Comparing Two Wiebull Distributions


Let’s look at Patty’s last day of class …

As she was driving north to teach her statistics class, Patty was sad to see her stint at Ivy U come to a close. She was even more nervous about her meeting with Dean Howard after the class.

Before she knew it, she was standing in front of the class, to start her last lecture on Weibull analysis.

“Are there any questions before I begin?” Patty asked.

Patty nodded to Megan Ramsey.

“Professor, last time we talked about when a few samples don’t fail in a test that they are often censored in Weibull analysis. You mentioned that many people probably think it is good that some samples don’t fail. However, if the samples did fail at a later time it increases the scatter and would make the data worse. I’m not sure I understand that concept, as the scale has increased and the the top 10% of the samples would have a much longer life,” Megan summarized.

“Megan has an interesting point. Let me put both the censored (blue) and hypothetical data if the fails came later (red) on one graph. Discuss it for a while with those sitting next to you and see if you can conclude which data are better,” Patty suggested.

About three minutes went by and Patty called the class to order.

Megan was the first to raise her hand, which Patty acknowledged.

“After discussing it with Pete, (there were a few rolled eyes and soft whistles as everyone knew that Megan and Pete were an ‘item’) we concluded that the censored data (blue) is better. The most critical reason is that it predicts the smallest number of fails at a lowest number of cycles. We think this will always be the critical concern in reliability,” Megan answered.

“Precisely! This reason is why unfailed samples are not an endorsement to superior reliability. The censored data predict twice as many cycles – at a 5% failure rate. It is almost certainly misleading,” Patty said.

She chuckled a little then said, “If you want to impress someone in a job interview, discuss this topic.”

Patty didn’t know it, but one of the reasons the students like her as an instructor was her experience as an engineer. The many professors at Ivy U were brilliant, but few of them had actually been an engineer or managed a manufacturing process.

“OK, we have one last topic: how to tell if two Weibull distributions are statistically different,” Patty said.

“Let’s look at Weibull plots of stress test failures of alloys 5 and 6,” Patty said.

Prashant Patyl raised his hand.

“Yes, Prashant,” Patty acknowledged.

“Well. Alloy 6 (red) has a slightly higher scale and steeper slope, suggesting it is better, but it would be hard to say if it is statistically significantly better,” Prashant answered.

“Precisely,” Patty answered.

“Let’s try the plain old two sample t test,” Patty went on and showed a boxplot of the data.

The class chuckled a bit, as this test would be considered much more mundane than Weibull analysis.

“The t test shows that there is only a 30% confidence that the means are different. Just by visual inspection, the boxplot (below) suggests as much. So it would be hard to argue that the data are different at a 95% confidence level,” Patty elaborated.

Her comments resulted in much lively discussion about the normality of the data, if the mean a reasonable metric for comparison, and other perspectives and other related topics.

The ending of the class was very upbeat, so Patty was feeling an emotional high, until she remembered that she had to meet with Dean Howard. With trepidation, she headed toward his office. As she headed in, she was shaking a little.

“Professor Coleman, it’s great to see you,” Dean Howard said with enthusiasm and warmth.

Patty still couldn’t get used to being called “Professor,“ but she had checked on the Ivy U website and she was listed as a “Visiting Associate Professor.” They even had a webpage for her. She thought the photo they used made her look too old.

Before she could answer, Dean Howard got to the point.

“We have really been impressed with the teaching job you have done. The students were especially appreciative of your teaching style,” Dean Howard started.

“Thank you,” Patty said, her relief palpable.

“It appears that Professor Harlow, whom you are filling in for, will require a longer recovery than thought. In addition, we need a course on manufacturing processes. The bottom line is we want you to join the faculty to help us with these courses,” Dean Howard continued.

Patty nearly swooned.

“But sir, I don’t have a Ph.D.,” Patty responded.

“Our plan is that you have done such significant work at ACME, that you don’t need to do a thesis. We want you to take four courses while you teach. After successful completion of these courses, we will award you a Ph.D.,” Dean Howard went on.

Patty was so stunned she didn’t know what to say. She was silent for a while.

The Dean continued, “We can’t quite match your salary at ACME, but we can come close. I have already discussed the situation with Mike Madigan. He is supportive, but said the decision is obviously up to you. What do you think?”

Patty’s mind was spinning. Rob was getting his Ph.D. here, so that would help.

It was as if she was outside of her body looking and she saw herself say, “I would love to.”

They talked for 10 more minutes about some of the details and Patty relaxed a little. It occurred to her that she had not discussed it with Rob yet. Oh well. She expected that he would be supportive.

As they were wrapping things up, Dean Howard appeared to want to discuss a different topic.

After a few minutes of additional discussion, Patty left with a smile on her face.


Pete, as usual, always knew what was going on. He had never felt so depressed. He and Patty were a team. They had traveled all over the world solving electronics assembly problems and she was abandoning him to got to Ivy U! He was also nervous. He wasn’t that thrilled with the other people he thought likely to be his new boss. So, with head hanging, he shuffled toward Patty’s office.

“Hey, Pete! It’s great to see you!” Patty said cheerfully.

Pete got all choked up and didn’t know what to say. Finally, he mumbled with a shaky voice, “You’re leaving.”

“So are you!” Patty responded. “Assuming you want to be the Senior Research Associate for Manufacturing Processes at Ivy U.” They are even offering you 10% more than you make here – and the benefits are great,” she finished.

“Right after my offer, Dean Howard asked if I knew someone who could fill such a position, so I immediately suggested you. Apparently my endorsement was enough to land you the job, if you want it. Don’t screw it up,” she teased.

Patty, The Professor, and Pete in one location. Only time will tell what new adventures await.


Dr. Ron


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Jerry Shore, RIP

I didn’t know Jerry Shore, except by name, so I can’t really comment directly on his passing this week at the age of 88. But he was a significant force in the printed circuit industry for decades, founding Park Electrochemical in 1954 and building it into a laminates powerhouse up until his retirement, in 2004.

My friend Gene Weiner did know Jerry well, however, and he offers his thoughts on his blog here.

To the entire Shore family, including son Brian, who has been running Park since Jerry stepped down as CEO in 1996, our sincere condolences.

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V-Score Panelization

V-score top view

My last post talked a bit about panelization, in general. Today, I’m taking a look at V-score panelization. V-score is created by running a V-shaped blade across the top and bottom of the panel without cutting all the way through. The board in the mini-image of my prior post is V-scored. Shown above is a closeup of the V-scoring.

(Note that the cross-hatched area is not in the active circuit portion of the panel. It’s in the rails. You’d never want to cut through copper like that in part of the board that will be used. Even here, it would be best not to have copper in the path of the v-scoring blade.)

You’ll note that it’s all straight lines. V-score can only separate rectangular panelized boards. For curves, you’ll need to use a different technique.

V-score edge onThe next image down, on the left, shows an edge-on view of the V-score. You can clearly see what I mean by “without cutting all the way through.” The cut leaves enough material to hold the boards solidly together during processing, but easy to separate.

V-score de paneled edgeBy the way, we generally don’t just snap them apart. We’ve got a special tool – a bit like a pizza cutter in a fixture – specifically designed to separate them without stressing or bending the board. If we feel there’s any risk of over-stressing, we’ll use the tool.

The next image, here on the right, shows a board edge after depanelization. Note that it’s not a smooth, flat edge.

In contrast, the next image down, on the right, shows a flat milled edge. Generally, though, you can’t visually tell the difference without close examination. You can, however, feel it if you run your finger lightly along the edge. Just be careful to not get slivers.

Next time, I’ll examine tab-routing, which will permit non-rectangular shapes.

Milled edgeDuane Benson
I saw two Buffalos, two Buffalos,
Buffaloes on my lawn,
Romping all around and stomping on the ground
And all of my grass was gone.

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Robots and the Law

In the April issue of PCD&F/CIRCUITS ASSEMBLY, I wrote about the need for a balance between autonomous machinery and human-operation equipment. I wrote the piece in the aftermath of the Malaysia Airlines Flight 370 disappearance, and referenced, among other things, the Toyota sudden unintended acceleration problems and the self-driving cars that are beginning to appear on US streets.

Seems I’m not the only one working their way through this. On May 5, a pair of researchers at the Brookings Institution began a series of papers (The Robots Are Coming: The Project On Civilian Robotics) that considers the legal ramifications of driverless cars.

That led me to Google, which uncovered a few more references to potential tort roadblocks.

While my work considered the technical and emotional issues that always factor into to any major technology shift, the legal aspects are equally in play here. For those interested in the subject, the Brookings Institution project is especially worth a read.





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PCB Panel Routing Technique

Most PCBs we receive are individually routed; i.e., not panelized. That doesn’t mean that, sometimes, sending them in a panel isn’t a good idea, or required. Generally, we don’t require panels (sometimes called a pallet), but there are some cases when we do.

V-score panelIf the individual PCB destined for Full Proto service is smaller than 0.75″ x 0.75″, it needs to be panelized. If a PCB needing Short Run production service is less than 16 sq. in., it needs to be in a panel of at least 16 square inches to qualify for Short Run.

So, you ask, why else might I want to panelize my PCBs? Keep reading and I’ll tell you why.

  • First, if you’ve got a lot of small boards, it’s easier to handle and protect then when they’re in a panel. A few panels can be more safely packed coming and going from our shop here.
  • You may be able to get the through our factory faster. If you have a really large number, and need them super fast, panelizing them may enable that fast turn. With a lot of boards, sometimes, it simply isn’t physically possible to put them all on the machine, run them and take them off, in a short turn time. Panelize them and the machine will be running longer for each board change, which reduces the total run time.
  • It may also cost you less. If you use leadless parts like BGAs, QFNs or LGAs, you can usually reduce your cost a bit by panelizing the boards. Leadless parts cost a little extra because of the X-Ray test needed, but the extra handling is mostly per board, rather than per part. One panel of ten boards with ten BGA, in total, will cost a little less than ten individual boards with one BGA each.

Stay tuned for my next few posts where I’ll cover the pluses and minuses of different panelization techniques.

Duane Benson
I looked outside my window and what do you think I saw?
The strangest sight I’ve ever seen you’ll never guess just what I mean,
I can’t believe it myself

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Weibull Analysis at Ivy U


Let’s check in on how Patty is doing at Ivy U.

Patty was nearing the end of her teaching stint at Ivy U. Only a few more classes remained. She had to admit that she was sad to see this adventure end. Oh, well, such is life.

The syllabus allowed for the last few lectures to cover “Selected Topics,” so Patty decided that her selected topics would be Weibull Analysis. She felt passionately that all engineers should have some exposure to failure analysis and this topic fit right in to engineering statistics.

Before she knew it, she was heading north up to Ivy U for her next-to-the-last lecture. She thought she should soak in the beauty of the campus as her car approached, for soon this would be her last time at Ivy U for a while. Today she was lucky, she found a parking spot right away.

As she walked into the main engineering building, she noticed a note in her mailbox. It was from Dean Howard. She quickly opened it. He was requesting a brief meeting after her last class.

“Yikes!” thought Patty, “Dean Howard wants to see me! I wonder if it’s serious. Did I goof up, somehow?”

She would have to wait for two days to find out what the Dean wanted and she couldn’t worry about it now, as her class was starting in 10 minutes.

Patty began the class by explaining the development of Weibull’s theory and gave a few examples. She showed where the scale factor and slope came from. Patty emphasized that a steep slope indicted a tight distribution of data (a good thing for prediction from the data) and that a larger scale suggested a longer mean life. She then discussed the importance of different types of tests in electronics, such as thermal cycle testing and drop shock testing. As an example, she thought she would share some accelerated thermal cycle data for two different alloys that are used in electronics assembly.

She showed the first set of data in a PowerPoint slide (Figure 1).

“Can someone explain these results to me?” Patty asked.

After some murmuring, Karen Armstrong raised her hand.

“Yes, Karen,” Patty responded.

“It appears that Alloy 2 demonstrated superior performance, as seen in its much steeper slope and slightly better scale,” Karen answered.

“Nice job, Karen,” Patty responded.

“What about this one point?” Patty asked as she pointed to the obvious outlier for Alloy 1.

There was more murmuring, but no one raise their hand. So Patty showed a slide with the outlier removed.

“I have removed the outlier because failure analysis showed it was atypical,” Patty said.

“As you can see, now alloy 1 has a slightly better slope. This suggested a tighter distribution and hence more ability to predict performance,” she went on.

There was now very loud murmuring, finally Scott Bryzinski raised his hand.

“Yes, Scott?” Patty responded.

“Professor, it just seems like cheating, dropping a bad data point because you claim it is not representative of the other samples,” Scott explained.

There were many loud echoes of agreement.

Patty chuckled a little.

“OK, OK, you are right. It is not fair to censor a data point in most cases. This is part of the lesson of this class. Don’t censor data lightly,” Patty said.

“Let’s look at data for Alloy 3 and 4,” Patty went on.

The students looked at the data for some time and finally Diane Pompey raised her hand.

“Yes, Diane,” Patty acknowledged.

“They look about as dead even as one could expect, except that the sample sizes are different. Alloy 3 has 15 samples and Alloy 4 only 13 samples, as can be seen in column ‘F’ in the ‘Table of Statistics’,” Diane explained.

“Nice work Diane, few people would have picked up on that difference,” Patty replied.

“I will tell you that both alloy 3 and 4 had 15 samples to start with in the test. What do you think happened?” asked Patty.

Very quickly, Fred Wilkins raised his hand. Patty nodded to him.

“I’ll bet that two of the samples from alloy 4 did not fail,” Fred suggested.

“Correct!” Patty responded enthusiastically.

“I want you all to take a few minutes to discuss this situation with those seated around you. I then want you to vote anonymously whether the two samples that did not fail make alloy 4 the same, better or worse than alloy 3,” Patty instructed.

After five minutes of noisy discourse, the students voted on a website, the results of which Patty could show on her laptop and project to the class. Twelve students thought the alloys were still the same. 24 thought alloy 4 was better, and 6 thought alloy 4 was worse.

“Any comments on the results?” Patty asked.

There were no takers.

“Let’s assume that the two samples that failed were tested for a much longer time and they finally failed at some very high number of cycles, say 2,000. Let’s look at what the Weibull plot would look like,” Patty said.

She then showed Figure 4.

“Can anyone explain it?” Patty asked.

After a short time, Young Koh raided his hand.

“Dr. Coleman, the added cycles increased the scale significantly, but ruined the slope, suggesting much more scatter in the data. As you suggested earlier, reliability testing is about hoping to have the ability to predict lifetime. With the large decrease in the slope, prediction becomes much more difficult, So, sample 4 is likely worse than sample 3, even though it has a large scale.” Young expounded.

“Precisely,” Patty answered.

“It is interesting to note that many engineers in the electronics industry today just ignore the samples that don’t fail,” Patty went on.

The class looked at her with shocked faces.

“Well, that’s all until next time,” Patty said.

“Two of the female students, Jessica Han and Mary Connor, stayed after the class to talk to Patty.

“Professor, there is a rumor that you will be teaching “Manufacutring Processes” next term, is it true?” Mary asked. Then went on, “We really hope so. You are best teacher here.”

Patty was so touched she started getting a little misty eyed, “Thank you for your kind comment, but I doubt that that will be the case,” she said as her voice quavered.

Will the Dean fire Patty or will she be teaching Manufacturing Processes the next term. Stay tuned to see.


Dr. Ron


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Could Foxconn Deal Bite Apple?

The notion that Foxconn might take a large stake in a major Taiwanese telecom equipment company poses a litany of interesting questions for its largest customer — Apple.

For example, Foxconn, which gets 40% of its revenue from Apple, could now be in position to become both a major Apple supplier and a major enabler, since millions of iPhones and iPads would conceivably be connected via Asia Pacific Telecom’s network. What influence could Foxconn thus have over Apple’s ability to operate in key Southeast Asia markets? Would it possibly seek to leverage that network by negotiating with Samsung to force better pricing from Apple? Will other major EMS/ODMs that play heavily in this space (Jabil, Pegatron, Compal, Wistron) follow Foxconn’s lead?

The EMS/ODM model continues to evolve. Foxconn seems intent on speeding that evolution ever faster.




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SEC Upholds Conflict Minerals Reporting Deadline

US Securities and Exchange (SEC) Commission Chair Mary Jo White on April 29 said that the agency will continue to implement the conflict minerals rule upheld by the US Court of Appeals.

The SEC has also issued guidance on meeting the May 31 reporting deadline. The gist is that companies must meet the deadline as expected, but may omit aspectsstruck down recently by the US Court of Appeals.

SEC Division of Corporation Finance Director Keith Higgins said companies should comply with parts of the rule that the court upheld and file initial reports by June 2 (reports will be due on June 2, 2014 as the May 31 deadline falls on a Saturday). Thing is, most parts of the rule were upheld, so there is very little change to requirements on the whole.

Higgins said no company will be required to describe products as “not been found to be ‘DRC conflict free’” but companies will still have to disclose the origins of the products.

Legal outlook.Insiders at IPC say that yesterday the industry petitioners, led by the National Association of Manufacturers, filed a Motion for a Stay with the SEC in the conflict minerals case. If the SEC denies the stay, the petitioners will consider filing a stay request with the DC Circuit.

On April 14, U.S. Court of Appeals for the District of Columbia Circuit ruled that the requirement that firms report whether their products have “not been found to be ‘DRC conflict free,’ included in the SEC conflict minerals regulation, violates the First Amendment.

If there is no stay requested or granted, and the case is remanded to the district court, that court may simply remand to the SEC to implement the DC Circuit’s decision in the first instance.

Do I have to file? So it’s business as usual for conflict mineral compliance. And the deadline at the end of May approacheth.

There are two categories of companies who must report.

  1. The first is standard: a company that uses minerals including tantalum, tin, gold or tungsten if that company a)files reports with the SEC under the Exchange Act, b) the minerals are “necessary to the functionality or production” of a product manufactured or contracted to be manufactured by the company. For more on this, visit this helpful FAQ.
  2. The second category of company that must report is a softer definition, for these are companies whose downstream customers demand information on raw materials so that the downstream company can then file with the SEC. So, even though your company may not have to file with the SEC, if you’re a supplier to a company that does, then you’ll have to report to them on your conflict mineral uses. Yes, it will be challenging. But it’s not impossible.
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Component Packages — Let’s Get Small

I’ve been on a bit of a package binge lately. First talking about metric vs. US passive sizes, and then a very tiny ARM Cortex M0 from Freescale.

The Freescale BGA part checks in at 1.6 x 2mm. That’s cool and I’m almost always in favor of making things as small as possible, but, as I wrote in my prior blog on the subject, it’s not always possible. The 0.4mm pitch BGA is problematic unless you can spend a lot of money on the raw PCBs, or will have super high volume.

All is not lost, though. You still can use a tiny ARM Cortex M0 part. Just not quite as tiny. That same part also comes in a 3 x 3mm QFN package. You lose four pins (16 vs. 20) going from the BGA to the QFN, but if you can handle that, it’s a very viable option that doesn’t require any exotic circuit board technologies.

A few years ago QFNs were scary, but not so much any more. I’ve designed a few of them in using Eagle CAD. Just be sure to pay attention to the footprint. A 6 mil trace is more than small enough for a 0.5mm pitch QFN.

Duane Benson
Strive at all times to bend, fold, spindle and mutilate

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‘Patty’ in the Real World


Every year, the wonderful folks at PCM host a visit from my class on manufacturing processes and provide a real-world tour of an electronics assembly facility. Our relationship has resulted in the class producing a video on electronics assembly. In addition, several class projects have been performed at PCM over the years; projects that have helped my students learn and have, hopefully, helped PCM’s operation.

A few weeks ago it was time for this year’s student visit. Rob Steele and Jon Scheiner were our hosts. During the tour, Rob mentioned that he and the PCM team have implemented many of the productivity concepts discussed in The Adventures of Patty and the Professor. Rob even mentioned that he thought the book, at some level, was a “page turner.” It is personally rewarding to see people benefiting from this book.

Anyway it is very clear from our tour that productivity is high at PCM. It is my hope that others might also benefit from the stories in The Adventures of Patty and the Professor. If you have benefited from the book, please let me know.


Dr. Ron


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