Use an SMT Pre-Test Before Presenting a Soldering Workshop


Let’s see how Patty is doing, it’s been a very, very long time …

Even though Patty and her husband Rob both worked at Ivy University, they seldom drove in together. It was just too difficult to organize their schedules so that it would work out. So, as Patty was driving in to Ivy U, she was listening to the last chapter of Ron Chernow’s biography of U. S. Grant. Her timing was excellent, since she, Rob, Pete, and the Professor were having their monthly book club meeting. Rob, Pete, and the Professor were always recommending books about World War II or the Civil War. Because of this trait, she groaned every time it was the three “boys” turn to suggest the next book. But, she had to admit that she always enjoyed the books much more than she thought she would. She especially liked a book Rob discovered, called A Simple Solder. Patty found this true story, about a young boy in the German army in World War II and how he survived to tell the tale, fascinating. She would never tell Rob, but she read it three times.

When it was Patty’s turn she made sure to avoid those military topics. Recently, she proposed another one of Chernow’s biographies on John D. Rockefeller. She also suggested  iGen: Why Today’s Super-Connected Kids Are Growing Up Less Rebellious, More Tolerant, Less Happy–and Completely Unprepared for Adulthood–and What That Means for the Rest of Us by Jean M. Twenge. This book convinced her and Rob to dramatically limit “screen time” for their 9-year-old twin boys.

As she approached her parking spot, the audio book on Grant finished. She was a bit sad, as she had enjoyed this book as much as any. Patty had the impression, from her high school history classes, that Grant led the Union to victory over Robert E. Lee only because he had superior forces, weapons, and supplies. Chernow’s book clearly dispelled that notion. Grant was a great general. In addition, he was an effective and honorable president, if a little too naïve and trusting to avoid numerous scandals among his subordinates.

In a few moments, they met in The Professor’s large office. After they finished their book club chat about Grant’s biography. Patty had a favor to ask.

“Mike Madigan asked me to give a three-day workshop on SMT 101 at one of ACME’s recently acquired facilities. He said he felt the technicians and engineers weren’t very knowledgeable. I’m having trouble deciding at what level to aim the workshop,” Patty began.

“You mean like for beginners, intermediate, or expert?” Pete asked.

“Yes,” Patty responded.

“Well, you should develop it in a logical sense, starting with what soldering is, discuss flux and solder paste, then stencil printing, component placement, reflow, test, etc,” Rob added.

“I agree with Rob’s outline, but you need to find out the current knowledge level of the students,” The Professor suggested.

“I once gave an eight-hour seminar on SMT Defect Modes and How to Fix Them. The workshop was advertised as for SMT engineers and technicians with intermediate experience. At the end of the workshop a person raised his hand and asked an unsettling question,” The Professor continued.

“And the question was?” Pete teased.

“Professor, you have used the word ‘SAC’ many times, what does ‘SAC’ stand for?” The Professor responded.

In unison, Patty, Rob and Pete groaned.

“That’s my concern! At which level do I aim the workshop? If I shoot too low, it might insult people. If I shoot to high it might go over their heads,” Patty responded.

“OK! So, how do I structure the workshop, not knowing the skill level of the students?” Patty asked a little frustrated.

“How about a pre-test?” The Professor suggested.

“OK! But how many questions?” Rob asked.

“It needs to be short, yet comprehensive,” The Professor suggested.

“Seems like a contradiction,” Pete grumbled.

“I think The Professor is right. Look at it this way, let’s say you want to assess if your 14 year old nephew knows much about The Civil War. Ask him three or at most five questions and you can determine if he does,” Patty suggested.

“How about some examples?” Pete asked a bit dubious.

“I’m getting it. How about when was the war fought, who was Robert E. Lee, what is the significance of Appomattox Court House?” Rob chimed in.

“OK, I see you point. If you know two or all three, you probably know a lot, one or less and you don’t know much,” Pete responded.

Patty then suggested, “OK let’s develop a list of ten SMT Pre-Test questions.”

After about 20 minutes of back and forth, our team of four converged on these 10 questions.

SMT Pre-Test

  1. What does the letter “S” in SAC stand for?
  2. How much silver is in SAC 305?
  3. PWBs are coming off of the final component placement machine at a rate of one every 20 seconds. The PWBs are 20cm long and should be placed with at least 4cm of space between them. What must the reflow oven belt speed be to accommodate this cycle time?
  4. The starting temperature is 25°C. It needs to be 145°C in one minute. What heating rate is needed, in °C/s, to achieve this temperature?
  5. About how much does silver cost per troy oz.? (+/- 30%)
  6. Which is a closest to typical stencil thickness?
    • 5 microns
    • 20 mils
    • 5 mils
    • 20 microns
  7. Which is closest to a typical lead spacing for a plastic quad flat pack (PQFP?)
    • 0.1mm
    • 0.1 mil
    • 0.4mm
    • 0.4 mils
  8. Which has finer solder particles, a Type 3 or 4 solder paste?
  9. What does OSP stand for?
  10. Place an arrow at the eutectic point of the tin-lead phase diagram below.

Would you like to try the pre-test? The answers have to be what you know without looking anything up. Send me your answers at The first person to get 100% will get an item of memorabilia signed by Patty, Rob, Pete, and The Professor.


Dr. Ron

On the Road at SMTA Pan Pac


I am giving a paper, chairing a session and hosting a panel at SMTA Pan Pacific on Feb. 6 at the Hapuna Beach Prince Resort in Hawaii.









The paper is “Using Cpk and Cpk Confidence Intervals to Evaluate Stencil Printing,” with my coauthor Chris Nash of Indium Corporation. In this paper I will discuss how to calculate confidence intervals when using Cpk to evaluate the quality of stencil printing.

By comparing the confidence intervals of Cpks one can determine whether or not there is a statistically significant difference between different samples of stencil printing data.

The session I am chairing is on “Advanced Materials.” The papers in the session are:

  • “Oxygen Vacancy Migration in MLCCs” by Dock Brown, CRE, DfR Solutions
    “Update on Cu-Ni/Sn Alloy Composite Solder Paste for Harsh Environments” by Stephanie Choquette, Ph.D., Iowa State University, and Iver Anderson, Ames Laboratory (USDOE)
  • “Resistivity Stain Analysis of Graphene Coated Frabric for Wearable Electronics” by Martine Simard-Normandine, Ph.D., S. Ferguson, MuAnalysis, and K. Manga, Q.-B. Ho Grafoid.
  • The panel topic is “Solders for Harsh Environments.” Brief presentations will be given by some of the panelists with a question and answer period to follow. The panelists are Dwight Howard of Delphi Automotive, Iver Anderson of Ames Lab, John Evans of Auburn University, and Prabjit Singh of IBM.

We expect to learn a lot. I hope to see you there!

Dr. Ron


Is Industry 4.0 around the Corner?


I attended a technical session on Industry 4.0 at SMTAI in Rosemont, IL, in September. I admit to not knowing much about it, so I found the topic fascinating. Industry 4.0 begs the question as to what were Industry 1.0 to 3.0 are (were?) The image below explains the progression, Industry 1.0 was mechanization with water and steam power, Industry 2.0 is mass production with the assembly line using electricity. Industry 3.0 adds computers and automation. Whereas Industry 4.0 is the age of cyber physical systems, the internet of things, cloud computing, and cognitive computing.

Industries 1.0 to 4.0. Source:

One could imagine an Industry 4.0 (I4.0) workplace something like the following in an electronic assembly factory. A customer places an order in the cloud. It is received by the factory and after some analysis performed by a “Watson”-type AI, the order is accepted. The I4.0 system then goes to work scheduling the job and ordering the correct components, PWBs and hardware. It designs the stencil from a Gerber file and so on and so on. There is little human interaction and the factory runs at about a 95% uptime and is profoundly efficient and profitable.

As with self-driving cars, I am a bit of a skeptic of I4.0. To be sure there may be a few factories that exhibit some of the Industry 4.0 technology, but I don’t see this major technological shift becoming mainstream for a generation or so.

One of the reasons is that I don’t think most factories today are even at Industry 3.0 (I3.0), they are more like Industry 2.5 (or less?). Many colleagues that I chat with about these types of things, and I have toured more than 100 factories world-wide and still marvel at how inefficient they are. I was once asked to give an executive, new to our industry, a tour of an electronics assembly facility. The facility that graciously offered to let us tour had six assembly lines. In the 90 minutes we were there, not one line was running. The reasons were typical: for line 1 the team could not find the right stencil, line 2 needed a reel of components that no one could locate, line 3 had an equipment malfunction, etc., etc. These types of experiences are discussed in The Adventures of Patty and the Professor.

Another example of electronics assembly being a bit short of I3.0 was demonstrated by a student project that was recently commissioned to measure uptime on a simple assembly line. The line consisted of a stencil printer, component placement machines, and a reflow oven. The engineers that worked for the company that sold the assembly line were confident that the students would have no difficulty measuring uptime by sampling signals from the computers controlling each piece of equipment. After hundreds of hours of work by the engineers and the students, it was concluded that it was not possible to measure line uptime without adding some type of sensors on the assembly line to detect the flow of the PWBs. Industry 3.0 indeed!

At SMTAI I was asked to participate on a two-person panel on the topic, Will Virtual Reality Soon be Used in Electronic Assembly? Readers will likely guess that I was the skeptic. Watch the video and see what you think.

As with self-driving autos, I think Industry 4.0 is a great idea and encourage the many people working on it, but I believe it will be quite a while before it arrives in any meaningful way to typical factories. In the meantime, let’s all work to ensure that the factories we currently operate approach Industry 3.0 are run efficiently with high uptimes.


Dr. Ron


Intermetallic Growth Rate is Strongly Temperature Dependent


In a previous post, I discussed that, contrary to popular belief, intermetallic compounds (IMCs) formed in soldering processes are not necessarily brittle. I reviewed some literature that indicated that failure modes are usually at interfaces between the IMCs themselves, the IMCs and the copper or solder and often in the bulk solder itself. The perspective that IMC growth may not significantly affect reliability is also supported by work performed by Lee, et al. Figure 1, from Lee’s paper, shows that aging for 250 hrs at 150°C does not significantly affect characteristic life in thermal cycle testing.

Figure 1. Aging for up to 250 hours at 150°C did not significantly affect characteristic life in thermal cycle testing in Lee’s referenced paper.

However, it would be prudent to minimize the thickness of IMCs. So this raises the question: how quickly do IMCs grow at any given temperature? Work performed by Siewert, et al[i] holds the answer. In this paper, Siewert supported past work that the thickness of IMCs grows as X=(kt)0.5 and added new data to support modeling using this equation. In this equation, X is IMC growth distance, k is a constant dependent on temperature, and t is the time. One might expect that X is strongly dependent on temperature (T) and it is. Using data from Siewert’s paper, I was able to generate values of k as a function of T and plot them in an Arrhenius plot. See Figure 2.

Figure 2. An Arrhenius plot for k.


I next used Figure 2 to obtain a value of k at 70°C and plotted the IMC growth X in microns as a function of time in hours. The result is in Figure 3.


Figure 3. IMC grow as a function of time at 70°C.

Note that about 40 years are required to obtain a little over 10 microns of growth. Figure 4 shows the results for IMC growth at 200°C. In this case, only 100 hours are required to obtain about 10 microns of growth. So going from 70 to 200°C produces an acceleration factor of over 30,000 in the effective IMC growth rate to 10 microns.

Figure 4. IMC growth as a function of time at 200°C.

These are theoretical calculations from data collected at different temperatures. Let’s see if the formulas work in real life. In another paper [ii]by Ma, et al. his team aged some solder joints at 125°C for 120 hours. The equations used above would predict IMC growth of 2.2 microns under these conditions. From Figure 5, we see about 2 microns of growth consistent with the calculation estimate.

Figure 5. Images from Ma’s paper of IMC growth at 125°C for 120 hours.

So although IMCs are not that brittle, it is wise to limit their growth. Hence, limiting exposure to very high temperature aging is wise, but certainly minimizing solder rework is advisable, as the molten solder enables very fast IMC growth.


Dr. Ron

[i] Siewert, T. A., et al, Formation and Growth of IMs at the Interface Between Lead Free Solders and Copper Interfaces, IPC Apex, 1994.

[ii] X. Ma, et al Materials Letters 57 (2003) 3361-3365.

How to Land That Job in an Interview


It’s a stressful time when you are interviewing for a job. As a former manager at IBM, Universal Instruments, and Cookson Electronics, I have interviewed more than 300 people for jobs. I’ve also interviewed for a few myself. As a result of these experiences, years ago some management friends and I collaborated on some of the best job interviewing tips.

Having taught about 3,000 students at Dartmouth over the last 15 years, I typically give a lecture on the last day of class entitled, “Tips for Success and How to Interview for a Job.” These Powerpoint slides have some of the ideas gleaned from what I learned above.

Some years ago I was interviewing for a job and the interviewing manager asked me, “Why should I give you this job?”

I answered without hesitation, “Because I led a team of engineers that contributed to the design and build this optoelectronic transceiver module.”

As I handed the optoelectronic transceiver module to the manager to look at, the non-verbal vibrations I received from him where very positive.

A few weeks after I got the job, he told me that handing him the hardware that I worked on was what sealed the deal.

Most of us recognize that an artist or writer should have a portfolio when they go on job interviews, but don’t appreciate that an engineer should have one too, even if like mine, it had only one item. I share this strategy with my current students and on a regular basis they tell me how this approach led to them getting a job.

Here is an email from a student who graduated more than 10 years ago, relating to a new job she just landed:

“I just wanted to thank you for a job interviewing tip from back when I was in school.  You suggested that we bring an example of something that we’ve worked on.  I’ve done that all these years, and I have to say, I’m pretty sure it’s gotten me several job offers!  I know at least one of my current employers’ interviewers definitely appreciated it.  Anyway, so thank you!”

So, hopefully you have a job you love and never have to interview again, but if you do, take something that you worked on as a “show and tell.” It also helps in that it focuses the interview on something you know about and will look good discussing.

BTW, if you would like a copy of my Powerpoint presentation mentioned above, send me a note ( and I will send you a copy.


Dr. Ron

Intermetallics and Kirkendall Voids Continue to Grow at Room Temperature


In my last post, I discussed intermetallic compounds (IMCs) and what I referred to as the “miracle of soldering.” I also mentioned that research focused on the brittle nature of IMCs suggests that failures in stress tests are more likely due to failures between the interfaces of the IMCs and the solder, the IMCs and the copper, or the IMCs (Cu6Sn5 with Cu3Sn) themselves and are not related to any perceived brittle nature of the IMCs.

Another weakening mechanism in soldering and thermal aging of solder joints is Kirkendall voids. Kirkendall voids form when one metal diffuses more rapidly into another metal than vice versa. A copper-tin interface displays such a mechanism. Copper diffuses into the tin more rapidly than the tin into the copper. This mechanism can result in actual voids in the copper at the metal interface. See the image below. In addition to causing a possible weakness at the interface, the excess copper that diffuses into the tin creates compressive stresses than can result in tin whiskers.

Kirkendall voids


IMCs and Kirkendall voids are formed quite quickly at soldering temperatures. However, even at room temperature IMCs and Kirkendall voids continue to grow, albeit at a much reduced rate. The reason for this continued growth is that on the absolute temperature or Kelvin scale, room temperature is a considerable fraction of the melting temperature of solders. As an example, the melting temperature of SAC is about 219°C, this temperature is equal to 492K (219+273), whereas room temperature is 295°K, so room temperature is 60% of the way to the melting point of SAC solder (295/492 = 0.60). Compare this situation to steel, which melts at about 1480°C. The steel would be red hot at 60% (780°C) of its melting point on the absolute scale. So, since room temperature is 60% of the way to melting, the IMC and Kirkendall forming processes don’t stop at room temperature. Hence, IMCs and Kirkendall voids continue to grow, as do related effects such as tin whiskers.

Stay tuned. Next time we will discuss IMC growth rates and resulting effects in stress testing as we wrap up this series on IMCs.


Dr. Ron


Copper-Tin Intermetallics: The Miracle of Soldering

Most articles discussing the copper-tin intermetallics that form during soldering refer to them as a necessary evil. The evil being the perception that intermetallics are brittle and can lead to failures in thermal cycling or drop shock.

I view the situation differently. From my perspective, the formation of copper-tin intermetallics is the miracle of soldering. Look at it this way, to assemble electronics, bonding copper to copper (the leads on the components to the pads on the PWB) in the presence of polymers (the PWB epoxies and the component cases) is required. These polymer materials can only take about 250°C for a few minutes. Copper melts at 1083°C, so bonding copper to copper in the presence of polymers would appear to be quite a challenge. Enter tin-based solder.

Lead-free (tin-based) solder, say SAC305, melts at about 219°C. So, with a peak temperature of about 245°C, in the reflow oven, solder can be melted and form an electrical and mechanical bond with the copper in the leads and pads. At 245°C, the many polymer materials are unharmed for the 90 seconds or so that soldering requires at this temperature.

But, what about the material properties of the intermetallics that are formed? Aren’t they too brittle? Lee et al* performed analyses that suggest that the intermetallics formed in soldering are not brittle. Their work also suggests that the failure modes are not in the intermetallics, but in the interfaces between the intermetallics and the solder, copper, or the different intermetallic compounds, Cu3Sn and Cu6Sn5. These two intermetallic compounds are shown in the figure below.

Copper tin intermetallics from Roubaud et al, “Impact of IM Growth on the Mech. Strength of Pb-Free Assemblies,” APEX 2001.


It has long been assumed that the thicker the intermetallics, the greater the risk of failure due to the intermetallic thickness. Lee’s work would appear to bring this concern into question.

Stay tuned for a continued discussion on intermetallics and their effect on reliability.

*Lee, C. C. et al, “Are Intermetallics Really Brittle,” IEEE Electronics Components and Technology Conference, 2007, pp. 648.

Dr. Ron

Calculating Confidence Intervals on Cpks

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

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

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

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

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

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


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

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

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

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

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

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

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

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

“How so?” Patty asked.

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

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

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

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

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

“Yikes!” Patty almost shouted.

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

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

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

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

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

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

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

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

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

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

“Perfect!” she thought.

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

She called Madigan at 3 pm.

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

“And the answer is?” Madigan asked expectantly.

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

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

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

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


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

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

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

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

“Wow! That’s great,” Patty replied.

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

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


Dr. Ron

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


Cpk is Still King in Evaluating an SMT Solder Paste Printing Process


If you think about it, to evaluate any process you typically want to know its precision and accuracy. Look at the dart players in the Figure 1 below. The yellow player has good precision, but his accuracy is off. The green player has such poor precision, it is hard to tell if his accuracy is good. The yellow player will typically be easier to correct, as she just needs to change her aiming point.

Figure 1. The yellow player has greater precision. She only needs to change her aiming point.











Recently I was asked to evaluate several solder pastes to determine which printed better. We used transfer efficiency (the volume of the stencil printed solder paste “brick” divided by the stencil aperture volume) as the evaluation metric, expressed in percent. So 100% would be the target. The lower specification limit we choose was 50% and the upper specification at 150%.

Figure 2. Data from Pastes A and B.


A good result would be an average of 100% with a “tight” distribution. The “tightness” of the distribution being determined by the standard deviation. Figure 2 shows data from two pastes. Note that Paste A has an average of 100% and a standard deviation of 16.67%, whereas Paste B has an average of 80% and a standard deviation of 30%. Clearly, Paste A is superior to Paste B in both accuracy and precision. But what is the best way to express this difference? Is there one metric that will do it? Cpk is the answer.

Cpk is one metric that is sensitive to both the accuracy and precision. Cpk is defined as:




Where x is the average and S is the standard deviation.

Using these equations, we see that the Cpk of Paste A is 1.0, whereas the Cpk of Paste B is 0.333. Note that Paste B has a significant number of data points (about 17%) outside of the specification limits, however, Paste A has almost no data points out of specification.
So when evaluating most processes, Cpk tells it all!

Dr. Ron


Solder Alloy Density Equation: Why What Most People Think is Right is Wrong


It’s hard to believe but I have been blogging for over 10 years. In all of this time, with the hundreds of posts I have made, the most popular topic by far has been calculating density in a metal alloy. One of the reasons for this popularity has been the belief that the density of an alloy is determined by the equation

Eq. 1     eq1

Where x is the mass fraction of metal 1, y the mass fraction of metal two, ? (rho) the respective densities and ?t the total or alloy density. I have shown in the past that the correct formula to calculate the alloy’s density is:

Eq. 2    eq2

This formula is derived below again.

People continue to ask why equation number 1 is not correct, so I have posted an explanation that has been modestly helpful.  I have thought of an example that shows that Eq. 1 cannot be correct and have now derived an equation in the form of Eq. 1 that uses volume fractions instead of mass fractions.  This derivation is also below and the equation is:

Eq. 3       eq3

However, Eq. 3 is not very useful as the volume fraction of each metal is not as readily available as the mass fraction, which is easily measured with a scale.

Now, to give an example that shows that Eq. 1 is unreasonable, let’s consider a thought experiment that will help us conclude that Eq. 1 can be way off. Consider a cubic meter of air in a container 1 meter on a side at room temperature. The cubic meter of air will weigh 1.225 kg. (The fact air weighs this much surprises many people.) Inside the container is 1.225 kg of a fine gold powder. We blow the gold powder into the air and it covers all of the inside with an equal concentration. The powder is so fine that it will remain suspended for a short time. So we will consider this an alloy of gold and air.  The mass fractions x and y are equal at 0.50.  So if Eq. 1 were to hold true the density of the “alloy” would be:

Eq. 4    eq4

Figure 1. The gold dust and air density experiment.

Figure 1. The gold dust and air density experiment.

The weight of the 1 cubic meter container would now be 9650.6 kg/m3 * 1 meter3 = 9650.6 kg!  Whereas we know it to be 1.225 kg + 1.225 kg = 2.45 kg. Eq. 2 or 3 will provide the correct answer.

The correct derivations are below:


Eq. 5 6


Dr. Ron