Pete announced. Pete had stopped calling her “kiddo” and now teased her by calling her “Professor Coleman.”

“We both know that’s impossible. Tell me more,” Patty answered.

“Well, ACME just hired our favorite SMT engineer … after Hal Lindsay,” Pete responded.

“Oh, no! Not Reggie Peirpont,” groaned Patty.

Reggie was a well-meaning sort of chap who had some good ideas. But, his follow through was often sloppy and only touched the surface of what was needed from an engineering perspective. He was a very good salesman of his ideas and had a following in some SMT circles.

“What is he foisting on ACME?, Patty asked.

“A zero defect program,” Pete replied.

“Sounds like a worthy goal. But, let me guess, he has convinced everyone that they can demonstrate with 95% confidence they have zero defects by only sampling 20 units,” Patty said.

“Precisely,” Pete chuckled.

“I’ll contact Mike Madigan,” Patty said.

Patty had agreed to Mike’s request that she be available to consult for a year or so. And, he also made her promise to contact him if she knew they were doing something foolish.

Patty sent Mike an email with her concerns, and with some analysis. She suggested a teleconference.

Time passed quickly and, before they knew it, Patty and Pete were on a telecon with Madigan, Peirpont, and a few staff people.

Their discussion started with the good points of a zero defects program. On this topic, everyone was in agreement. Eventually, Madigan grew impatient.

“Peirpont! According to Coleman, your assessment that we only need to sample 20 units to demonstrate zero defects with 95% confidence is bull s__t.” Mike began, always getting quickly to the point.

Patty then said, “Let’s let Reggie explain his analysis.”

“Well it’s simple,” Reggie began. “All you have to do is recognize that 1 is 5% of 20, so if you sample 20 and don’t get a defect you can be 95% confident you have no defects,” he finished.

“Yikes,” Patty thought.

“Well, Coleman?” Madigan asked.

“That approach is not correct. A correct method is what I sent to Mike in an email” Patty answered.

“Before we begin the analysis, look at the photo I sent. The red bead is one bead in 2,000 white ones. Ask yourself how you could detect this one “defect” by sampling only 20 beads?” Patty said.

There was some murmuring and groaning, Patty could tell this visual really help to define the issue.

“OK, Patty. Please explain your analysis,” Mike asked.

“Let’s say that the defect level is 1 in a thousand. If I sample the first unit, the chance it is good is 0.999. What is that chance that the first two units would be good?” Patty began.

“0.999*0.999,” Pete answered.

“Correct!” Patty said.

“Let’s say I keep sampling until the likelihood that I have still found no defects is 0.05,” Patty went on.

“Let me take this one,” Madigan said.

“You now have 0.999^n = 0.05. So there is only a 0.05 chance you would not have found a defect if the defect rate is one in a thousand,” Madigan continued.

“So what could you say about the defect rate if you found no defects in n units? Patty asked.

“I got it! I got it!” Madigan shot back enthusiastically.

Patty was incredulous. Mike Madigan, CEO of multibillion dollar ACME Corp, was like a second grader excited to show the teacher he understood.

“You can say that the defect rate is 1 in a 1000 with a confidence of 1–0.05, or 95%,” Madigan said with excitement.

“Actually, you can say that the defect rate is 1 in a thousand or less,” Patty said.

“But we need to know n,” Madigan implored.

“Well, let’s solve for n with logarithms,” Patty suggested.

Groaning was heard over the telecon. No one likes logarithms!

Since their telecom was on GoToMeeting, Patty showed the solution:

n = log 0.05/log .999 = 2994.23

“Man! So we have to sample almost 3,000 units with no defects to demonstrate 1 defect per 1,000 or less?” Madigan asked with disappointment in his voice.

“Yes,” Patty responded.

She continued, “It ends up with a good rule of thumb. Since n is close to 3,000, let’s say that is the number we need to analyze. To demonstrate 1 in 10,000 defects or less, n is 30,000, one in a million or less, and n is 3 million.”

“So, n is 3 times 1 divided by the defect level you are trying to establish?” Madigan asked.

“Exactly,” Patty answered.

Patty wrote it on the PowerPoint slide:

To establish a certain defect level or less with 95% confidence, one must sample n units with no defects

n = 3 x 1/defect level

“That means to establish zero defects, we need an infinite sample,” Madigan sighed.

“Yep!” Patty replied.

“Peirpont! What do you have to say for yourself?” Madigan barked.

“Well, in the first case, Patty said 1 defect per thousand or less. It still could be zero defects,” Peirpont responded glumly.

Patty was going to respond, but Madigan beat her to it.

“But, you can’t prove it is zero. Only 1 in a thousand or less. So, to be conservative, we would say that the defect level would be 1 in a 1,000. That’s what is proved,” Madigan opined testily.

The meeting ended with Madigan expressing his thanks, an unusual thing for him. Peirpont said little else. It was clear he was probably going to get a talking to by Mike Madigan.

Patty was a little wistful after the meeting. She missed ACME and the folks there, even the occasionally cranky Mike Madigan. But every day she felt more like her home was at Ivy U.

Cheers,

Dr. Ron

Epilogue. As with all Patty and the Professor posts, this one is based on a true story. After sharing this concept with a colleague who had to get FDA approval for drug trials, she decided to ask statistician job applicants: “Do you think you could develop a sampling plan that could assure with 95% confidence that there were no defects in a population?” The last I talked to her, most job candidates had said yes.

Sample Size is Important in Weibull Analysis Too

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Some time ago I posted on “The Curse of the Early First Fail” and “Interpreting Weibull Plots.” Both of these posts related to using Weibull analysis to make sound engineering decisions.

Recently, a reader asked if sample size is important in Weibull analysis. It is interesting that few who do Weibull analyses discuss the effect of sample size. So, let’s do it now. Consider Figure 1. This figure shows Weibull analysis used to compare cycles to fail for Alloy 1 and Alloy 2. Considering that the slope of each curve is about the same, most people would say that since the scale for Alloy 2 is greater (1320 versus 1172), Alloy 2 is superior. But, is the difference statistically significant? By using a simple Two Sample t Test, we can analyze the data and find that there is only a 62% confidence that Alloy 2 is better than Allot 1. Flipping a coin gives us 50% confidence, so this result is not encouraging. Four samples is seldom enough to make a confident engineering decision.

Figure 1. A Weibull plot of Alloy 1 and 2 with only four samples.

If we perform the experiment again with 20 samples, we get the Weibull analysis as shown in Figure 2. Note that although the scale parameters have not changed too much, the shape parameters have changed significantly. The original 4 sample test is just not enough to really lock in on the real shape numbers for the samples. By also performing a two sample t test on the 20 sample data, we now find we have a 99.6% confidence that Alloy 2 is superior to Alloy 1. So, with 20 samples we can confidently say that Alloy 2 is superior to Alloy 1.

 

Figure 2. A Weibull plot of alloys 1 and 2 with 20 samples.

What is the minimum sample size for your test to be confident in the result? It can vary quite a bit and only by analyzing the data with a t test, after the experiment, can you know for sure. But my experience would suggest that you should never have less than 10 samples, and preferably 15 or more.

Cheers,

Dr. Ron

 

An Example of Cpk and Non Normal Data In Electronics Assembly Soldering

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Folks,

Let’s see how Patty is doing after teaching her first class at Ivy U…

Patty arrived at home after teaching her first class at Ivy U and she couldn’t contain her excitement. For the next couple of hours her husband, Rob, had to politely listen to her talk about how amazing it was to teach the young, bright, enthusiastic, future engineers.

Time went quickly and, before she knew it, she was standing in front of the class for her second lecture.

Patty reviewed quickly the fact that it was incorrect to average Cpks and that, to calculate a Cpk, the data should be normally distributed.

“The question was asked last time, how one can tell if the data are normal? Minitab can be used to plot the data on a normal probability plot. By eye, we can get a good sense if the data are normal or not. In addition, Minitab will perform various tests, one of them being the Anderson-Darling Normality Test,” Patty began.

“Let me show you some real data to demonstrate this,” Patty continued.

“When assembling a smartphone like the new Druids, the mechanical tolerances for the many tiny capacitors and resistors are very precise. One common capacitor size is only 0.6mm long.” Patty paused as she saw a student’s hand raised.

“Yes, Martin?” Patty asked.

“Professor, you mean 0.6cm, right?” Martin asked.

“No, 0.6mm,” Patty answered.

Patty’s answer caused quite a bit of murmuring, finally Patty had to ask for order.

“Why is everyone surprised?” Patty asked.

“Professor, that is much smaller than a grain of rice, it is more like the size of a grain of sand,” Alison March responded.

“This is fun,” Patty thought, “and good timing.”

Patty showed a slide of passives on a match head and passed around a teardown of Druid smartphone with a magnifying glass so that the students could see how small the passives were.

It took a while for the class to calm down.

Patty then said, “And about 200 to 500 capacitors and resistors of this size are individually placed and soldered in the electronics assembly process in each smartphone.”

The student’s mouths were agape.

“OK, let’s discuss how these little rascals relate to SPC. My company orders billions of these electrical components each year. We are sent a sample lot to approve a larger order. For the components of interest, we already know that the mean length is 0.6mm, the 3 sigma (standard deviation) tolerance is +/-0.03mm. So, the lower spec limit is 0.57mm and the upper spec limit is 0.63mm. This equates to a Cpk = 1.00,” Patty went on.

Patty put a PowerPoint slide up that showed the data.

“The data for the sample lot is on the left. What is the problem?” Patty asked.

Charles Parsons raised his hand.

“Yes, Charles?” Patty asked.

“Well, Dr. Coleman, the standard deviation for the data is 0.15 and the resulting Cpk is only 0.67, so the targets are not met” Charles answered.

“Precisely,” Patty replied.

“We then went back to the supplier and asked them to fix the problem. The graph on the right is from the capacitors they sent us 3 weeks later, after they claimed to have solved their manufacturing process problems,” Patty explained.

“What do you think?” Patty asked.

There was a lot of murmuring. Finally DeShaun Martin raised his hand.

“Yes, DeShaun?” Patty acknowledged him.

“Well, Professor, it looks like they simply sorted out the parts to make the sigma lower and Cpk higher,” DeShaun responded.

“Precisely,” Patty said.

“I don’t see what is wrong with sorting,” Sandy Lisle commented.

“You see from the Druid smartphone that I passed around that it is so densely packaged with components that there is hardly any room in it. To achieve this density we have to perform tolerance analyses to assure everything will fit. In all of these analyses we model with normal distributions. With a sorted distribution we will likely have more tolerance interferences,” Patty answered.

“Look at the red arrow. There will be an excess of components with this size and a lack of components of the size where the green arrow is pointing. These differences will cause some tolerance interferences with the pads on the printed wiring board where the passive will be assembled,” Patty continued.

“Can you review? How we can tell that the distribution on the right is not normal?” Conor Stark asked.

“Sorry, I almost forgot. Look at the normal probability plot for the sorted data. Note how it diverges from the straight line on the ends. Also the Anderson-Darling value for p is <0.05. These two criteria are cause to reject the hypothesis that the data are normal,” Patty finished.

Patty was just wrapping the class up when someone raised their hand.

“Yes, Natalie?” Patty asked.

“What was the final outcome?” Natalie asked.

Patty chuckled, obviously she should share he result of this adventure.

“Oh, yes. We could not use the parts for the Druid smartphones, but they were OK for some toys we were assembling. In addition we insisted on a 30% discount, since the passives did not meet the specification,” Patty answered.

As she was cleaning up, two of the female students came up to Patty. One them, Justine Randall spoke for the two.

“Professor Coleman, you are an inspiration for us. We hope in 20 years we can be just like you,” Justine said with emotion.

Patty was indeed touched, but as she left the classroom, she decided that she had to start dyeing her hair.

Cheers,

Dr. Ron

 

Cpk Can Only be Calculated from Data that are Normally Distributed

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Folks,

Let’s look in on Patty….

Patty was really nervous. As a matter of fact, there was no time she remembered being this nervous. The cause of her nervousness? She was going to teach a series of classes at Ivy University.

This opportunity came about because one of the professors at IU was in a serious accident. A full recovery was expected, but there was no way the prof could finish the last three weeks of the statistics course she was teaching. Things are hopping in the Engineering Department at IU, and the Dean could not find another prof to take over.

The Professor himself was too busy, however, when the Dean asked his advice he immediately recommended Patty. Patty was honored by the request and would be more so if she knew the behind-the-scenes story. IU has an unwritten rule that all teaching profs had to have a Ph.D., which Patty did not. However, if Bill Gates wanted to teach, an exception would be made, as he is a world class technical executive. Patty was hired under that exception. She was stunned to see she was on the front page of “The Ivy U Review,” under the headline, “Famed Executive to Teach at IU.”

Well, her first class was tomorrow and she took comfort in the fact that her husband, Rob, told her she shouldn’t be nervous. Pete wasn’t much help. He told her he would be so nervous that he wouldn’t be able to eat. It was just unnerving teaching the best and the brightest. She was proud of her academic accomplishments at Tech, but this was IU, arguably one of the top 10 universities in the country.

“Rob, I have to tell you, even though I’m still nervous, it comforts me to know that you wouldn’t be nervous,” she said to her husband.

“I never said I wouldn’t be nervous, I said you shouldn’t be nervous. After all, you’re Patty Coleman,” Rob replied.

At this Patty burst into tears and Rob came over and gave her a big hug.

“But, you’re smarter than me,” Patty insisted.

“No way,” Rob replied.

They then spent the next 10 minutes arguing that the other was smarter. Patty always felt she had a good business sense, but for understanding deep technical things, she believed Rob was her superior. After a while they looked at each other and laughed.

“Not too many couples would get in to an argument, saying that the other person was smarter,” Rob teased.

Time passed quickly and Patty was soon in front of the 35 students in the class. The topic was Cpk as the most important metric to determine the quality of a lot of material or product. She asked the students if it was OK to average Cpks from different lots. A student raised her hand.

“Yes Emily.” said Patty. (Patty had ask the students to use nametags.)

“No, Professor Coleman. One can’t average Cpks. The reason being that Cpk goes as one over the standard deviation and standard deviation is a squared term. So one can’t average two lots and get the same result as taking the Cpk of all of the two lot data.

Patty responded, “Emily is 100% correct. Remember, when you get out in the working world, to always check to see that your suppliers are not averaging Cpks. This might happen when half of the lot is below the spec, say the Cpk is 1.4 and the spec is 1.5 and the other half is over the spec, say 1.7. The supplier will say that the lot is in spec because the average Cpk is 1.55. This isn’t necessarily so, as Emily points out. You should only accept a calculation of Cpk for the entire lot.”

Patty chuckled that Emily thought she was a Professor, at Ivy U. Right!

The class continued to go well and Patty began to relax. As the class began to end, she mentioned another important point.

“What important criteria must the data have to be considered acceptable to calculate Cpk?” Patty asked.

There was a bit of murmuring and finally a boy (man?) raised his hand. He looked 12 years old to Patty.

“Yes, William,” Patty acknowledged him.

“Dr. Coleman, I think the data must be normal,” William answered.

“Dr. Coleman?” Patty thought.

“Absolutely correct, William,” Patty responded.

“Class, remember this point when you get out into industry. Almost no one checks to see that the data are normal before calculating Cpk. The data must be normal to calculate Cpk. I can’t tell you how many times I have rejected a lot of incoming material because the Cpk was calculated from non-normal data. In some cases non-normal data can be transformed so that the data are normal, “ Patty continued.

“Professor, how do we know if the data are normal?” a student named Kathy asked.

“Stay tuned for the next lecture,” Patty chuckled and dismissed the class.

As she was gathering her laser pointer, lap top etc., a number of students came to talk to her. Emily was with a group of about six of them.

“Professor, we just wanted to tell you that we are thrilled to have you as our instructor. We appreciate your practical, real world perspective on statistics,” Emily said.

Patty responded warmly and was close to being choked up by this show of respect and appreciation. She decided she would walk to The Professor’s office to tell him how it went.

On the way out, she heard one of the male students say to his friend, “You know, she is quite attractive for an older woman.”

Patty didn’t know whether to laugh or cry.

Cheers,

Dr. Ron

Lack of Concern for Tin Pest as a Reliability Issue in Mission Critical Products Still Hard to Understand

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Folks,

My recent post on tin whiskers sparked the memory of tin pest in my mind. I have to admit, that with all of the legitimate reliability concerns related to tin whiskers, I am surprised that there has been essentially no parallel concern for the risks of tin pest.

Admittedly, tin pest is much more rare than tin whiskers. Although many complain that we don’t understand tin whiskers, we can create them easily and make the vast majority of them go away. Whereas, it has been shown to be very difficult to create tin pest.

For those who want a refresher on tin pest see this blog posting or my survey paper “Tin Pest: Elusive Threat in Lead-Free Soldering?” Journal of Failure Analysis and Prevention, vol. 10, no. 6, December 2010 , pp. 437-443(7).

Tin pest is a result of an allotropic transformation of tin from its beta phase (white or normal tin) to its alpha phase (gray tin) at temperatures below 13oC. This transformation is accompanied by a change in density from 7.31 g/cm2 to 5.77 g/cm2. The reduction in density requires the tin to expand, thus destroying the structure of the original tin object or solder joint as seen in the figure below.

With tin pest being so rare, why am I concerned with it as a reliability exposure? With billions of solder joints in mission critical circuit boards exposed to cold for many years, it would seem inevitable that some tin pest would form. The effect of the cold is cumulative, it does not get reversed when the weather becomes warm. Applications most at risk would be automobiles, mobile phone towers, and military equipment.

I wouldn’t be surprised that, with typical tin whisker mitigation, that unmitigated tin pest might be more common.

What is the fix? By adding about 0.5% antimony or 2% bismuth to lead-free solder, tin pest can be essentially eliminated. An added blessing would be suppression of tin whisker formation also. However, adding even these small amounts of antimony or bismuth to lead-free solders would require a thorough evaluation. Even these small additions of alloying elements can dramatically change the properties of a solder.

Best Wishes,

Dr. Ron

Density Calculation Still Raises Questions

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Folks,

It is hard to believe, but I have been blogging now for over 8 years. In all of that time, the most popular topic by far has been the calculation of alloy densities. Many people are troubled by the required equation. At first blush it doesn’t seem logical. I have derived it, but here is an effort to try and make it more intuitive.

A reader wrote the following, which inspired my explanation that follows.

Craig writes:

Why do we calculate the theoretical density of an alloy by using the formula of:
1/Da = x/D1 + y/D2 (binary) or
1/Da = x/D1 + y/D2 + z/D3 (ternary) as opposed to multiplying the individual metals’ densities by their percentages in the alloy and adding them together ? I thought the density of an alloy would be analogous to a weighted average of the densities of the metals in the alloy. Obviously, that is wrong, but I don’t understand why?

The reason you have to use the non-obvious formula is that density is given as mass/volume. So there are two quantities to be concerned with, and one is inverse (i.e. volume is 1/volume in the density formula). So you have to use the equations above, or you will be in error. I derived these equations in a previous post. However, many people do not find the result intuitive.

Here is, hopefully, a more intuitive example. Let’s say, for some strange reason, you were interested in inverse height. So let’s say John is 5 feet at his shoulders, or 1/5 inverse feet. His girlfriend Kathy is 5 feet tall, also 1/5 inverse feet. Kathy stands on John’s shoulders. How many inverse feet is their total height? The tendency would be to say they are 1/5 +1/5 = 2/5 inverse feet. But we know that when Kathy stands on John’s shoulders they span 10 feet, so they must be 1/10 inverse feet. So, to calculate their height in inverse feet, we need to use:

1/IFT = 1/John IF + 1/Kathy IF = 1/(1/5) +1/(1/5) = 10

IFT = 1/10

Note: (IFT = Inverse Feet Total)

The same is true for density, since density = mass/volume (inverse volume is like inverse feet).

Another engineering example is electrical resistivity and conductivity. If the resistance of one wire is 2 ohms, and another is 1 ohm, and we connect them in series, the total resistance is 3 ohms. However, if we consider conductivity, one wire has a conductivity of 0.5 mho and the other 1 mho. Again, to get the total conductivity we don’t add the conductivities, we must use:

1/Ctotal = 1/C1+1/C2 = 1/0.5 + 1/1 = 2+1 = 3. So Ctotal = 1/3 mho.

I hope this helps.

Cheers,

Dr. Ron