Author Archives: Dr. Ron

About 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.

Hypothesis and Confidence Interval Calculations for Cp and Cpks

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Folks,

I am reposting an updated blog post on Cp and Cpk calculations with Excel, as I have improved the Excel spreadsheet. If you would like the new spreadsheet, send me an email at [email protected].

One of the best metrics to determine the quality of data is Cpk. So, I developed an Excel spreadsheet that calculates and compares Cps and Cpks.

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Folks,

It is accepted as fact by everyone that I know that 2/3 of all SMT defects can be traced back to the stencil printing process. A number of us have tried to find a reference for this posit, with no success. If any reader knows of one, please let me know. Assuming this adage is true, the right amount of solder paste, squarely printed on the pad, is a profoundly important metric.

In light of this perspective, some time ago, I wrote a post on calculating the confidence interval of the Cpk of the transfer efficiency in stencil printing. As a reminder, transfer efficiency is the ratio of the volume of the solder paste deposit divided by the volume of the stencil aperture. See Figure 1. Typically the goal would be 100% with upper and lower specs being 150% and 50% respectively.

Figure 1. The transfer efficiency in stencil printing is the volume of the solder paste deposit divided by the volume of the stencil aperture. Typically 100% is the goal.

I chose Cpk as the best metric to evaluate stencil printing transfer efficiency as it incorporates both the average and the standard deviation (i.e. the “spread”). Figure 2 shows the distribution for paste A, which has a good Cpk as its data are centered between the specifications and has a sharp distribution, whereas paste B’s distribution is not centered between the specs and the distribution is broad.

Figure 2. Paste A has the better transfer efficiency as its data are centered between the upper and lower specs, and it has a sharper distribution.

Recently, I decided to develop the math to produce an Excel® spreadsheet that would perform hypothesis tests of Cpks. As far as I know, this has never been done before.

A hypothesis test might look something like the following. The null hypothesis (Ho) would be that the Cpk of the transfer efficiency is 1.00. The alternative hypothesis, H1, could be that the Cpk is not equal to 1.00. H1 could also be that H1 was less than or greater than 1.00.

As an example, let’s say that you want the Cpk of the transfer efficiency to be 1.00. You analyze 1000 prints and get a Cpk of 0.98. Is all lost? Not necessarily. Since this was a statistical sampling, you should perform a hypothesis test. See Figure 3. In cell B16, the Cpk = 0.98 was entered; in cell B17, the sample size n = 1000 is entered; and in cell B18, the null hypothesis: Cpk = 1.00 is entered. Cell B21 shows that the null hypothesis cannot be rejected as false as the alternative hypothesis is false. So, we cannot say statistically that the Cpk is not equal to 1.00.

Figure 3. A Cpk = 0.98 is statistically the same as a Cpk of 1.00 as the null hypothesis, Ho, cannot be rejected.

How much different from 1.00 would the Cpk have to be in this 1000 sample example to say that it is statistically not equal to 1.00? Figure 4 shows us that the Cpk would have to be 0.95 (or 1.05) to be statistically different from 1.00.

Figure 4. If the Cpk is only 0.95, the Cpk is statistically different from a Cpk = 1.00.

The spreadsheet will also calculate Cps and Cpks from process data. See Figure 5. The user enters the upper and lower specification limits (USL, LSL) in the blue cells as shown. Typically the USL will be 150% and the LSL 50% for TEs. The average and standard deviation are also added in the blue cells as shown. The spreadsheet calculates the Cp, Cpk, number of defects, defects per million and the process sigma level as seen in the gray cells. By entering the defect level (see the blue cell), the Cpk and process sigma can also be calculated. 

Figure 5. Cps and Cpks calculated from process data.

The spreadsheet can also calculate 95% confidence intervals on Cpks and compare two Cpks to determine if they are statistically different at greater than 95% confidence. See Figure 6. The Cpks and sample sizes are entered into the blue cells and the confidence intervals are shown in the gray cells. Note that the statistical comparison of the two cells is shown to the right of Figure 6.

Figure 6. Cpk Confidence Intervals and Cpk comparisons can be calculated with the spreadsheet.

This spreadsheet should be useful to those who are interested in monitoring transfer efficiency Cpks to reduce end-of-line soldering defects. It is not limited to calculating Cps and Cpks of TE, but can be used for any Cps and Cpks. I will send a copy of this spreadsheet to readers who are interested. If you would like one, send me an email request at [email protected].

Cheers,

Dr. Ron

Solution to Moore’s Law

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Folks,

In a recent post, I discussed Moore’s Law. I challenged readers to solve for “a” and “b” from the equation a*2^(b*(year-1970)) from the graph in Figure 1.

Figure 1. Moore’s Law: Note that in 1982, ICs had about 100,000 transistors, whereas in 2016, they had about 10^10.

Moore’s Law posits that the number of transistors doubles every two years. If so, “b” should be 0.5. It ends up that “b”, from the solution in Figure 2, is 0.4885, so a double occurs about 1/0.4885 =2.047 years, but this number is really close to two years. The solution follows:

Figure 2. The Solution of a and b in the Moore’s law equation. 

BTW, congrats to Indium Corporation’s Dr. Huaguang Wang as he got a close solution.

Cheers,

Dr. Ron

Checking Moore’s Law

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Folks,

Moore’s Law was developed by Gordon Moore in 1965. It predicted that the number of transistors in integrate circuits would double approximately every two years. Surprisingly, it has held true up to today. Figure 1 shows some of the integrated circuit transistor counts as a function of time. The red line is a good fit.

Figure 1. A plot of transistor count in selected ICs as a function of the year.

A reasonable equation for the red line is Transistor Count = a*2^(b*(year-1970)). What should “b” be if the count doubles every two years? To the first person that can solve for “a” and “b” using the red line and the equation above, we will send a Dartmouth sweatshirt.

Cheers,

Dr. Ron

Lighthouse Factories

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Folks,

I recently read an article about “Lighthouse Factories” which appear to be implementations of Industry 4.0. It is encouraging that engineers and scientists are working on these complex systems that are implementations of artificial intelligence (AI), the internet of things (IoT), and other examples of modern technology. According to the “Lighthouse Factories” article above, there are 54 such factories that now join the World Economic Forum’s Global Lighthouse Network.

But, I have to admit to being somewhat of a skeptic. Are all, or even most, of these factories up and running without a hitch? I have toured a 100 or so factories world-wide, and most are in Industry 2-3.0.

The multiple AI and IoT technologies that have to be connected and work flawlessly to get the Lighthouse factory to work is daunting. To me, it is like self-driving cars: they are 95% to full self-driving capability today, but the last 5% may not be obtained for decades…if ever.

A recent article in the Washington Post presents a similar perspective. The author Dalvin Brown, argues that robotics and AI firms have struggled to make something like robot butlers. However, these efforts have only had success on very focused tasks. Nothing like a robot butler will exist for decades. Stephen Pinker’s argument that no AI can empty a dishwasher is still the most powerful way to clarify the primitive state of practical, common sense, robot-type machines.

Figure 1. Dalvin Brown points out in his article that nothing like The Jetsons’ Rosey the Robot exists today. Image source is here.

As I always state, we in electronics assembly should be cheering these folks on, as more electronics will be required than predicted with the slow emergence of complex interdependent technologies.

In addition, I think the hype around Industry 4.0 always neglects the important role that people have to play. When we watch something as complex as a landing of a spacecraft on Mars, we always see the Control Center with scores of people cheering the success. All of the important tasks were not handled by AIs.

So if anyone reading this article would like to invite me to a Lighthouse factory, please do. If I am wrong, I will write a retraction.

Cheers,

Dr. Ron

Tin: The Foundation Metal of Soldering

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Folks,

The vast majority of solders used in electronic assembly have, as their base metal, tin. There are some specialty gold solders, like gold-copper or gold-indium, indium based solders, and a few others that do not contain tin. Although these solders have important applications, the sheer volume of tin-based solders is overwhelming in comparison.

Tin was a metal known to the ancients, and it led them out of the Copper Age into the Bronze Age. Ten to twelve percent tin in copper yields bronze, which is much stronger than copper (see Figure 1) and has the added benefit of melting at about 950°C vs. copper’s 1085°C.

Figure 1. The addition of alloying elements, such as tin and zinc solid solution, strengthen copper. Note that about 8% tin in copper increases the copper yield strength by two and one half times. The solid solution effect also lowers the melting temperature. Find the image source here.

This difference in temperature is significant in that with primitive heating technology, 1085°C is hard to achieve. In addition, since bronze freezes at a lower temperature, it fills molds much better. This property enabled the casting of much more complex shaped objects. See Figure 2. All of these benefits resulted in a dramatically increasing demand for tin. This demand established much more sophisticated trade routes for tin and its most common ore, cassiterite; this enhanced overall trade and accelerated the spread of civilization and learning.

Figure 2. The addition of tin to copper created bronze, which is much harder and also easier to cast than copper. This castability enabled complex designs like this dirk. Image: Wikipedia

Back to solder. Soldering is a technology that has existed almost as long as the copper age. It is thought to have originated in Mesopotamia as long ago as 4000BC. Soldering was used for joining and making jewelry, cooking tools, and stained glass. Today, in addition to these applications, plumbing, musical instrument repair, and plated metal are common uses. However, electronics assembly is the largest user of tin-based solder by far. See Figure 3.

Figure 3. More than 50% of tin is used in solder. Source: Wikipedia 

One of the greatest benefits of solder is its reworkability. This property enables rework of electronics assemblies, plumbing, jewelry, and musical instruments. Without the ability to rework electronics, the industry would struggle to be profitable. Another benefit, of course, is the miracle of soldering I discussed in another post.

So, the next time you stare at your smartphone, tablet, TV, etc., remember tin-based solder and soldering are fundamental to its existence.  

Cheers,

Dr. Ron

SMT Assembly is an Optimization Process

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Folks,

SMT assembly is an optimization process. There is no single stencil printing process for all PWB designs. The stencil printing parameters of stencil design, squeegee speed, snap off speed, stencil wipe frequency, and solder paste for assembling all PWBs will not be the same; just as there is no single reflow oven profile for all PWBs. Fortunately, most solder paste specifications give good boundaries for all of these parameters, but typically some trial and error experiments will be needed when assembling a new PWB design that is not similar to past assemblies.

The need for optimization is most obvious when trying to minimize defects. As an example, minimizing graping is often facilitated by using a ramp to peak reflow profile. However, the ramp to peak profile may acerbate voiding. See Figure 1.

Figure 1. The ramp to peak reflow profile may minimize graping, but acerbate voiding.

Figure 1. The ramp to peak reflow profile may minimize graping, but acerbate voiding.

Thankfully your SMT soldering materials and equipment suppliers deal with these optimization issues on a daily basis. So if you are ever stuck with some challenging SMT assembly process, contact these solder materials and equipment experts first.

Cheers,

Dr. Ron

Is Quantum Computing Emerging to Solve Practical Problems?

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Folks,

I read with interest Zohair Mehkri’s SMTAI 2020 paper titled “How Quantum Computing (QC) will Revolutionize Electronics Manufacturing.” I will start by saying that he gives a very good Quantum Computing 101 overview. This is no easy feat, as QC is a difficult technology to understand. I will humbly state that I still struggle to understand the basics, and I’m sure I don’t understand QCs as well as he does.

Figure 1. IBM is a leader in QC. Image source: https://www.ibm.com/quantum-computing/

However, I have two main concerns with Zohair’s paper. One is that it may give the impression that QC is becoming a practical technology and will soon be widely available — to the point that we can use it to solve electronics manufacturing problems.

QCs are rare; there are about 30 worldwide, 15 of which are owned by IBM. Although to be fair, Shenzhen SpinQ Technology gave this recent announcement: “On 29 January 2021 Shenzhen SpinQ Technology announced that they will release the first-ever desktop quantum computer. This will be a miniaturized version of their previous quantum computer based on the same technology (nuclear magnetic resonance) and will be 2 qubit device. Applications will mostly be educational for high school and college students. The company claims SpinQ will be released to the public by the fourth quarter of 2021.”

Since the device has only two qubits, it will more than likely be for educational purposes not intended to solve real problems. It will be interesting to see how it emerges later in the year. 

Almost all QCs are superconducting, meaning that they require very low temperatures to operate as cold as -460°F, which is colder than liquid helium. They are also extremely delicate; even slight vibrations causes them to fail.

So, we might be able to rent time on a useful QC sometime in the future, but QCs won’t be common any time soon.

The other concern I have is what is the need for QCs? Most of the practical problems that face us can be solved by conventional computers. In addition, only certain types of problems can be solved by QCs. As stated in Wikipedia: “However, the capacity of quantum computers to accelerate classical algorithms has rigid upper bounds, and the overwhelming majority of classical calculations cannot be accelerated by the use of quantum computers.”

QC is an exciting technology and many wonderful discoveries will no doubt come from it. However, I am skeptical that it will solve practical problems anytime soon.

Cheers,

Dr. Ron


The Rule of 72

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Four years ago, the big boss, 6′ 6″ tall, 350 pound Mac Savage, said that the goal for the sales of a new product was at least 20% growth rate per year. The team is in a room prepping for a review with Savage (sometimes called Big Mac or, in jest, “The Whopper”) when the person responsible for analyzing the data, Charlie, comments:

“Well in 2016, sales were 100K units and four years later in 2020 they are 200K. So, in four years, sales increased 100%. Therefore, the yearly increase was 100/4 or 25%. So, we beat the goal by 5. So, Big Mac should be happy,” Charlie says.

There is a murmur of agreement among the 10 or so people in the room. And a few comments like, “It’s always good when The Whopper is happy,” were quietly said.

Helen chimed in, “That’s not true; using the ‘Rule of 72,’ the growth rate is 72/4 = 18%. So, we are a bit short.”  

Fred, who was always a bit annoyed at smarty-pants Helen chimed in, “I think Charlie is right, 100% growth in four years is 25% per year.”

Helen responded, “With your logic, if the growth rate was 25% after the first year, sales would be at 125%, right?”

Everyone in the room murmured in agreement.

Figure 1. The Team: Helen is to the far left. Charlie is the bald guy with the beard holding a sheet of paper. John is the chap wit his laptop open. Fred has the red shirt on and June is to the right with the long blond hair. 

“But would second year sales be 150%?” Helen went on.

There was some mumbling, then John, a young new hire said, “You would add 25% of 125%. My calculator says the total would be 125% plus 31.25% equals 156.25%, not 150%.”

John, then got excited and did some more calculations, “The third year is not 175% with 25% growth per year, but 195.3%, and then the fourth year is 244.14%… much higher than 200%. The growth compounds.”

Everyone groans anticipating the disapproval of “Big Mac.”

Charlie finally asks, “is Helen’s 18% growth rate right?”

John makes a few trial and error calculations and says, “18% seems a little low; it’s more like 18.9%, but it’s not 25% or even 20%. But 18% was a pretty good first estimate.”

“The rule of 72 is an estimate, it gets more accurate around 8 years,” Helen chimed in.

“Jeepers, look at the clock, we only have 45 minutes before Mr. Savage comes to the meeting and wants our report,” June warned.

After a brief chuckle that June was the only one to call the big boss Mr. Savage, instead of Big Mac or The Whopper, the team got to work putting together Power Point slides for Charlie’s presentation. They finished with 5 minutes to spare, enough time to freshen their coffee cups or hit the restroom.

At 11AM sharp, Savage came into the room and Charlie started his presentation. Everyone was nervous about Savage’s response.

Charlie summarized that by using the Rule of 72, the growth rate was short of the 20% per year target, but was more like 72/4 or 18%. He pointed out that a more precise calculation showed that the growth rate was 18.9%.

The entire group expected that Savage was going to blow his top that the 20% target was missed. But, he calmly said, “Well, the 1.1% shortage is unfortunate, but I’m impressed that you didn’t say the growth rate was 25%. I am more impressed that that you knew to use the Rule of 72 and more so that you were able to fine-tune your work to get the more precise. Great work Charlie!”

Everyone in the room rolled their eyes, especially Helen and John. Someone from the group was about to speak up, when Charlie, red faced said, “Sir, I should point out that Helen suggested using the Rule of 72, and John did the more precise calculations.”

“Charlie, you are a good leader, giving credit where it is due. Let’s have this team develop an action plan to improve the growth rate. We should meet in a week to review your plan,” Savage said.

There was a palpable sigh of relief among the team.

Savage, ended with, “Who is this new guy John?”

John was introduced by Charlie as a recent grad of Tech.

“John, I got my MBA from Tech,” Savage said.

“John, I want you to derive The Rule of 72; it will be a good experience for you. See if you can do it without looking anything up,” Savage went on.

John was a bit shaken, but he was able to derive The Rule of 72. See his derivation below.

The derivation of The Rule of 72

Cheers,

Dr. Ron

The Miracle of Soldering

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Folks,

Imagine you are Guglielmo Marconi, and you opened the first radio factory in Chelmsford England in 1912. Using Lee De Forest’s 1906 invention, the triode vacuum tube, your early radios needed a way to connect the various electronic components together. Enter soldering. Soldering is the most cost effective and reliable, some might say only, way to connect electronic components together. It has been since the birth of electronics with the radio.

It is interesting to ponder some of the effects that the radio had on civilization and society. Before the radio, most of the United States was disconnected. People in California didn’t know what was happening in New York in anything like real time. There was also no national entertainment. Following early broadcasts in the 1920s, radio was a staple of most American homes by the 1930s. Families would gather around the radio after dinner to listen to the news and comedy, drama, music, etc. This golden age of radio lasted from the 1920s through the 1950s until radio was supplanted by television. See Figure 1.

Figure 1. A young girl listens to the radio in the 1930s. It would be difficult to overstate the impact of radio…all enabled by soldering.

Electronic soldering, in a sense, is a miracle of technology. It enables connecting copper to copper at a temperature of less than 230°C. The connection is reversible, conducts electricity well, and is mechanically strong. This soldering temperature is crucial for electronics, as the printed wiring boards and component packages contain polymer materials that cannot withstand temperatures much higher than 230°C. This low soldering temperature is especially impressive when considering that to bond copper to copper without solder would require temperatures near that of the melting point of copper or 1085°C.

To work its magic, solder forms intermetallics with copper. See Figure 2. The intermetallic closest to the copper is rich in Cu3Sn, and that closest to the solder is rich in Cu6Sn5.

Figure 2. A schematic cross section of a component lead soldered to a PWB pad. 

It is important that the soldering bond is reworkable. The electronics industry would have difficulty being profitable without this important feature of soldering as most assembly processes have some yield loss that requires rework.

So, the next time you use your smartphone, PC, or TV, remember it wouldn’t be possible without the miracle of soldering.

Cheers,

Dr. Ron

Figure 1 source: By Franklin D. Roosevelt Library Public Domain Photographs – This media is available in the holdings of the National Archives and Records Administration, cataloged under the National Archives Identifier (NAID) 195876., Public Domain, https://commons.wikimedia.org/w/index.php?curid=2151524


AI and Autonomous Vehicle Challenges: Common Sense, Flexibility, Dexterity, and Situational Awareness

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I have been following advances in artificial intelligence (AI) and autonomous vehicles (AV) for some time now. At first, I was a cautious; then I became a skeptic; and now I am a doubter.

AI can do some amazing things. More than 20 years ago, Deep Blue beat World grandmaster Garry Kasparov. Today, AIs can routinely beat chess grandmasters and other world experts at games like Go.

Although impressive, these accomplishments play to AI’s strengths. Any activity that can be reduced to algorithms are natural for AIs. These AI victories have created a belief by many that AIs will soon take over most jobs and eventually become our masters. Witness such motion picture franchises as The Matrix and The Terminator. Some serious intellects buy into this concern as shown in the book Our Final Invention. This book posits that AIs pose a threat to human existence. The book extrapolates the successes of AIs discussed above and predicts that AIs will eventually be many times more intelligent than humans and will somehow develop something like consciousness. Ultimately, the AIs will seek to eliminate us.

I find these concerns almost comical. AIs connected to robots can do some very impressive things. In electronic assembly, they can hand solder very effectively. Perhaps better than humans, and they don’t get tired. But, they are not flexible. If the hand soldering operation changes to a different design, the AI must be reprogrammed. Whereas a human can quickly change from design to design. Lack of flexibility is a major AI drawback.

AIs also lack common sense. As Stephen Pinker has pointed out, no AI can empty a dishwasher. This is a profoundly common sense operation for humans. Yet this task is not only beyond AIs of today, but likely will be for a long time. Even something as simple as unloading boxes from a truck is a challenge to AIs as pointed out recently in Bloomberg BusinessWeek.[i]

This lack of flexibility and common sense makes it very hard for AIs to compete against humans when multiple tasks are required.

It is also difficult for AI robots to display dexterity. They may be able to pick up a chestnut, but crush a strawberry. This task is simple for an 18-month-old human.

The promise of autonomous vehicles is also greatly exaggerated. For a few years, some self-driving cars have been able to drive 95% of the route from my house in Woodstock, VT, to Boston’s Logan airport. However, they have made little progress in negotiating country roads, detours, and routes with complex signage. In addition, AVs lack situational awareness. As an example, AVs can’t look at a group of people near a street corner and sense if they are planning to cross or not.

Detours are hard for AVs. (Source: https://nj1015.com/is-the-detour-sign-a-thing-of-the-past-in-nj/)

So, I don’t see AIs taking all of our jobs or AVs putting truck drivers out of work any time soon. But the good news is that more electronics will be needed as these technologies make their slow advancements. So I see a busy future in the electronics assembly world.

Cheers,

Dr. Ron