Demonstrating Zero Defects In SMT Production?

Folks, let’s see how Patty is doing at Ivy U …

Patty had to admit that she really liked being a professor at Ivy University. No, that wasn’t strong enough; she was ecstatic. The combination of the stimulating and collegial environment and the flexible schedule was terrific. She was able to play a little more golf and spend more time with Rob and the boys. 

In addition to developing a course on manufacturing processes, she was asked to teach an additional offering on statistics. Engineering enrollments had increased so much that another stats class was needed. Teaching stats gave her an opportunity to delve into topics she was interesting in learning more about, such as non-parametric analysis, cluster analysis, and numerous other statistical concepts.

She was also happy for Pete. As much as he enjoyed working with her at ACME, he, too, was thrilled to be at Ivy U. As a research associate, he spent a lot of time working with students on projects for their classes. He was surprised at how grateful the students were for his practical experience.

As Patty was thinking these pleasant thoughts in her office, suddenly Pete was at the door.

“Hey, Professor Coleman! The folks we left behind at ACME are being asked, forced really, to guarantee zero defects by examining a small sample size, say 20 samples,” Pete announced. Pete had stopped calling her “kiddo” and now teased her by calling her “Professor Coleman.”

“We both know that’s impossible. Tell me more,” Patty answered.

“Well, ACME just hired our favorite SMT engineer … after Hal Lindsay,” Pete responded.

“Oh, no! Not Reggie Peirpont,” groaned Patty.

Reggie was a well-meaning sort of chap who had some good ideas. But, his follow through was often sloppy and only touched the surface of what was needed from an engineering perspective. He was a very good salesman of his ideas and had a following in some SMT circles.

“What is he foisting on ACME?, Patty asked.

“A zero defect program,” Pete replied.

“Sounds like a worthy goal. But, let me guess, he has convinced everyone that they can demonstrate with 95% confidence they have zero defects by only sampling 20 units,” Patty said.

“Precisely,” Pete chuckled.

“I’ll contact Mike Madigan,” Patty said.

Patty had agreed to Mike’s request that she be available to consult for a year or so. And, he also made her promise to contact him if she knew they were doing something foolish.

Patty sent Mike an email with her concerns, and with some analysis. She suggested a teleconference.

Time passed quickly and, before they knew it, Patty and Pete were on a telecon with Madigan, Peirpont, and a few staff people.

Their discussion started with the good points of a zero defects program. On this topic, everyone was in agreement. Eventually, Madigan grew impatient.

“Peirpont! According to Coleman, your assessment that we only need to sample 20 units to demonstrate zero defects with 95% confidence is bull s__t.” Mike began, always getting quickly to the point.

Patty then said, “Let’s let Reggie explain his analysis.”

“Well it’s simple,” Reggie began. “All you have to do is recognize that 1 is 5% of 20, so if you sample 20 and don’t get a defect you can be 95% confident you have no defects,” he finished.

“Yikes,” Patty thought.

“Well, Coleman?” Madigan asked.

“That approach is not correct. A correct method is what I sent to Mike in an email” Patty answered.

“Before we begin the analysis, look at the photo I sent. The red bead is one bead in 2,000 white ones. Ask yourself how you could detect this one “defect” by sampling only 20 beads?” Patty said.

There was some murmuring and groaning, Patty could tell this visual really help to define the issue.

“OK, Patty. Please explain your analysis,” Mike asked.

“Let’s say that the defect level is 1 in a thousand. If I sample the first unit, the chance it is good is 0.999. What is that chance that the first two units would be good?” Patty began.

“0.999*0.999,” Pete answered.

“Correct!” Patty said.

“Let’s say I keep sampling until the likelihood that I have still found no defects is 0.05,” Patty went on.

“Let me take this one,” Madigan said.

“You now have 0.999^n = 0.05. So there is only a 0.05 chance you would not have found a defect if the defect rate is one in a thousand,” Madigan continued.

“So what could you say about the defect rate if you found no defects in n units? Patty asked.

“I got it! I got it!” Madigan shot back enthusiastically.

Patty was incredulous. Mike Madigan, CEO of multibillion dollar ACME Corp, was like a second grader excited to show the teacher he understood.

“You can say that the defect rate is 1 in a 1000 with a confidence of 1–0.05, or 95%,” Madigan said with excitement.

“Actually, you can say that the defect rate is 1 in a thousand or less,” Patty said.

“But we need to know n,” Madigan implored.

“Well, let’s solve for n with logarithms,” Patty suggested.

Groaning was heard over the telecon. No one likes logarithms!

Since their telecom was on GoToMeeting, Patty showed the solution:

n = log 0.05/log .999 = 2994.23

“Man! So we have to sample almost 3,000 units with no defects to demonstrate 1 defect per 1,000 or less?” Madigan asked with disappointment in his voice.

“Yes,” Patty responded.

She continued, “It ends up with a good rule of thumb. Since n is close to 3,000, let’s say that is the number we need to analyze. To demonstrate 1 in 10,000 defects or less, n is 30,000, one in a million or less, and n is 3 million.”

“So, n is 3 times 1 divided by the defect level you are trying to establish?” Madigan asked.

“Exactly,” Patty answered.

Patty wrote it on the PowerPoint slide:

To establish a certain defect level or less with 95% confidence, one must sample n units with no defects

n = 3 x 1/defect level

“That means to establish zero defects, we need an infinite sample,” Madigan sighed.

“Yep!” Patty replied.

“Peirpont! What do you have to say for yourself?” Madigan barked.

“Well, in the first case, Patty said 1 defect per thousand or less. It still could be zero defects,” Peirpont responded glumly.

Patty was going to respond, but Madigan beat her to it.

“But, you can’t prove it is zero. Only 1 in a thousand or less. So, to be conservative, we would say that the defect level would be 1 in a 1,000. That’s what is proved,” Madigan opined testily.

The meeting ended with Madigan expressing his thanks, an unusual thing for him. Peirpont said little else. It was clear he was probably going to get a talking to by Mike Madigan.

Patty was a little wistful after the meeting. She missed ACME and the folks there, even the occasionally cranky Mike Madigan. But every day she felt more like her home was at Ivy U.


Dr. Ron

Epilogue. As with all Patty and the Professor posts, this one is based on a true story. After sharing this concept with a colleague who had to get FDA approval for drug trials, she decided to ask statistician job applicants: “Do you think you could develop a sampling plan that could assure with 95% confidence that there were no defects in a population?” The last I talked to her, most job candidates had said yes.

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Alloy Density Calculator Generates Most Interest of All Blog Posts


In the nearly 10 years that I have been blogging, I am continually surprised by the interest in a spreadsheet I created that calculates alloy densities.  I get about numerous inquiries a year on this topic.  We just renewed the link to the software, so I thought I would write a summary blog on its use and applicability.

First of all, the algorithm is intended for metals that form an alloy. Examples would be most solders and other metal systems where the metal atoms replace each other in the lattice. So, in addition to solders, copper and nickel would also work. The calculation assumes perfect mixing and that the sum of the initial volumes of the metals equals the total final volume. The correct formula for calculating densities is:

1/Da = x/D1 + y/D2 + z/D3


Da = density of final alloy

D1 = density of metal 1

x = mass fraction of metal 1

And the same for metals 2 and 3. 

This formula was derived in a past blog post. People are often surprised that the simple formula Da = xD1 + yD2 + zD3 is not correct.  The reason it is not correct is that density is inversely proportional to volume.  The error with this formula is discussed in another post.  The error, by using this formula, can be quite large. See the graph below for gold and copper. In some cases the error is more than 15%.

One example where the algorithm does not work would be for intermetallic compounds. The reason is that an intermetallic is a compound, not an alloy. Another example where the formula does not work is carbon in iron. The carbon atom is so small that it fits in between the iron atoms.

How accurate is the formula?  Work that I have performed with solder alloys suggests is it about 1-2% accurate. The accuracy can be affected by grain boundaries and the small amount of intermetallics that can form in some solder alloys.  An example is the small amount of  intermetallic “silver plate” (Ag3Sn) that can form in SAC alloys. I hope that many readers continue to find the density calculator useful.


Dr. Ron

Math musings. I read a fun book, The Joy of X. In the book, the author, Steven Strogatz, pointed out that the sum of consecutive odd numbers is always a perfect square. Try it: 1+3 = 4 = 2^2,  1+3+5 = 9 = 3^2 , 1+3+5+7 = 16 = 4^2, and so on.

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Panel Rails — What Are They?

I referred to “panel rails” in my blog about V-score panels, but I didn’t explain the “whats” and whys” of panel rails. You might find yourself asking “what are panel rails and why would I want to use them?”

Well, first of all, for our Full-Proto service, we don’t require panels or panel rails. We’ll take just about any old board that’s bigger than 0.75″ x 0.75″ and smaller than 14.5″ x 19.5″ and run it through our machines. For our short-run production service, we only require panelization for boards less than 16″ sq.

That being said, panel rails do have a purpose. They give the machines a spot to grab onto without coming close to components. They’re also a convenient place to put fiducials (more fiducial info here).

As you can see in the image below, the panels give a clear area for handling the panel.

Tab routed panel

There are two important things to note about this panel. First, look closely at the four outside corners. You can see the scoring for easy separation of the rails. This designer made sure that there isn’t any copper where the scores are. That’s the right way to do it. The V-Score blog shows a panel rail done the wrong way – with copper across the cut.

Next, this board has fiducials. Good. But, the fiducials are in a symmetrical pattern. Not so good. IPC-7351b-3-10 specifies a non-symmetrical pattern so that the board can only be processed in one orientation.

Duane Benson
Once I build a panel rail, now it’s done
Brother can you spare a diode

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How Far Should Sustainability ‘Standardization’ Go?

My longtime friend and industry colleague Pam Gordon blogged today about the role trade associations should play in driving the industry toward sustainability practices. In it, she writes

Associations will not necessarily push members to the next level of sustainability practices. But members can raise the baseline through their involvement and commitment — emphasizing that the industry’s continued profitability and continuity rests in good part on meeting customers’ increasing efficiency requirements, avoiding dependence on dwindling materials, and reducing costs through design-for-environment principles.

I agree with all that. But Gordon also mentions a colleague’s discussion of the possibility of trade groups offering certification in supply-chain sustainability, suggesting that those that do not are behind the curve. There, I’m very reluctant to concur.

I am a huge fan of standards, but I also recognize their limits. I view sustainability as an extension of innovation. And innovation is not something that can be standardized. Those companies that consistently adapt fastest to market demands are always the winners in the long run. I think the same will be true with design for recycling and reuse and other such initiatives. Companies will either pursue that course or not, but to add a layer of bureaucracy in the form of yet another pursuit of paper isn’t the way to go.

Pam writes that some associations help members raise their own sustainability goals above the level of current regulations by giving them workable frameworks, such as the codes of conduct from the Electronics Industry Citizenship Coalition. I have long felt the EICC’s code of conduct is a sham. Under Labor, for instance, the first rule is, “Participants are committed to uphold the human rights of workers, and to treat them with dignity and respect as understood by the international community.” Yet EICC members include Foxconn and Pegatron, which are routinely cited by watchdog groups for worker abuse. It may be a code, but its toothless.

Pam is tuned in to the industry and always makes her readers think. Her note that the industry lacks roadmaps for best practices in sustainability is dead on. A roadmap isn’t a certification, however, and that’s where I call on trade associations to draw the line.

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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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