Wave Soldering is Here to Stay

Patty was just getting ready to leave her office for a bi-weekly luncheon with the Professor, Pete, and Rob. They had regular meetings like this to discuss new technical topics or to review books. It was Patty’s turn to take the lead in discussing the new book, Rust: The Longest War.

As Patty arrived at the faculty dining room, everyone else was already seated. After ordering, she began the discussion.

“I thought that, overall, the book rated 4 out of 5 stars,” Patty stated.

“It had many interesting stories and brought home that fighting rust is the ‘longest war,’” she went on.

“But shouldn’t the book really be called ‘Corrosion’?” Pete interjected.

“I agree. After all, the best story was about the work that was done to refurbish the statue of liberty, and most of that is copper.  By definition, only iron rusts; copper corrodes. We try to be very specific about the differences in our undergraduate materials classes,” Rob chimed in.

“Rob, I remember you telling us that one student wrote a paper that referred to wood corroding,” the Professor said.

At that comment everyone chuckled.

“We can all agree that corrosion is a big challenge to civilization. But, can anyone think of a big downside if iron didn’t rust?” the Professor asked.

Patty, Rob, and Pete looked at each other and then the Professor as they shrugged their shoulders.

“Think biological processes,” the Professor encouraged.

It hit them all at once, but Pete was the first to comment.

Figure 1.  Rust: The Longest War

Figure 1. Rust: The Longest War

“Blood!” he cried out.

“Precisely! Without ‘rust’ we wouldn’t be here.  Iron’s unique ability to combine with oxygen in the hemoglobin of our blood makes ‘rust’ a requirement for human life,” the Professor explained.

None of them recalled seeing this point in the book.

“So, the conclusion is that rust costs the US over $400 billion per year. But, without it we wouldn’t be here,” Pete summarized as he chuckled.

“Patty, I understand that you had to fill in for Professor Croft as he recovers from a broken leg. The course was Everyday Technology as I recall. How did it work out?” the professor asked.

“Well, first of all, Pete agreed to help. And, it was only for the last two weeks of the term.  The final assignment for the students was to perform a teardown analysis on some electronic product, such as a DVD player, blender, hair dryer, etc.  They had to write a report and give a presentation on their findings.  They worked in teams of 2 or 3,” Patty summarized.

“It’s important to remember that the students that take this course are not engineering or science majors.  The course fulfills a technology requirement for non-technical students.  Most of them had never taken anything apart before,” Pete chimed in.

“Hey! Don’t forget that Patty made me sit in on all of the presentations,” Rob added teasingly.

“So, what were your impressions?” the Professor asked.

“I was impressed by how professional their presentations were and what a thorough job they did,” Pete responded.

Their work was especially impressive considering that almost all of them had never done anything like this this before,” Rob added.

“Anything else?” the Professor asked.

“I was surprised that all of the photos that the students took were taken with a smartphone, even macro shots of small components.  I remember photos from smartphones of 6 or 7 years ago were almost unusable. Those that the students took this semester looked high definition to my eyes,” Patty added.

There was a little more discussion and, finally, the Professor had one last question.

“You all had a chance to see many teardowns. How did it impact your understanding of the state of technology?” the Professor asked.

Patty began, “Pete, Rob, and I discussed this topic quite a bit.  We had to admit that the thing that surprised us the most was that, of the 18 devices that the students analyzed, almost all had a wave soldered PCB with through-hole technology.”

“I agree, we noticed that every power supply board was a through-hole wave soldered board.  I think we only saw a PCB or two that was all SMT.  If the boards weren’t pure through hole, they were mixed technology.  Through-hole and wave soldering are here to stay,” Pete added.

Figure 2. A Typical Wave Soldered Through-Hole Power Supply Board

Figure 2. A typical wave-soldered through-hole power supply board.

“We have to consider that most of the devices were lower tech: blenders, toasters, and one hair dryer,” Rob pointed out.

“But, the DVD player struck me the most. It had a mixed technology board in which one side was wave soldered, and a power supply board that was all through hole and wave soldered,” Pete added.

“I think those of us in the electronics assembly field become so enamored with smart phones and other high tech devices that have SMT-only PCBs that we forget that there are billions of lower tech devices that still use wave soldered through-hole boards.  The technology is cheap and it works, so why change?” the Professor summarized.

“So, wave soldering will likely be around for my grandkids!” Patty chuckled.

Electronics Assembly Process Optimization

Mike Madigan was not used to feeling intimidated.  After all, as the CEO of ACME, a multi-billion US dollar EMS company, he was used to doing the intimidating.  However, he had just finished a meeting with the CEOs of his two biggest customers and it was a disaster.  They asked to “do lunch” with Mike and, after this event, Mike’s stomach was churning.  If Mike was honest with himself, if he was them he would have been tougher.  But, it was their teasing demeanor, punctuated with laughs and jokes, that made it all the worse.

That these gentlemen had some points to make was inarguable.  First-pass assembly yields were down 4%, and Mike’s answer, that it was because the technology was more challenging to assemble, did not fly.  They told him to get that 4% back or they will find a company that can.

Both of these gents had been process engineers when they were younger, so they “knew the ropes.”  In a recent audit of one of ACME’s facilities, they found one process engineer, responsible for the stencil printing process, that didn’t know how to run the stencil printer. And this lad also could not locate the solder paste spec.  Additionally, he could not explain what “response to pause” was.  Another process engineer did not know how to match the reflow profile to the solder paste spec (after they finally located the spec). Mike’s answer, that ACME’s recent growth made it hard to keep the training of the engineers up to snuff, only made things worse.

When asked what percent of his engineers hired in the last two years were SMTA certified, Mike didn’t know.  He expected it was 0.

Then, one of the CEOs said, “Things seemed to be much better when you had that Advanced Processes VP. What was her name? Patty something or other?”  That was a big part of the problem. Patty Coleman was gone and, with her departure, things had gone to h#!!.

Mike thought of asking Patty to fix things, but that would be unfair.  She had only been at Ivy U for a year or so and was still getting established.  Maybe the Professor could help.  Mike hoped so. The CEOs wanted a plan in two weeks.

Ten days later…

Patty had just finished getting ready for a meeting with her husband Rob, Pete, and the Professor.  Ten days ago, the Professor asked if they could help him develop a software tool that would be used by ACME as a self-audit of their practices related to electronics assembly.  The Professor said it was a request from Mike Madigan himself.

Patty had a little time before the meeting, so she decided to check her email.  Suddenly, she was disturbed by a knock at the door.

“Professor, we wanted to ask you a question about probability. Is now a good time?”, a young lad who looked 11 years old asked.

“Sure.” said Patty.  “But tell me your names first.”

“Oh!, Sorry! I’m Henry Finn. But everyone calls me ‘Huck’. And this is Chris Jenkins.  We’re both sophomores.  You spoke about statistics at our Introduction to Engineering Class a few days ago. We’re hoping you can settle an argument,” Finn began.

“What is it?” Patty asked,

“Well, Huck says that since the Patriots are one of 32 teams in the NFL, the chances of them winning 4 Super Bowls is (1/32)^4 = 9.5×10-7, or about one in a million – if they had only an average skill level.  I think it is more than that.  Huck says the rarity of them winning four Super Bowls shows how much above average they are,”  Jenkins jumped in.

“Your analysis is not quite right. You calculated the likelihood of 4 wins in a row. They have won 4 out of the last 14 Super Bowls,” Patty said. Patty was on top of the Patriots stats as she was a big fan.

“To perform the analysis, you have to use the Binomial Distribution.  Let me see if I can calculate it using Minitab 17,” Patty said.

She went to her laptop and, in no time, had a graph that explained the problem.

“So, the chances of a team possessing only average skill winning 4 out of 14 Super bowls is less than 1 in a thousand.  I’ll leave it to you two to decide what that means,” Patty summed up.

Patty chuckled to herself as she saw the two sophomores arguing as they walked away.

She looked at her watch and saw it was time to head to the Professor’s office.

Patty was the last to arrive as Rob and Pete were already there. As she sat down, the Professor began.

“Thank you for coming.  I have incorporated all of your input and am pleased with the results.  I’m hoping that we can review the resulting web application that was developed,” the Professor began.

“Is it in English or one of the 17 other languages you speak?” Pete joked.

“English, Pete. English,” the Professor chuckled.

In reality, Patty, Pete, and Rob were thrilled to help the Professor develop this self-auditing software.  They all knew that it isn’t that often that one can help someone like him.

The Professor was only able to come up with 20 questions for the software.  Patty, Pete, and Rob increased it to 40. Pete was proud that he contributed 8 of the additional twenty questions.

The Professor flicked on his projector and displayed the first page of the self-auditing software.

“This is the first of the four sheets for the software tool.  I think Rob’s suggestion to name it ‘AuditCoach’  is a great idea.  Let’s take a look and see what we think,” The Professor said.

“I think it’s good that you have the questions about the process engineers knowing how to run and optimize the equipment.  It is surprising how many times that is not the case,” Patty commented.

“That was Pete’s idea,” the Professor replied. Pete beamed from the recognition of the Professor.

“I like the idea of making the first question count 3 times as much since it is so critical,” Rob chimed in.

“Agreed,” Patty and Pete murmured.

The Professor pressed on, “I thought it might be best to break the questions in to four categories:

  1. DfM, Processes
  2. Equipment, Materials Supply and Validation
  3. DOE, SPC and CIP, and
  4. Training and Failure Analysis.

Over the next hour the group reviewed all 40 questions on the four sheets of AuditCoach. Some minor improvements were made.

As they were wrapping up, the Professor had one last comment, “I asked Mike Madigan if he would make AuditCoach available to others.  We both thought that doing so was a good idea.”

Cheers,

Dr. Ron

 

 

The False Positive Paradox

Folks,

Let’s check in on Patty…

Patty was intensely preparing a lecture on Bayes’ Theorem. She always felt that this theorem was the most profound in probability and statistics. She remembered a real application, when her best friend took the Tine test for tuberculosis before she got married – and tested positive. The test claimed to be 99.9% accurate in identifying someone with TB. Her friend was devastated to find out that she apparently had this ancient, dreaded disease. Further investigation uncovered that the 99.9% number was more accurately stated as, “if you have the disease, this test will pick it up 99.9% of the time.” There was an important number not told: false positives. This rate was 5%. With so few people having TB, a 5% false positive rate would indicate that almost everyone that tested positive for TB, would be a false positive, hence not have TB. So it was, much to the relief of many, with her friend. This situation is an example of the false positive paradox.

While Patty was deep in thought, she was startled by the sound of her phone ringing. She looked at the area code and exchange and knew it was from her old company, ACME. She picked up the phone.

“Professor Coleman,” Patty answered. She liked the sound of that.

“Hey, Patty! It’s Reggie Pierpont!” the cheery voice declared.

Patty’s heart sank. Reggie was an OK guy, but he always got involved in things he didn’t understand and often convinced management to pursue expensive and ineffective strategies. He was that persuasive.

“Reggie, what’s up?” Patty said half-heartedly.

“Well, Madigan insisted I call you before we order some new testers. I think it is a waste of your time, but I’m following orders,” Pierpont said.

“What are the details?” Patty asked.

“We have a contract to produce one hundred thousand Druid mobile phones a week. We are confident our first pass yield is greater than 99%,” he began.

“Impressive,” Patty said with sincerity.

“I want to order some testers that identify a defective phone in a rapid functional test with 99.9% certainly. The testers are very expensive, so Madigan wants a sanity check before buying them. The other important info is that we get a huge penalty from the customer for any defected phone we ship,” Reggie continued.

“Well, with a large penalty, 99.9% is the right number. What do you do with the units the tester determines are defective?” Patty asked.

“Well, it is a good thing yields are high. The phones are so complex that we have quite a drawn out process to find the defect and fix it. Just finding a defect can cost $5 to $10 dollars in burdened labor, but, considering the value of a phone, it’s worth it. Like I said, it’s a good thing yields are high so we don’t have too many units needing this procedure,” Pierpont continued.

“What about false positives by the tester?” Patty asked.

“Shouldn’t be a problem, remember the tester is 99.9% accurate,” Pierpont answered.

Patty knew that Pierpont was missing her point, but she didn’t want to embarrass him……too much.

“Reggie, from what you told me, if a unit is defective the tester will catch it 99.9% of the time. What I am asking is, if a unit is good, how often does the tester say it is bad? This situation is usually called a ‘false positive’,” Patty responded.

“Well, it would be 100 – 99.9 or 0.1%,” Pierpont replied.

“That’s the percentage of bad units that would be called good. These units are often called ‘escapes.’ The only way to determine false positive rate is by a test, you can’t determine it from the 99.9% number,” Patty went on.

There was silence at the other end of the phone.

“What do I need to do to get the false positive number?” Reggie asked.

“You need to test about a 1,000 known good units and see how many the tester says are bad,” Patty said.

“I’ll do that with the loaner tester the tester company is letting us use and get back to you,” Pierpont replied.

Patty hung up the phone. She thought it interesting that Pierpont’s problem was so closely related to both Bayes’ Theorem and her friend’s false positive with the Tine test.

Two days went by and Patty, Rob, and Pete had just returned from lunch with the Professor. They would all meet with him quite often to discuss technical problems they were having. So, they offered to treat him to lunch.

As she walked into her office, Pete spoke up.

“Did Reggie Pierpont ever get back to you?” Pete asked.

“No, maybe I’m off the hook,” Patty chuckled.

At that instant, her phone rang. It was Pierpont.

“Hey, Reggie! What’s up?” Patty asked with more enthusiasm than she felt.

“Well, the tester says 5% of the good units are bad, I think you are going to tell me this is a problem,” Peirpont began.

“What if you run them through the tester again?” Patty asked.

“That IS running them through two or more times! If we run them through just once, it was 7%,” Reggie sighed.

“Well, let’s look at the numbers. You are making 100,000 units a week, with a 5% false positive rate that’s 5,000 units. Your yield loss is 1% or 1,000 units. So, you will have about 6,000 units the tester will declare as bad when only 1,000 really are. These numbers are off a little bit. Bayes’ Theorem would give us the precise numbers, but these are very close. Since your process to analyze fails after the tester costs at least $5 per unit, you will be losing $25K per week due to false positives,” Patty elaborated.

“Time for a new strategy,” Pierpont sighed.

Patty and Pete agreed to help Pierpont work with the tester vendors to develop a better strategy.

Epilogue

Patty and Pete helped Pierpont develop an effective test strategy working with a tester vendor. Neither Patty nor Pete had known Reggie well before… but, after this joint effort, they grew quite close. Reggie became quite engaged in the process and seemed to learn quite a bit. Patty was able to use some of the data in her classes.

A few weeks later she got a beautiful card in the mail. She opened it. It read, “Dear Patty, Thanks for all of your help. We wouldn’t have made it without you and Pete helping us with our testing strategy. Best Regards, Your faithful student, Mike Madigan.”

Patty got a little choked up.

Cheers,

Dr. Ron

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.

Cheers,

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.

Comparing Two Wiebull Distributions

Folks,

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.

Epilogue

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.

Cheers,

Dr. Ron

 

Weibull Analysis at Ivy U

Folks,

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.

Cheers,

Dr. Ron

 

‘Patty’ in the Real World

Folks,

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.

Cheers,

Dr. Ron

 

An Example of Cpk and Non Normal Data In Electronics Assembly Soldering

Folks,

Let’s see how Patty is doing after teaching her first class at Ivy U…

Patty arrived at home after teaching her first class at Ivy U and she couldn’t contain her excitement. For the next couple of hours her husband, Rob, had to politely listen to her talk about how amazing it was to teach the young, bright, enthusiastic, future engineers.

Time went quickly and, before she knew it, she was standing in front of the class for her second lecture.

Patty reviewed quickly the fact that it was incorrect to average Cpks and that, to calculate a Cpk, the data should be normally distributed.

“The question was asked last time, how one can tell if the data are normal? Minitab can be used to plot the data on a normal probability plot. By eye, we can get a good sense if the data are normal or not. In addition, Minitab will perform various tests, one of them being the Anderson-Darling Normality Test,” Patty began.

“Let me show you some real data to demonstrate this,” Patty continued.

“When assembling a smartphone like the new Druids, the mechanical tolerances for the many tiny capacitors and resistors are very precise. One common capacitor size is only 0.6mm long.” Patty paused as she saw a student’s hand raised.

“Yes, Martin?” Patty asked.

“Professor, you mean 0.6cm, right?” Martin asked.

“No, 0.6mm,” Patty answered.

Patty’s answer caused quite a bit of murmuring, finally Patty had to ask for order.

“Why is everyone surprised?” Patty asked.

“Professor, that is much smaller than a grain of rice, it is more like the size of a grain of sand,” Alison March responded.

“This is fun,” Patty thought, “and good timing.”

Patty showed a slide of passives on a match head and passed around a teardown of Druid smartphone with a magnifying glass so that the students could see how small the passives were.

It took a while for the class to calm down.

Patty then said, “And about 200 to 500 capacitors and resistors of this size are individually placed and soldered in the electronics assembly process in each smartphone.”

The student’s mouths were agape.

“OK, let’s discuss how these little rascals relate to SPC. My company orders billions of these electrical components each year. We are sent a sample lot to approve a larger order. For the components of interest, we already know that the mean length is 0.6mm, the 3 sigma (standard deviation) tolerance is +/-0.03mm. So, the lower spec limit is 0.57mm and the upper spec limit is 0.63mm. This equates to a Cpk = 1.00,” Patty went on.

Patty put a PowerPoint slide up that showed the data.

“The data for the sample lot is on the left. What is the problem?” Patty asked.

Charles Parsons raised his hand.

“Yes, Charles?” Patty asked.

“Well, Dr. Coleman, the standard deviation for the data is 0.15 and the resulting Cpk is only 0.67, so the targets are not met” Charles answered.

“Precisely,” Patty replied.

“We then went back to the supplier and asked them to fix the problem. The graph on the right is from the capacitors they sent us 3 weeks later, after they claimed to have solved their manufacturing process problems,” Patty explained.

“What do you think?” Patty asked.

There was a lot of murmuring. Finally DeShaun Martin raised his hand.

“Yes, DeShaun?” Patty acknowledged him.

“Well, Professor, it looks like they simply sorted out the parts to make the sigma lower and Cpk higher,” DeShaun responded.

“Precisely,” Patty said.

“I don’t see what is wrong with sorting,” Sandy Lisle commented.

“You see from the Druid smartphone that I passed around that it is so densely packaged with components that there is hardly any room in it. To achieve this density we have to perform tolerance analyses to assure everything will fit. In all of these analyses we model with normal distributions. With a sorted distribution we will likely have more tolerance interferences,” Patty answered.

“Look at the red arrow. There will be an excess of components with this size and a lack of components of the size where the green arrow is pointing. These differences will cause some tolerance interferences with the pads on the printed wiring board where the passive will be assembled,” Patty continued.

“Can you review? How we can tell that the distribution on the right is not normal?” Conor Stark asked.

“Sorry, I almost forgot. Look at the normal probability plot for the sorted data. Note how it diverges from the straight line on the ends. Also the Anderson-Darling value for p is <0.05. These two criteria are cause to reject the hypothesis that the data are normal,” Patty finished.

Patty was just wrapping the class up when someone raised their hand.

“Yes, Natalie?” Patty asked.

“What was the final outcome?” Natalie asked.

Patty chuckled, obviously she should share he result of this adventure.

“Oh, yes. We could not use the parts for the Druid smartphones, but they were OK for some toys we were assembling. In addition we insisted on a 30% discount, since the passives did not meet the specification,” Patty answered.

As she was cleaning up, two of the female students came up to Patty. One them, Justine Randall spoke for the two.

“Professor Coleman, you are an inspiration for us. We hope in 20 years we can be just like you,” Justine said with emotion.

Patty was indeed touched, but as she left the classroom, she decided that she had to start dyeing her hair.

Cheers,

Dr. Ron

 

Cpk Can Only be Calculated from Data that are Normally Distributed

Folks,

Let’s look in on Patty….

Patty was really nervous. As a matter of fact, there was no time she remembered being this nervous. The cause of her nervousness? She was going to teach a series of classes at Ivy University.

This opportunity came about because one of the professors at IU was in a serious accident. A full recovery was expected, but there was no way the prof could finish the last three weeks of the statistics course she was teaching. Things are hopping in the Engineering Department at IU, and the Dean could not find another prof to take over.

The Professor himself was too busy, however, when the Dean asked his advice he immediately recommended Patty. Patty was honored by the request and would be more so if she knew the behind-the-scenes story. IU has an unwritten rule that all teaching profs had to have a Ph.D., which Patty did not. However, if Bill Gates wanted to teach, an exception would be made, as he is a world class technical executive. Patty was hired under that exception. She was stunned to see she was on the front page of “The Ivy U Review,” under the headline, “Famed Executive to Teach at IU.”

Well, her first class was tomorrow and she took comfort in the fact that her husband, Rob, told her she shouldn’t be nervous. Pete wasn’t much help. He told her he would be so nervous that he wouldn’t be able to eat. It was just unnerving teaching the best and the brightest. She was proud of her academic accomplishments at Tech, but this was IU, arguably one of the top 10 universities in the country.

“Rob, I have to tell you, even though I’m still nervous, it comforts me to know that you wouldn’t be nervous,” she said to her husband.

“I never said I wouldn’t be nervous, I said you shouldn’t be nervous. After all, you’re Patty Coleman,” Rob replied.

At this Patty burst into tears and Rob came over and gave her a big hug.

“But, you’re smarter than me,” Patty insisted.

“No way,” Rob replied.

They then spent the next 10 minutes arguing that the other was smarter. Patty always felt she had a good business sense, but for understanding deep technical things, she believed Rob was her superior. After a while they looked at each other and laughed.

“Not too many couples would get in to an argument, saying that the other person was smarter,” Rob teased.

Time passed quickly and Patty was soon in front of the 35 students in the class. The topic was Cpk as the most important metric to determine the quality of a lot of material or product. She asked the students if it was OK to average Cpks from different lots. A student raised her hand.

“Yes Emily.” said Patty. (Patty had ask the students to use nametags.)

“No, Professor Coleman. One can’t average Cpks. The reason being that Cpk goes as one over the standard deviation and standard deviation is a squared term. So one can’t average two lots and get the same result as taking the Cpk of all of the two lot data.

Patty responded, “Emily is 100% correct. Remember, when you get out in the working world, to always check to see that your suppliers are not averaging Cpks. This might happen when half of the lot is below the spec, say the Cpk is 1.4 and the spec is 1.5 and the other half is over the spec, say 1.7. The supplier will say that the lot is in spec because the average Cpk is 1.55. This isn’t necessarily so, as Emily points out. You should only accept a calculation of Cpk for the entire lot.”

Patty chuckled that Emily thought she was a Professor, at Ivy U. Right!

The class continued to go well and Patty began to relax. As the class began to end, she mentioned another important point.

“What important criteria must the data have to be considered acceptable to calculate Cpk?” Patty asked.

There was a bit of murmuring and finally a boy (man?) raised his hand. He looked 12 years old to Patty.

“Yes, William,” Patty acknowledged him.

“Dr. Coleman, I think the data must be normal,” William answered.

“Dr. Coleman?” Patty thought.

“Absolutely correct, William,” Patty responded.

“Class, remember this point when you get out into industry. Almost no one checks to see that the data are normal before calculating Cpk. The data must be normal to calculate Cpk. I can’t tell you how many times I have rejected a lot of incoming material because the Cpk was calculated from non-normal data. In some cases non-normal data can be transformed so that the data are normal, “ Patty continued.

“Professor, how do we know if the data are normal?” a student named Kathy asked.

“Stay tuned for the next lecture,” Patty chuckled and dismissed the class.

As she was gathering her laser pointer, lap top etc., a number of students came to talk to her. Emily was with a group of about six of them.

“Professor, we just wanted to tell you that we are thrilled to have you as our instructor. We appreciate your practical, real world perspective on statistics,” Emily said.

Patty responded warmly and was close to being choked up by this show of respect and appreciation. She decided she would walk to The Professor’s office to tell him how it went.

On the way out, she heard one of the male students say to his friend, “You know, she is quite attractive for an older woman.”

Patty didn’t know whether to laugh or cry.

Cheers,

Dr. Ron

Is the PC Dead?

Folks,

Let’s see how Patty is recovering from her conflict with Hal Lindsay.

Patty saw a link on one of the daily industry newsletters that piqued her interest. It was titled, “A New Alloy for Medical Electronics Applications.”

The paper talked about a new SAC (tin-silver-copper) lead-free solder alloy that contains a small amount of manganese. Apparently, the manganese modifies the metallurgical structure and enables the alloy to perform well in both drop shock and thermal cycle tests.

She finished the article and decided that she needed to look into this alloy more. It isn’t common for an alloy to perform well in both drop shock and thermal cycle. The title also reminded Patty how relieved she was that their St. Paul facility was getting ready for Medical RoHS on July 22, 2014.

She then checked her email and saw she had a note from ACME CEO Mike Madigan.

Coleman,

I just read an article about the death of the PC. PC sales are off by 10% per year. That means in 10 years they will be gone. PCs are 30% of our business. Develop a plan to modify our business so that we can replace this loss. Be ready in two weeks.

Madigan

Patty had to chuckle at Mike Madigan. He seemed to totally lack social skills. She wondered how someone could get so far in the company without them. Anyway, she had a new assignment. Also, she quickly determined that a business decreasing 10% per year would still be at about 35% (0.9^10= 0.349) of its original size in 10 years.

Right off the bat, her sense was that the “Death of the PC” was exaggerated and misunderstood. She performed a search and read some more articles, finding several that talked about the surge of tablets like the iPad and the Kindle Fire as being behind the PC’s decline. She and Rob owned two iPads and one Kindle Fire. Were they part of the trend? She suspected that there was more to the story and thought that discussing this topic with The Professor would be interesting. She was visiting him at Ivy University later in the week.

The week went by quickly and, before Patty knew it, she was in her car with her husband Rob, driving the two hours from Exeter, NH, to Ivy U. Rob was getting his Ph.D. there, part-time, and made the trip several times a month. The Professor was his advisor.

Rob needed an hour with The Professor. During that time, Patty checked her email. After he and Rob were finished, The Professor said, “Let’s go the lunch at Simon Pearce and chat about your latest adventures.”

“That’s great! Simon Pearce is my favorite restaurant, Professor,” Patty responded. Simon Pearce Restaurant in Quechee, VT.

They both looked at Rob, but he had so much work to do that a slice of pizza from the student union was his destiny for lunch today.

As Patty and the Professor arrived, Simon Pearce was at its most beautiful. The sky was blue and the leaves were just starting to turn. Patty had alerted The Professor that she wanted to talk about the “Death of the PC,” so he was ready as they sat down.

“Patty, I have read all of the articles that you sent. They emphasize the impact on the PC by tablets and mobile phones, but they miss an important point,” The Professor began.

“What’s that?” Patty asked. “The effect of the constancy of ‘Memory Metrics,’” The Professor replied.

“What are ‘Memory Metrics?’” Patty asked.

“Let me explain with a story,” The Professor answered.

“When you were a toddler, back in 1986, my family got our first computer, an IBM PC XT. It cost $6,000 and had 0.512MB of RAM and 20MB on the hard drive. We had it for 3 years and needed a replacement. Can you guess why? The Professor asked. The IBM PC XT circa 1986.

“You ran out of memory,” Patty answered.

“Yes, the Kids where playing, ‘Where in the World is Carmen Sandiego,’ and some other games,” The Professor said.

“Then we had to get another computer in 1989 with 4 MB of RAM and a 200MB hard drive. We tripled the hard drive memory and still needed a new computer in 1995. This trend continued until about 5 years ago, but it then slowed down,” The Professor continued.

“Why did the trend slow down?” Patty asked.

“Before I answer that, we need to discuss ‘Memory Metrics,’” The Professor said. “How much memory does a decent photo require?”

“About 1MB,” Patty answered.

“A song?” The Professor quickly shot back.

“About 5MB,” was Patty’s fast reply.

The banter continued.

“A book?”

“About 1MB.”

“A full length movie?”

“About 5,000MB.”

The Professor was impressed.

“Wow, Patty! It’s amazing that you know all of the critical ‘Memory Metrics.’ Where did you learn them?” The Professor said.

“Rob went to lunch with the professor who teaches a class called Everyday Technology. They discussed these metrics. It helps me to estimate how much memory I need on my smartphone to store all of my photos, songs, and books,” Patty answered.

“So how many songs could you store on the hard drive of my first computer?” The Professor asked.

“Only 4 or only 20 photos or books,” Patty answered.

“So, we weren’t putting songs, books or photos on early computers. Even the $10,000 laptop that I needed for my research in 1996 only had a 1000 MB hard drive … only 200 songs,” said The Professor.

“I get it,” Patty responded, “Let me see if I can fill in the blanks.”

“Memory Metrics, are close to constant, with the exception of perhaps photos with more megapixels. Anyway, the memories on new computers have gotten so large that we don’t need to replace them as often, we just don’t fill the memories up any more. Unless we store movies,” Patty continued.

“Add in the advent of smartphones and tablets and see if you can make an argument for why PC sales are down,” The Professor said, beaming at his favorite student.

“Well, before smartphones and tablets you might get a new PC even if you didn’t need it. But, now you have two or three devices to buy, so you may put off a new PC for awhile to buy a new smartphone or tablet,” Patty responded.

“So, what will happen to smartphones and tablets?” The Professor asked.

“A similar thing. They are developing so many features, memory, and computing power, that their sales will slow done in a few years,” Patty thoughtfully said.

“So, the PC is not dying!” Patty exclaimed.

“But, what about the tablet forcing out the PC as a replacement?” Patty asked.

“Let’s ask my statistics class after lunch,” The Professor suggested.

Although Patty had been around campus off and on, she was immediately struck by how young everyone in the class looked. Just last night, Rob was teasing her about her first gray hair. That, no doubt, added to this effect. As the class of 60 students settled down, The Professor began to speak.

“Before we start the lecture, my colleague, Patty Coleman, would like to ask you a few questions,” The Professor said.

“The Professor calls me a colleague! Wow!” Patty thought.

So, Patty stood up and started speaking. “If you could only have one device, a PC or a tablet, who would choose the PC? “ Patty asked.

Everyone raised their hand.

“Why?” Patty asked.

A boy, who looked, to her, to be about 12 years old, answered, “Well, Dr. Coleman, it is very difficult to write a 10-page paper on a tablet, or perform Excel calculations, or prepare a PowerPoint file on a tablet.”

“How many of you own a tablet?” Patty asked.

Only about 20% of the students raised their hands.

“How about a smartphone?”

Everyone raised their hands.

“Any thoughts on why many people think the PC is dead and the tablet is the future?” Patty asked.

After a little murmuring a female student raised her hand. Patty was relieved that she looked to be about seventeen. Patty acknowledged her.

“Well, Professor Coleman, my family has two tablets at home. My 7- and 9-year old brother and sister play games on them all the time. My mom and dad use one as an e-reader, and they use one to control our TV. But, for any serious work, even they prefer a PC. Only my kid brother and sister would prefer a tablet over a PC. But, the most recent devices we bought were tablets. Our PCs just haven’t needed replacing,” the young women said.

“Why do so few of you have tablets at school?” Patty asked the group.

Again more murmuring ensued and, finally, a graduate student raised his hand. Patty acknowledged him.

“Professor Coleman, I find that the combination of a PC and a smartphone fills all of my needs. I can listen to music or read a book on my smartphone. I can’t not have a smartphone and function at today’s university. A tablet would be a luxury, I don’t feel I need or can afford,” he said.

With that Patty sat down. This information on tablets and the college scene was consistent with what Patty had read. The Professor’s lecture was on Bayes Theorem and Patty decided to stay. She chuckled that the students thought she had a Ph.D. and was a professor. “Yikes, does this mean they think I am old?” she thought.

After the lecture Patty thanked The Professor and went to find Rob. She now felt she understood why PC sales were down. Tablets had some effect, but the near stability of Memory Metrics and the tremendous computing power and increased memory of a modern PC simply meant people didn’t need to upgrade as often. She expected similar trends for smartphones and tablets. As she organized her backpack, she put her 6 month old laptop, with its 16,000MB of RAM and 1,000,000MB hard drive away.

The PC was alive and well.

Best wishes,

Dr. Ron