Hypothesis and Confidence Interval Calculations for Cp and Cpks

Posted on by

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.

———————————————————————————————————-

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

An Antidote to a Complex Environment

Posted on by

Years ago, ahead of a US election, I used this space to pen an open letter to the new president. I wrote that the race for office was heated and intense, but the winner should put aside any ill feelings and work toward the betterment of all Americans.

The column was timed to hit readers’ desks in November, just after the election results were announced. Magazine deadlines being what they were, of course, I wrote it in early October – more than four weeks prior to election day. In short, I submitted it to the printer having no clue who was actually going to win.

More than a few readers didn’t catch that little nuance, and they filled my inbox with screeds both positive and negative about the outcome, projecting their own biases on my musings and utterly missing the point I was trying to make about leadership.

Since then, I’ve stayed away – far away – from anything that even hints of politics, sensing it’s too charged a subject to use even as a metaphor for a larger point.

So, when an industry friend whom I respect more than he will ever know suggested I write an editorial about electronics companies requiring vaccination, and, in his words, “come out swinging in favor of it,” my first reaction was indifference.

Then we conducted a survey of US readers and found just under 60% plan to attend face-to-face events this year, and the top reason for staying home is, of course, Covid-19. That’s no way to get business done, not when there’s a perfectly good vaccine – more than one, actually – available and in most cases free.

As Covid-19 cases increase across the nation, primarily with unvaccinated persons, it’s hard not to be frustrated at the current state of the world. This is a largely preventable disease, , provided we choose to prevent it.

Although I will probably pay dearly for using this space as a soapbox for something that goes beyond electronics engineering, I can’t keep quiet knowing just how badly it’s affecting our industry, not to mention our world.

With that, I strongly encourage all companies – not just US-based ones – to mandate vaccinations for all workers, full-time, part-time and contract-based. Any visitors to their offices should be required to show proof of vaccination too. 

I realize that the unvaccinated have their reasons, and I’m not going to argue with them. But let it be known I wholly disagree with their stance. We must ensure we are doing everything we can to protect the health of our employees and each other. It’s time to take a stand.

Would-Be Foxconn Beneficiaries: Always A Bridesmaid

Posted on by

The University of Wisconsin this week became the latest would-be benefactor of Foxconn’s pretend largesse to acknowledge that it has been, in fact, jilted.

A UW-Madison response to a public records request by the Wisconsin State Journal on Monday shows the Taiwanese electronics company gave $700,000 in the first year of a five-year agreement and no money in the second or third year. The amount to date represents less than 1% of the original commitment.

“I am not at this point expecting to receive that gift,” Blank said in an interview with the State Journal editorial board last week. “It’d be nice. I think it’s unlikely.”

— UW Chancellor Rebecca Blank

UW should feel no embarrassment at falling for the Taiwanese ODM’s promises of riches — in this case, $100 million in grants. The list of brides left standing at the altar by Foxconn is long and global.

Perhaps one day, when Foxconn comes knocking, the prospective bride will demand the ring — and the cash — upfront.

Somehow, however, I tend to doubt it.

From Boards to Brews

Posted on by

In case you were wondering whatever happened to IBM’s once sprawling campuses in Endicott, East Fishkill, and other western New York towns, where Big Blue made everything from semiconductors to laminates to circuit boards, the New York Times has the story.

Spoiler alert: Like so many other old mill buildings, breweries, among other businesses, are moving in.

Solution to Moore’s Law

Posted on by

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

All in on Altium?

Posted on by

Autodesk’s bid — declined, so far — for Altium took me by surprise. In retrospect, it probably shouldn’t have.

As I’ve noted many times, I fully expect Altium to be acquired. It’s just I was looking more in the direction of Dassault and PTC, the big mechanical CAD (MCAD) players. I should kept Autodesk in my field of view, especially after it acquired Eagle five years ago. I think I was lulled to sleep, as that was a small acquisition and Autodesk hasn’t made much of a push since to burrow into the ECAD space.

The proposal was hefty, valuing Altium at $3.91 billion. That’s not much lower than Siemens paid for the considerably larger and more profitable Mentor Graphics in 2107. Yet Altium thinks it can do better.

It just might. Autodesk’s bid prices each Altium share at AU$38.50, a 41.5% premium over Altium’s closing price on Jun. 4 and a premium of over 47.4% to the one-month volume-weighted average price. Prior to the offering, however, Altium’s stock had peaked at a 52-week high of AU$39.34 in last October. So at $38.50, Autodesk was actually underbidding a bit.

An Autodesk-Altium merger wouldn’t change the face of the ECAD industry immediately. Altium would still run neck-and-neck with Zuken for third place in revenues behind Cadence and Mentor. But it would give Altium the backing of a industry leader in 3-D CAD, and accelerate the inevitable MCAD-ECAD merger.

Checking Moore’s Law

Posted on by

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

Posted on by

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

New Semi Group Needs to Talk Bigger Goals than Just Subsidies

Posted on by

“You never want a serious crisis to go to waste. And what I mean by that is an opportunity to do things that you think you could not do before.” ? Rahm Emanuel

Indeed.

In the wake of the latest components inventory crisis, the lobbyists are out in full-force trolling for subsidies for the semiconductor industry.

And if the usual suspects weren’t enough, many of the blue chip (no pun intended) companies that make up the Semiconductor Industry Association and SEMI this week launched yet another industry organization, the Semiconductors in America Coalition. the group supports the allocation of $50 billion by the US government (read: taxpayers) to fund advanced semiconductor manufacturing. The announcement came at almost the same time – coincidence? – IBM reported successful development of 2nm process using a 300mm wafer.

That prompted a longtime friend and industry observer to suggest, “rather than spending money directly, the US and state governments offer the same deal to the supply chain as a whole as do the South Korean, Chinese, and Taiwanese governments. A holistic response is needed. Maybe a carrot to keep 2nm tech onshore.

“We need to bring a number of critical technologies back; chips, packaging, HDI, transposers and even certain components,” he went on.

“Apple has been using black solder mask for decades now to prevent piracy and it has worked. Their keiritsu approach works. Keeping key technologies within the kimono, as the Japanese say, and bringing those key industrial components back, would help to reaffirm North American industrial security and protect our supply chain.”

I can see where he’s coming from, but Apple really doesn’t have the scale of the other communications and computing OEMs; it’s share of the worldwide smartphone market is about 15%, and it has only 8% of the PC market. It’s probably not the model to emulate in that regard. More interesting is its recent decision to go full bore with its own M1 processor, which is made by TMSC.

I know Samsung and TMSC are also working on (close to?) 2nm. I don’t think IBM alone has the scale anymore to be a difference-maker, which is where the other fabs need to step up. They all smell an opportunity, and it’s hard to blame them for trying to get their hands on “free” money.

What I haven’t seen is an overarching policy proposed by the various trade groups/lobbyists promoting onshore wafer production. It seems more piecemeal to me, with new associations stacked atop legacy ones, all promoting the same message (subsidies) but with no promise of tangible returns.

I’m not against government subsidies for critical tech – and semi is absolutely one of those – but it seems to me they should start with a goal and then fill in the rest (processes, funding, etc.).

Sans a clear objective, the game plan will not only be expensive and a hard sell, but doomed to break down.

US Semiconductor Independence Comes a Little Late for EI

Posted on by

“Rebuilding the US packaging industry would not only insulate chip companies and their customers from political risk, it could also help them break free of the long cycles involved in creating new chips, said Tony Levi, a professor of electrical and computer engineering at the University of Southern California.”

Reading that, I can’t help but think of Endicott Interconnect Technology and what might have been.

It must have been 15 years ago when I toured EI, the one-time IBM campus where bare board fabrication, assembly and chip packaging all took place. So self-contained was the operation, in fact, they had their own laminate treater.

EI was where the HyperBGA and CoreEZ high-speed flip-chip BGA packages were invented, as well as custom laminates for semiconductor packages. The engineering talent was second to none. They really could do it all.

What they never mastered, however, was the right scale. Agreements to license their products went nowhere. The layout complicated process flow: I remember having to duck to avoid banging my head as I would my way through the partially subterranean assembly facility. Dwindling revenues coupled with the high cost of doing business in New York ultimately scuttled the company, and the assets were sold to TTM in 2019.

With today’s emphasis from President Biden on down on rebuilding the US semiconductor industry, however, one can’t help but wonder whether EI was the right idea, just 20 years ahead of its time.