The Rule of 72

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

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

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

The Pareto Chart: Crucial in a Continuous Improvement Plan

The Pareto Chart is a simple way to plot failure data that gives priority to the failure modes with the highest number of fails. This technique was developed by Vilfredo Pareto in the late 1800s to early 1900s. Pareto was studying social and economic data in Italy. He was one of the first to observe the 80/20 rule. In that, about 80% of property in Italy was owned by 20% of the people. Today many people use this rule. I have heard salespeople say that 80% of their business is from 20% of their customers as one of many applications of this rule.

In categorizing fails in electronics assembly, about 80% of fails are in 20% of the failure modes. Let’s look at an example (Figure 1). In this figure, we have plotted the number of fails versus the failure mode. Note that shorts is the most common failure at about 300, whereas opens is 75, missing components is about 50, and solder balls about 35.

 

Figure 1. A Pareto Chart of Electronic Assembly Failure Modes

These data should be used to develop a continuous improvement plan. Obviously, shorts should be focused upon first. Typically, one would use process data such as statistical process control (SPC) data to solve the shorts problem, most likely looking at a process metric like the volume of the stencil printed deposit.

I developed a graph similar to Figure 1 when I visited a client. The manager was convinced that solder balls were a big problem. When I asked the quality engineer for the supporting data, he said there was none. So, I asked if they collected failure data; he said they did. I then asked what they did with the data; he said they filed it away having never looked at it!

I asked to see the last several weeks of data and I plotted the data similar to that in Figure 1. It ended up that solder balls was the fourth biggest defect, not the first. As a result of using a Pareto Chart, the company focused on fixing their defect with the greatest number first, etc.

Pareto Charting is a simple yet crucial process in continuous improvement.

Cheers,

Dr. Ron


Answers to the SMT IQ Test

Folks,

Here are the answers to the SMT IQ Test of a short while ago.

  1. What does the “A” in SAC305 stand for?
    ANSWER: 
    SAC stands for tin (Sn), silver (Ag), and copper (Cu). The “305” indicates 3.0 percent by weight silver, 0.5% copper, and the balance (96.5%) tin.
     
  2. The belt speed on a reflow oven is 2 cm/s. The PCB with spacing is 36 cm. What is the maximum time that the placement machines must finish placing the components on the PCB to keep up with the reflow oven?
    ANSWER: 
    Time (s) = product length (cm)/belt speed (cm/s) = 36 cm/2 cm/s = 18 sec.
     
  3. In mils, what is a typical stencil thickness?
    ANSWER
    : In range of 4 to 8 mils.
     
  4. BTCs are one of the most common components today; a subset of BTCs is the QFN package.
    1. What does BTC stand for? ANSWER: Bottom terminated component
    1. What does QFN stand for? ANSWER: Quad Flat Pack No Leads.
       
  5. What is the melting temperature of tin-lead eutectic solder?
    ANSWER:
     183° C.
     
  6. In mm, what is the finest lead spacing for a PQFP?
    ANSWER:
     Most common is 0.4 mm. A few have 0.3 mm, but these smaller spacings are hard to process.
     
  7. Are solder pastes thixotropic or dilatant?
    ANSWER:
     Thixotropic; the viscosity of solder paste drops when it is sheared (i.e forced through a stencil). Dilatant materials stiffen when sheared.
  8. In stencil printing, what is response to pause?
    ANSWER:
     When stencil printing is paused, the viscosity of the solder paste can increase; this situation would be considered a poor response to pause. Pastes that have stable viscosities during pausing are considered to have good response to pause.
     
  9. For a circular stencil aperture for BGAs or CSPs, what is the minimum area ratio that is acceptable?
    ANSWER:
     Typically greater than 0.66, although some solder pastes can print well a little lower than this.
     
  10. What are the approximate dimensions of a 0201 passive in mils?
    ANSWER: Approximately 20 by 10 mils.

Test Your SMT IQ

Folks,

Mary had worked at a small SMT “mom and pop” shop for 12 years. Business was always good and she moved up to CFO of the 60 person company. Revenue had been over $12 million for a few years with profits north of $1 million each year. She marveled how well Fred, the owner,  managed the small firm. As CFO, she was well aware of the strong financial strength of the company.

Mary was stunned when 18 months ago, Fred said he wanted to retire in less than two years, and he wanted her to “buy him out.” Fred was fit and spunky, but 75 years old was now in the rear view mirror.

Mary was more than stunned by the price Fred wanted; it was way, way too low. She even “complained” about this. But, Fred considered her more as a daughter and insisted on the low price. However, one of the concerns they both had was that Fred was really also the chief engineer. They had many loyal workers, as Fred paid 50% over the local rate and provided great benefits, but no one could fill in for Fred in the technical aspects of running the shop.

Fred had been trying to coach Mary for the past 18 months so that she would understand the technical aspects of SMT assembly better. Mary was a fast learner, but with only 6 months left before Fred’s retirement, they both agreed they needed to hire a chief engineer.

So, Fred developed an SMT IQ Test for the candidates. If they could not get at least 80%, they would not be considered. Fred argued that if you were really good enough, you had to know 80% of these questions. Here they are:

  1. What does the “A” in SAC305 stand for?
  2. The belt speed on a reflow oven is 2 cm/s. The PCB with spacing is 36 cm. What is the maximum time that the placement machines must finish placing the components on the PCB to keep up with the reflow oven?
  3. In mils, what is a typical stencil thickness?
  4. BTCs are one of the most common components today. A subset of BTCs is the QFN package.
    • What does BTC stand for?
    • What does QFN stand for?
  5. What is the melting temperature of tin-lead eutectic solder?
  6. In mm, what is the finest lead spacing for a PQFP?
  7. Are solder pastes thixotropic or dilatant?
  8. In stencil printing, what is response to pause?
  9. For a circular stencil aperture for BGAs or CSPs, what is the minimum area ratio that is acceptable?
  10. What are the approximate dimensions of a 0201 passive in mils?

Try the test. Stay tuned for the answers.

Cheers,

Dr. Ron

Low-Temperature Reflow, High-Temperature Use

Folks,

Soldering enables modern electronics. Without solder, electronics would not exist. Copper melts at 1085°C, yet with solder, we can bond copper to copper at about 235°C or less with current lead-free solders. These lower temperatures are required, as electronic packages and PWBs are made of polymer materials that cannot survive temperatures much above 235°C.

Before the advent of RoHS, tin-lead solders melted at about 35°C less than lead-free solders. So today, soldering temperatures are at the highest in history. For some applications, it would be desirable to have solders that melted at closer to tin-lead temperatures. This desire has increased interest in low-melting point solders, such as tin-bismuth solders. Eutectic SnBi melts at 138°C, so reflow oven temperatures in the 170°C range can be used. These lower reflow temperatures are easier on some fragile components and PWBs and will reduce defects such as PWB popcorning and measling. However, the lower melting point of SnBi solders limits their application in many harsh environments, such as automobile and military applications. As a rule of thumb, a solder should not be used above 80 to 90% of its melting point on the Kelvin scale. For SnBi solder, this temperature range is 55.8 – 96.9°C. These temperatures are well below the use temperature of some harsh environments. In addition, SnBi solders can be brittle and thus perform poorly in drop shock testing.

So, the electronics world could use a solder that can reflow at a little over 200°C, but still have a high use temperature. This situation would appear to be an unsolvable conundrum. However, my colleagues at Indium, led by Dr. Ning-Cheng Lee, have solved it. They used an indium-containing solder powder, Powder A, that melts at <180°C and combined it with Powder B that melts at ~220°C. By reflowing at about 205°C, Powder A melts and Powder B is dissolved by the melted Powder A. To achieve this effect, the 205°C temperature must be held for approximately two minutes. The remelt temperature of the final solder joint is above 180°C. I discussed the phenomenon of a liquid metal dissolving another that melts at a higher temperature before. An extreme example of this effect is mercury dissolving gold at room temperature. So, don’t drop any gold or silver jewelry into a wave soldering pot and expect to fish it out an hour later!

Powder A would not be a candidate on its own as it displays some melting at 113°C and some at 140°C.

Using the criteria above, the use temperature of this new solder powder mix can be in the 89.4 – 134.7°C range, after reflow, as the remelt temperature is above 180°C. Tests performed by Dr. Lee and his team have shown the resulting solder joints also have good to excellent thermal cycling and drop shock performance.

Figures 1-3 show schematically how the melting of the two powders would melt at a peak reflow temperature of 205°C.

Figure 1.  Powder A and Powder B at room temperature.


Figure 2. At 205°C, Powder A has melted and it is starting to dissolve to Powder B.


Figure 3. After about a minute at 205°C, Powder B starts to dissolve. Given enough time, it will completely dissolve in Powder A, resulting in a new alloy that has a remelt temperature over 180°C, as well as good to excellent thermal cycle and drop shock performance. 

To me, this invention is one of the most significant in SMT in a generation. It could be argued that it is like finding the holy grail of soldering: melting at low-temperature with a service life at high-temperature.

Cheers,

Dr. Ron

PS. I developed an Excel spreadsheet to calculate the use temperatures. It converts degrees C into K. I used it to calculate the use temperatures above. If you would like a copy, send me a note at rlasky@indium.com.

Tin Pest in Medieval Culture

Folks,

Readers may remember that I have had an interest in tin pest for some time. Tin pest can occur if nearly-pure tin is exposed to cold temperatures (<13.2oC) for long periods of time. At the end of this post, I provide a short summary of the tin pest phenomenon. See this striking time lapse video of tin pest forming; I assume the time period is over many months.

The reason for this post is that a medieval scholar, Beata Lipi?ska, from Poland is studying tin pest and its effects on medieval culture, most notably in church organ pipes. She has contacted me to see if I can help her find papers that discuss tin pest from a historical point of view. If readers have any references that could help Beata, please contact her directly at beata.e.lipinska@gmail.com.

Figure 1. Tin pest forms in Sn .05 Cu alloy from Plumbridge. See the paper referenced below.

What is Tin Pest?
Tin is a metal that is allotropic, meaning that it has different crystal structures under varying conditions of temperature and pressure. Tin has two allotropic forms. “Normal” or white beta tin has a stable, tetragonal crystal structure with a density of 7.31g/cm3. Upon cooling below 13.2oC, beta tin slowly turns into alpha tin. “Grey” or alpha tin has a cubic structure and a density of only 5.77g/cm3 . Alpha tin is also a semiconductor, not a metal. The expansion of tin from white to grey causes most tin objects to crumble.

The macro conversion of white to grey tin takes on the order of 18 months. The photo, which is likely the most famous modern photograph of tin pest, shows the phenomenon quite clearly.

This photo is titled “The Formation of Beta-Tin into Alpha-Tin in Sn-0.5Cu at T <10oC” and is referenced from a paper by Y. Karlya, C. Gagg, and W.J. Plumbridge, “Tin Pest in Lead-Free Solders,” in Soldering and Surface Mount Technology, 13/1 [2000] 39-40.

This phenomenon has been known for centuries and there are many interesting, probably apocryphal, stories about tin pest. Perhaps the most famous of stories is that of the tin buttons on Napoleon’s soldiers’ coats disintegrating from tin pest while on their retreat from Moscow. Another common anecdotal story during the middle ages was that Satan was to blame for the decline of the tin organ pipes in Northern European churches, as tin pest often looks like the tin has become “diseased”. 

Initially, tin pest was called “tin disease” or “tin plague”. I believe that the name “tin pest” came from the German translation for the word “plague” (i.e., in German, plague is “pest”).

To most people with a little knowledge of materials, the conversion of beta to alpha tin at colder temperatures seems counter-intuitive. Usually materials shrink at colder temperatures; they do not expand. Although it appears that the mechanism is not completely understood, it is likely due to the grey alpha tin having a lower entropy than white beta tin. With the removal of heat at the lower temperatures, a lower entropy state would likely be more stable.

Since the conversion to grey tin requires expansion, the tin pest will usually nucleate at an edge, corner, or surface. The nucleation can take 10’s of months, but once it starts, the conversion can be rapid, causing structural failure within months.

Although tin pest can form at <13.2oC, most researchers believe that the kinetics are very sluggish at this temperature. There seems to be general agreement in the literature that the maximum rate of tin pest formation occurs at -30o to -40oC.

Cheers,

Dr. Ron

Stencil Aperture Design for the Pin in Paste (PIP) Process

Peter writes,

Dear Dr. Ron,

I am trying to implement the Pin-in-Paste (PIP) process. The PWB is 63 mils thick, the component pin diameter is 47 mils, the PWB hole diameter is 87 mils, and the PWB pad diameter is 120 mils. I used the Indium StencilCoach software and the result said that I needed a stencil aperture with a 416 mil diameter for the 5 mil thick stencil I was using.

That stencil aperture diameter is way too big. What gives?

Best,

Peter

Dear Peter,

The issue is that your PWB hole diameter is too large. It is 40 mils greater than the component pin diameter. This situation results in a very large amount of solder required to fill the mostly empty PWB hole. See Figure 1. Since solder paste is about 50% by volume flux, quite a bit of paste is often needed to form a good solder joint.

Figure 1
Fig. 1. This figure is a cross-section schematic of a component mounted on a PWB. The fillet, hole, and pin volumes are shown and the resulting solder volume needed. If the component pin is much smaller than the PWB hole diameter, more solder paste will be needed than the pin-in-paste printing process can provide.

Chatting with my friends, Jim Hall and Phil Zarrow of ITM and Jim McLenaghan of Creyr Innovation, they all recommend that the PWB hole diameter be in the range of 10 to 12 mils larger than the pin diameter. In your case, this would be a hole diameter of 58 mils (I chose 11 mils greater than the pin diameter) and a PWB pad diameter of say 80 mils. The software calculates that a stencil aperture diameter of 194 mils is required (see Figure 2). It might be better to choose a square aperture of 172 mils on a side as seen in the output below. If this size stencil aperture is still too large, solder preforms can help. I will discuss using them in a future post.

Figure 2
Figure 2. The right hand column of this figure shows that a round stencil aperture diameter of 194 mils (2 x 97.184, the third cell from the bottom) is required to form a good solder joint in this application. It might be advantageous to use a square aperture of 172 mils on a side, as show in the fourth cell from the bottom in the right column.

By the way, Jim McLenaghan refined some earlier work that resulted in the formula for the fillet volume used in StencilCoach. Zarrow and Hall just released a book called Troubleshooting Electronic Assembly: Wisdom from the Board Talk Crypt. These three folks are some of the most knowledgeable people in electronics assembly today.

Cheers,

Dr. Ron

The Area Ratio for Odd-Shaped Stencil Apertures

Joey writes:

Dear Dr. Ron,

I have a stencil aperture with an unusual shape. See Figure 1. How do I calculate the area ratio? The stencil thickness is 5 mils. The dimensions of the aperture are also in mils.

Figure 1. Joey’s Stencil Aperture

Joey,

The area ratio is simply the area of the stencil aperture opening divided by the area of the sidewalls. For common aperture geometries such as circles, squares, etc. it is easy to derive formulas. See Figure 2.

Figure 2. Formulas can be developed for common aperture shapes.

For an unusual shape like yours, it is easiest to simply calculate and divide the areas. From Figure 1, we get that area of the aperture opening as: 40*24+ the area of the two triangles. A little geometry (can you do it?) shows each triangle to have an area of 89 sq mils. So, the total area is 960 + 2*89 = 1138 sq mils. The perimeter is 40+24+16+16+28+12+16+16 = 168 mils, hence the area of the sidewalls is 168*5 = 840 sq mils. Therefore, the area ratio is 1138/840 = 1.355. Experience has shown that an area ratio of > 0.66 is needed for good solder paste transfer efficiency, so this stencil aperture will do well for transfer efficiency.

Careful thought would suggest that the triangular protrusions alone do not have a good area ratio. Calculations show their area ratios to be 0.37. So, the transfer efficiency in this part of the aperture might not be good. However, the area of the rectangle is so great, more than five times that of the triangles, as to alleviate this concern.

Dr. Ron



Autonomous Vehicles Even Farther Out in Time

Folks,

Readers of this blog will remember that I have been a skeptic of self-driving cars emerging in the near term. I am even less sanguine today. A recent article supports my perspective. Humans just do so many things effortlessly that sensors and computers cannot duplicate.

As an example, suppose there are five people at a street corner. These individuals non-verbally communicate intent that other humans easily pick-up on. If they are talking to each other and not facing the road, a human rightly concludes they are not planning on crossing. If they are facing the road and looking at the traffic, a human expects they plan to cross. This intuition is well beyond any AI’s ability to interpret and will be for decades to come.

Figure 1. A human recognizes that these students aren’t planning on crossing the street.

Autonomous vehicles are typically over designed to not cause accidents. Therefore, in some cases, if a pedestrian sticks their hand out into a road to wave at a self-driving car, it will stop. Whereas a human would recognize that the person is just goofing-off or being friendly.

All of this new information makes Elon Musk’s claim that Tesla will have a car on the road in 2022 without a steering wheel hard to accept.

To be fair, self-driving cars in controlled conditions, such as low traffic, well-marked routes, in good weather, will become more common in the decade ahead. However, an autonomous vehicle that can pick me up from my poorly marked 200 foot driveway, off an unmarked country road in Vermont, and then drive me to terminal C at Boston’s Logan airport is many decades away.

So, if you know someone who wants to be a truck driver, I feel that that will continue to be a fruitful career for a long time. In addition, those of us who manufacture electronics can take comfort in the fact that autonomous vehicles will need much more electronics than originally thought.

Cheers,

Dr. Ron