Category Archives: Dr. Ron

Materials expert Dr. Ron Lasky is a professor of engineering and senior lecturer at Dartmouth, and senior technologist at Indium Corp. He has a Ph.D. in materials science from Cornell University, and is a prolific author and lecturer, having published more than 40 papers. He received the SMTA Founders Award in 2003.

Alloy Melting

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Folks,

Richard asks:

Dear Dr. Ron,

Recently we had a solderability problem with tin-finished component leads and SAC305 solder paste.  One of our engineers claimed that the problem was that the tin finish melts at too high a temperature (Tm= 232°C) for the SAC305 solder paste (Tm = 219°C) to melt it.

My understanding is that certainly above 232°C both will melt and form a good solder joint, but even if the temperature was less than 232°C, say 225°C, the tin would melt. Can you explain this phenomenon?

Richard,

Thanks for this question, which can be interpreted two ways. The first would be that, in a reflow oven at temperatures above the melting point of both metals, the one with higher melting temperature prevents the metal with a lower melting temperature from melting it. This is not true, since both metals would come near to the temperature of the air in the reflow oven and melt.

The other perspective would be that the temperature in the reflow oven is above the melting temperature of SAC 305, but below that of tin. So, how can the tin melt?  To consider this situation let’s say the oven is at 228°C. Will the tin on the lead or pad finish melt? The answer is yes. But, let’s try to understand the phenomenon with gold and tin first.

Metals that have extreme melting point differences often dissolve in each other. As you stated, tin melts at 232°C, whereas gold melts at 1064°C.

This phase diagram can be found here.

Figure 1. The gold tin phase diagram

To make a gold-tin solder, all one has to do is have a bath of tin at some moderate temperature, say 350°C. Insert the gold and the gold will melt and flow into the molten tin. This is true even though the gold melts at 1064°C. This effect can be shown experimentally. A similar phenomenon exists with gold and mercury. Mercury reacts with gold at ambient temperatures. The phenomenon can be used to extract tiny gold particles from soil and is commonly used today in artisanal gold mining. Unfortunately this use of mercury is often toxic to the miners and pollutes the environment.

Considering electronics assembly solders again, let’s assume that some liquid tin-lead solder is heated to 200°C. See Figure 2a. As seen in this figure, a ball of tin at 25°C is held above the molten tin-lead solder. The ball of tin is immersed into the molten tin-lead solder in Figure 2b. The tin-lead solder forms a meniscus around the solid tin. Even at room temperature the tin atoms are vibrating, and as a result, some of these atoms on the tin ball will end up flowing into the tin-lead solder. This action will leave a vacancy in the tin ball that may be filled by a lead atom from the tin-lead solder. In the vicinity of the newly arrived lead atom, the melting temperature of this micro spot of tin-lead alloy will be lowered as tin-lead solder has a melting temperature below that of tin. This process will continue until all of the tin will intermix with the tin-lead solder and flow into it as seen in Figures 2c through 2f.

Figure 2a Figure 2b Figure 2c Figure 2d

 

Figure 2e

 

Figure 2f

Cheers,

Dr. Ron

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.

Electronics Assembly Process Optimization

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Mike Madigan was not used to feeling intimidated.  After all, as the CEO of ACME, a multi-billion US dollar EMS company, he was used to doing the intimidating.  However, he had just finished a meeting with the CEOs of his two biggest customers and it was a disaster.  They asked to “do lunch” with Mike and, after this event, Mike’s stomach was churning.  If Mike was honest with himself, if he was them he would have been tougher.  But, it was their teasing demeanor, punctuated with laughs and jokes, that made it all the worse.

That these gentlemen had some points to make was inarguable.  First-pass assembly yields were down 4%, and Mike’s answer, that it was because the technology was more challenging to assemble, did not fly.  They told him to get that 4% back or they will find a company that can.

Both of these gents had been process engineers when they were younger, so they “knew the ropes.”  In a recent audit of one of ACME’s facilities, they found one process engineer, responsible for the stencil printing process, that didn’t know how to run the stencil printer. And this lad also could not locate the solder paste spec.  Additionally, he could not explain what “response to pause” was.  Another process engineer did not know how to match the reflow profile to the solder paste spec (after they finally located the spec). Mike’s answer, that ACME’s recent growth made it hard to keep the training of the engineers up to snuff, only made things worse.

When asked what percent of his engineers hired in the last two years were SMTA certified, Mike didn’t know.  He expected it was 0.

Then, one of the CEOs said, “Things seemed to be much better when you had that Advanced Processes VP. What was her name? Patty something or other?”  That was a big part of the problem. Patty Coleman was gone and, with her departure, things had gone to h#!!.

Mike thought of asking Patty to fix things, but that would be unfair.  She had only been at Ivy U for a year or so and was still getting established.  Maybe the Professor could help.  Mike hoped so. The CEOs wanted a plan in two weeks.

Ten days later…

Patty had just finished getting ready for a meeting with her husband Rob, Pete, and the Professor.  Ten days ago, the Professor asked if they could help him develop a software tool that would be used by ACME as a self-audit of their practices related to electronics assembly.  The Professor said it was a request from Mike Madigan himself.

Patty had a little time before the meeting, so she decided to check her email.  Suddenly, she was disturbed by a knock at the door.

“Professor, we wanted to ask you a question about probability. Is now a good time?”, a young lad who looked 11 years old asked.

“Sure.” said Patty.  “But tell me your names first.”

“Oh!, Sorry! I’m Henry Finn. But everyone calls me ‘Huck’. And this is Chris Jenkins.  We’re both sophomores.  You spoke about statistics at our Introduction to Engineering Class a few days ago. We’re hoping you can settle an argument,” Finn began.

“What is it?” Patty asked,

“Well, Huck says that since the Patriots are one of 32 teams in the NFL, the chances of them winning 4 Super Bowls is (1/32)^4 = 9.5×10-7, or about one in a million – if they had only an average skill level.  I think it is more than that.  Huck says the rarity of them winning four Super Bowls shows how much above average they are,”  Jenkins jumped in.

“Your analysis is not quite right. You calculated the likelihood of 4 wins in a row. They have won 4 out of the last 14 Super Bowls,” Patty said. Patty was on top of the Patriots stats as she was a big fan.

“To perform the analysis, you have to use the Binomial Distribution.  Let me see if I can calculate it using Minitab 17,” Patty said.

She went to her laptop and, in no time, had a graph that explained the problem.

“So, the chances of a team possessing only average skill winning 4 out of 14 Super bowls is less than 1 in a thousand.  I’ll leave it to you two to decide what that means,” Patty summed up.

Patty chuckled to herself as she saw the two sophomores arguing as they walked away.

She looked at her watch and saw it was time to head to the Professor’s office.

Patty was the last to arrive as Rob and Pete were already there. As she sat down, the Professor began.

“Thank you for coming.  I have incorporated all of your input and am pleased with the results.  I’m hoping that we can review the resulting web application that was developed,” the Professor began.

“Is it in English or one of the 17 other languages you speak?” Pete joked.

“English, Pete. English,” the Professor chuckled.

In reality, Patty, Pete, and Rob were thrilled to help the Professor develop this self-auditing software.  They all knew that it isn’t that often that one can help someone like him.

The Professor was only able to come up with 20 questions for the software.  Patty, Pete, and Rob increased it to 40. Pete was proud that he contributed 8 of the additional twenty questions.

The Professor flicked on his projector and displayed the first page of the self-auditing software.

“This is the first of the four sheets for the software tool.  I think Rob’s suggestion to name it ‘AuditCoach’  is a great idea.  Let’s take a look and see what we think,” The Professor said.

“I think it’s good that you have the questions about the process engineers knowing how to run and optimize the equipment.  It is surprising how many times that is not the case,” Patty commented.

“That was Pete’s idea,” the Professor replied. Pete beamed from the recognition of the Professor.

“I like the idea of making the first question count 3 times as much since it is so critical,” Rob chimed in.

“Agreed,” Patty and Pete murmured.

The Professor pressed on, “I thought it might be best to break the questions in to four categories:

  1. DfM, Processes
  2. Equipment, Materials Supply and Validation
  3. DOE, SPC and CIP, and
  4. Training and Failure Analysis.

Over the next hour the group reviewed all 40 questions on the four sheets of AuditCoach. Some minor improvements were made.

As they were wrapping up, the Professor had one last comment, “I asked Mike Madigan if he would make AuditCoach available to others.  We both thought that doing so was a good idea.”

Cheers,

Dr. Ron

 

 

What is Cicret and Why is It Important?

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Folks,

Let’s check in on Patty …

Patty had to admit that she was getting annoyed. Two of the female engineering students were always going to her husband Rob’s office for help with their homework. At first glance this would seem like a normal thing to do, as Rob was a teaching assistant for the materials science class they were taking as part of his Ph.D. program at Ivy U. But they were there every day. And Patty could tell that they had more on their minds than materials science.

Rob was approaching his mid-thirties now, but had boyish good looks and was in athletic physical condition. He looked just like all of the twenty-something PhD students that were his peers. Patty remembered when she and Rob became engaged, her best friend Jan Curtis said, “Patty you are a lucky girl. In addition to being smart, successful, kind, fun, and interesting, Rob is handsome and cute!”

So it is not surprising that these two engineering females would find Rob attractive. To add insult to injury, these two young ladies just happened to be Justine Randall and Jessica Wu. They were the two students who innocently said to Patty, “Professor Coleman, you are an inspiration for us. We hope, in twenty years, that we can be just like you.”

This quote triggered the beginning of Patty’s relationship with hair dye.

It didn’t help that Rob could not wear his wedding ring, because it was a danger in the experiments he was doing for his research. It had been off for so long that even the tan line had faded.

To Rob’s credit, he was doing nothing to encourage any interest, but Patty wanted to set these two young girls straight. She had purposely not told Rob that she could not pick their twin sons up from daycare. She would do so when Justine and Jessica were in Rob’s office. She would know they were there, as they had to pass by her office on the way to Rob’s.

Just then, they walked by. Patty gave them a few minutes and then she went straight to Rob’s office. She tapped on the open door and stuck her head in.

“Honey, I forgot to tell you that I can’t pick the boys up from day care, I have a meeting with the Dean,” Patty said to Rob.

“No problem. It’s way past my turn to get them anyway,” Rob responded.

Justine and Jessica looked like they just found out spring break was cancelled.

“Justine, Jessica, I believe you have met my lovely wife, Professor Coleman?” Rob said.

After a few pleasantries, Patty left, feeling relieved. However, she decided Rob definitely needed a photo of her and the boys prominently displayed on his desk.

After entering her office, she set her new adjustable desk to the standing position. She then noticed that she had just received an email from Mike Madigan. It read as follows:

Patty,

The board is considering buying a start-up that has developed a new device called The Cicret. See this video.

They claim they can develop a prototype for $1 million. My gut tells me that they are dreaming. But, if I am wrong, it is too good of an opportunity to pass up.

I’m hoping you can meet with Jan Curtis and Phil Anderson and come to a consensus on what the opportunity is.

Let’s have Anderson write the report to reduce any extra workload on your part.

Your faithful student,

Mike,

BTW, thanks for helping my son at West Point. Fortunately he has inherited all of my wife’s good points and none of my bad ones!

Patty continued to marvel in the change in Mike Madigan. Much of his aloofness and grouchiness had worn off. Patty then went and looked at the video and was blown away. Her first thought was, “I want one.” Then she went to the company’s website and saw that they had yet to make a prototype. She thought that the company’s request for donations was comically cute, but did not foster confidence.

As she was mulling this over in her mind, Pete came to the door.

“Hey Professor! Jan and Phil are coming to visit!” Pete exclaimed.

As usual, Pete was a step ahead of Patty.

Two days later, Jan, Phil, Rob, Pete, and Patty were in a small conference room at Ivy U. Patty forgot how much she missed them all and got a little misty eyed thinking about it.

“Well Professor Coleman, what do you think about the Cicret Bracelet?” Phil teased.

“I want one!” Patty joked loudly.

“But, I’m not sure I will ever have one,” she continued.

Figure 1. The Cicret Bracelet. Will it look this bright in sunlight?

“It seems a challenge to get all of the electronics into such a small form factor,” Pete chimed in.

There was a murmur of agreement.

“Can you even find an IC with dimensions as small as the width of the bracelet?” Jan asked.

“I did a little checking and the new Apple A8 processor is quite small, a little less than 1 cm on a side. But that is about the width of the bracelet and some margin will be needed,” Rob added.

“Let’s see if we can estimate the dimensions of the bracelet and compare them to an iPhone 6,” Patty suggested.

Figure 2. The Cicret Bracelet teardown.

The team went to different websites to get the answers. As usual, it took a little longer than expected. Within an hour, they had a summary.

The dimensions of the Cicret Bracelet were 20 cm long, by 1 cm wide and 0.5 cm thick for a volume of 10 cc. The iPhone 6’s dimensions are 13.8 cm by 6.7 cm wide by 0.69 cm thick equaling a volume of 63.8 cc, over 6 times the volume of the Cicret.

“I think we might be unfair in comparing the Cicret to an iPhone 6. The video doesn’t suggest it can do all that the iPhone does,” Jan commented.

“Perhaps, but a factor of 6 in volume difference is a lot,” Rob responded.

“The battery seems like a show stopper, the iPhone battery is 9.5×3.8×0.33 cm = 12 cc, more than the entire volume of the Cicret,” Patty said.

While the team hashed all of these issues out, Pete obtained a teardown analysis of an iPhone 6.

Figure 3. The iPhone 6 teardown.

“Look at the teardown of the iPhone 6, it has more than 20 ICs. The Cicret has only about 5,” Phil sighed.

“To make the Cicret in its proposed form factor, one would almost surely have to work with IC and component vendors and have them develop special ICs and components to fit into the bracelet. This would certainly add to the cost,” Jan added.

“Let’s see if we can summarize what we have learned,” Patty suggested.

Since Phil was to write the report, he went to the white board and queried the team. The following summary resulted.

  1. The Cicret, at this time, appears to be a design concept. The videos were clever digital creations, not the viewing of a working prototype.
  2. It is quite a stretch to think that a working prototype can be developed in anything close to the form factor shown in the video. The reasons for this are:
    • The integrated circuits required are likely to be smaller than the width of the bracelet, as some margin will be needed. So, smaller-than-typical ICs will be needed. If this is the case, special ICs must be developed at considerable cost.
    • The volume of the Cicret is 10 cc vs over 60 cc for a smartphone. Although the Cicret may not need all of the function of a smartphone, this volume difference appears to be too much.
    • The volume for a battery, using current technology, will be the biggest challenge. Current battery sizes are greater in volume than the Cicret.
    • The parts list that the Cicret offers appears to us to be too low. There are likely quite a few components needed that may not be listed.
  3. We question that the projector lights will be bright enough to be viewed in sunlight as the video suggests.
  4. One million dollars (US) seems to be a very optimistic cost to develop a working prototype in anything like the form factor shown in the video. Component and (especially) battery sizes will be issues. We think this cost could be off by a factor of 10 or more.
  5. These conclusions may be too negative. It would be helpful if one member of our team could visit Cicret to discuss these concerns.

“Nice summary everyone,” Patty said.

“Who will go to Cicret? It’s in France, right?” Jan asked.

“How about Phil? Maybe he can at last find a girlfriend,” Rob teased.

And with that the meeting ended.

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

Calculating Optimal Solder Paste Printing Aperture Parameters

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Folks,

A while ago, I developed an Excel-based spreadsheet, StencilCoach, that calculates optimal stencil aperture parameters for several common SMT solder paste printing applications. These applications include standard apertures, passive apertures, pin-in-paste (PiP) apertures, and preforms with pin-in-paste (PiP+) apertures. These algorithms are now online at http://software.indium.com/. Over the next several posts, I will review the use of this software tool.

Let’s first look at standard apertures. After logging into to the website, click on “Stencil Coach” and then “Standard Apertures.” The page gives the definitions for “Aspect Ratio” for a rectangular aperture and “Area Ratio” for circular and square apertures. The aspect ratio, which is defined as the width of the rectangular aperture divided by the stencil thickness, should be greater than 1.5. Whereas the area ratio, for circular or square apertures, is given as the area of the opening divided by the area of the sidewalls. This formula simplifies to D/4t, where D is the diameter of a circular aperture or the width of the square aperture. The area ratio should be greater than 0.66. These recommendations are not standards, but are good rules of thumb.

Let’s consider a situation where a PWB has rectangular apertures with a pitch of 35 mils and circular and square apertures with pitches of 40 mils each. The stencil thickness is 6 mils. See if you can develop the pad and aperture sizes and reproduce the figure below. Hopefully this tool will help you design your stencils.

Cheers,

Dr. Ron

PS: If you need a hand, feel free to contact me at rlasky@ indium com.

Low-Temperature Solders: Niche No More?

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Folks,

It surprises many people that the foundation metal of almost all solder alloys is tin. Alloy elements such as lead, silver, copper, indium, etc., are extremely important, as they lower the solder melting temperature below tin’s relatively high 232°C and often improve wetting and other process or performance properties.

Figure 1. Bismuth metal. (Source: Indium)

As an example, tin-bismuth near-eutectic solders have a melting range around 140°C with a processing temperature of about 170°C, putting tin-bismuth solders 50°C or so below most common lead-free solders such as SAC 305. A while ago, I posted on tin-bismuth solders, asking if their time had come. This post generated follow-on questions that were answered in a second post.

iNEMI predicts that low-temperature solders, such as these tin-bismuth solders, may become main stream as soon as 2017. In light of this situation, my colleague and friend, Dr. Ning-Cheng Lee, is presenting a workshop on “Properties and Applications of Low Temperature Solders” at SMTAI on Sept. 29, from 8:30-12 noon in room 54.

The course summary is: Since the dawn of the electronic industry, the soldering process has encompassed mainly component manufacturing and printed circuit board assembly, with a hierarchic solder melting range. Components are made using solder alloys with melting temperatures around 300°C, which will not melt in the subsequent PCB assembly process, where the solders typically melt around 200°C. Low-temperature solders, with melting temperatures less than 170°C, are currently used mainly for niche applications. However, the iNEMI roadmap predicts low-temperature soldering to become a mainstream processes by 2017. Low-temperature soldering is greatly desired for assemblies such as heat-sensitive devices, systems with more hierarchic levels, parts with significant differences in their coefficients of thermal expansion, components exhibiting severe thermal warpage, or products with highly miniaturized design. This course will cover several varieties of low-temperature solders with an emphasis on lead-free alloys, their physical, mechanical, and soldering properties, and the applications involved with those alloys.

And the topics covered will be:

· Design of low-temperature solder alloys.

· Indium-bearing solder systems and their properties.

· Bismuth-bearing solder systems and their properties.

· Recent development in bismuth-bearing low-temperature solder alloys.

· Mechanisms of reliability enhancement of new bismuth-bearing solder alloys.

· Applications of low-temperature solders.

Be sure to add this workshop to your list of things to do at SMTAI.

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.