Hypothesis and Confidence Interval Calculations for Cp and Cpks

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 rlasky@indium.com.

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 rlasky@indium.com.

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.

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

Become a Part of Patty and The Professor!

I have enjoyed writing the Patty and the Professor blog for about 10 years now. I’ve written about numerous real-life electronics assembly examples that I have encountered in my career, all disguised, of course.

To continue keeping things real, and to keep my readers involved, I am inviting you to submit an authentic story from your career. That’s right! You’re being invited to submit an idea, story, or experience that can be built into the Patty & The Professor series.

Your experience will help many other electronics assembly practitioners resolve their issues and avoid problems.

So, get your thoughts together, then shoot me an email at rlasky@indium.com. Share the details of your experience or observation. I may ask a few questions to help me comprehend the full story. Then, I will write up the segment and let you read it before posting. You will be credited, of course.

Bonus: You will also receive either a Dartmouth hat or coffee mug (similar to, not exactly like, those pictured below)!

Contact me if you are interested in submitting a story. I look forward to hearing from you!

 Cheers,

 Dr. Ron

The Professor’s second visit to ACME … continued

.

“Well what should we do Professor?” John said weakly. 

“Clearly, not shut the line down over the lunch break,” The Professor responded quickly. 

“We can’t!” said John, “The operators are all friends and they count on having lunch together.” 

“How much are they paid per hour?” asked The Professor. 

“Ten dollars,” replied John. 

 “You can pay them $15 per hour and still make more profit if they keep the line running over the lunch break,” The Professor opined. 

“Fifteen dollars per hour for the lunch time or the entire 40 hour week?” John asked nervously. 

“For the whole week,” was The Professor’s reply. 

“I find that hard to believe,” John shot back.

“Consider this,” said The Professor. “Your line is up only 9.7% of an 8 hour shift, that’s only 47 minutes. Today you lost 95 minutes over the lunch hour. You may be able to increase your uptime to greater than 15% by keeping the line running over lunch. I modeled your business with ProfitPro3.0 cost estimating software. Your company will make millions more per year if you keep the lines running over lunch. I have worked with other companies to make this change; it is really easy with a 30 minute lunch period. If 5 people normally run the line, you have just one stay back during lunch. That way each person only misses the regular lunch break once a week.”

John thought optimistically, “There is such a thing as a free lunch.”

“Now, let’s talk about what we can do to double the uptime from the 15% we will get by running the lines over lunch,” said the Professor.

Patty listened to all of this in amazement. The Professor was helping ACME more than she thought possible.

Next steps? Yes, John will keep his job. But, what is The Professor’s plan to get uptime to 30% or more? And, we still haven’t learned where Patty will go to dinner.  Stay tuned for the latest.

Cheers,

Dr. Ron

Dr. Ron note:  As surprising as this may seem, this story is based on real events. The uptime numbers and improvements are from real examples. Any company that can achieve 35% or more uptime can compete with anyone in the world, even in low labor rate countries. Sadly, few companies know their uptime or have an urgency to improve it.

Best Wishes,



Soldering 101: The Simplicity of Soldering – The Complexity of Solder Paste

Folks,

Soldering copper to copper with a tin-based solder, such as tin-lead eutectic solder or a common lead-free solder like SAC 305, requires only the liquid solder and copper to form the tin-copper intermetallic bond. This simplicity, with one small catch, was brought home to me by some colleagues at Speedline Technologies. They took a PWB with through-hole components mounted and ran it through a wave-soldering machine without using any flux. The result was comical. The PWB weighed about 10 pounds as it had huge solder ice cycles hanging off of it. Oxides that form on the copper created this mess. Running the board though again with a nitrogen blanket produced a beautifully wave-soldered board that could be ready to ship. So in reality, either a flux or nitrogen, preferably both are needed for successful wave soldering in addition to the solder and copper; however, it is still relatively simple.

Have sympathy for the solder scientists of the late 1970s and early 1980s. SMT was an emerging technology and the world wanted to buy solder paste; however, the only experience many solder scientists had was with wave soldering. In wave soldering, the flux’s main job is to remove the oxides from the PWB pads and components. The solder is in a molten state and its oxidation is not a main concern. In the soldering process, the solder only touches the board for a few seconds and the board only experiences the high temperatures during this brief period.

I imagine some early solder pastes consisted of solder powder with fluxes similar to those used in wave soldering. If so, they probably didn’t work too well. Consider the dramatic differences that solder paste experiences as compared to solder in wave soldering. The “flux” in solder paste has to remove oxides from the PWB pads, component leads, and solder particles, but it also has to protect all of these surfaces from re-oxidation for several minutes while in the reflow oven. To achieve this protection, the “flux” has to contain materials that act as an oxygen barrier. The most common materials used in no-clean solder pastes are rosins/resins. Rosins, or resins which are modified or synthetic rosins, are generally medium to high molecular weight organic compounds of 80-90% abietic acid. They are typically found in coniferous trees. Rosins/resins are tacky in nature, and provide some fluxing activity and oxidation resistance during the reflow process.

The reason I wrote “flux” in the above paragraph is that what most people call the flux in solder paste is a complex combination of materials. These “fluxes” will consist of:

    • Rosins/resins: for oxygen barrier and some fluxing activity
    • Rheological additives: to give the best printing properties, e.g., good response-to-pause, good transfer efficiency, excellent slump resistance, good tack, etc
    • Solvents: to dissolve the other materials
    • Activators: to perform the main fluxing action (removing oxides)

      Figure. Solder pastes are one of the most highly engineered materials.

Modern solder pastes must have good oxygen barrier capability. In most reflow profiles, the solder paste is at temperatures above 150ºC for more than several minutes. During this time, an oxygen barrier is needed to protect both the solder particles and the surfaces of the pads and leads.

A common example of an insufficient solder barrier is the graping defect or its relative, the head-in-pillow defect. If you are experiencing one of these defects, a solder paste with better oxygen barrier properties is bound to help.

Before reflow, the solder paste must print well, possess good response-to-pause, not shear thin, resist cold slump, and have good “tack” to support the components after placement. During reflow, in addition to the oxygen barrier challenge, the solder paste must not exhibit hot slump, should “Avoid the Void,” not create the “head-in-pillow” (HIP) defect, work with all common PWP pad finishes, and produce reliable solder joints in thermal cycling, drop shock, and vibration environments. Whew! What a complex challenge.

As a result I would argue that solder paste is a candidate to be the most highly engineered material in the world… and it certainly is NOT a commodity.

Cheers,
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.

Cheers,
Dr. Ron

Area Ratios for Elongated “D” Apertures

Folks,

Ismail writes: Dr. Ron, I know that the area ratio for circular and square stencil apertures is 4d/t.  What is it for an elongated “D” aperture?

 

The area ratio of a stencil aperture is the area of the aperture opening divided by the area of the side walls.  It is interesting, as Ismail points out, that the area ratio of a circular aperture is the same as that of a square aperture.  A little 10th-grade geometry will point this fact out.  It ends up that the area ratio of an elongated “D” is a little more complex.  All of these aperture shapes and that for a rectangle aperture are shown in Figure 1.   The area ratio formulas are at the bottom of the figure.

 

Figure 1. The area ratio for several shaped apertures. The elongated “D” aperture is third from the left.

 

 

 

 

 

 

 

 

 

A rule of thumb that still seems to hold is that the area ratio should be 0.66 or greater for the best printing result.  It is possible to do somewhat better (i.e with an area ratio less than 0.66) with a superior solder paste and/or some of the new stencil nano-coatings.

The derivation of the area ratio for the elongated “D” is in Figure 2.

Figure 2.  The derivation of the area ratio for an elongated D shaped aperture.

 

 

 

 

 

 

 

Cheers,

Dr. Ron