Estimated reading time: 5 minutes

Maggie Benson's Journey: Solving for 'X'

Editor’s note: Indium Corporation’s Ron Lasky continues this series of columns about Maggie Benson, a fictional character, to demonstrate continuous improvement and education in SMT assembly.

Andy and Sue were having pizza before they went to their pre-calculus class.

“Now I’m really confused,” Andy sighed. “Limits!”

“How so?” Sue inquired.

“I don’t see how the limit of sin(x) divided by x equals 1 as x goes to 0,” Andy groaned.

“Remember the professor told us that sin(x) can be expressed in a power series and the first term is x. All other terms are higher order, and they go to 0 much more quickly as x goes to 0. So, for small values of x, sin(x) = x,” Sue explained.

“I see it now. It’s actually kind of obvious the way you explained it,” Andy said as a compliment.

“You know, you are better at math than you think,” Sue said, encouragingly. “You have almost a 95% on the three quizzes and that is an A.”

“But you have three 100s. The prof even said if he was sick, you could sub for him,” Andy teased.

They chuckled and both sensed it was time to change the topic.

“I still can’t believe your parents want me to go with you and them to Colonial Williamsburg,” Andy said. “They want to pay for everything, but I still feel that I should pay my own way.”

“I was kicking you under the table so that you would know that they really wanted to treat,” Sue said with a little exasperation. “You know they really like you.”

“I don’t understand why, I’m nothing special compared to you, the ‘math star,’” Andy groaned.

“You don’t get it, do you?” Sue asked. “What?” Andy questioned.

She elaborated: “You are a natural leader, everyone senses that. And you are very determined. It’s clear you are going to be successful. And there is the language thing.”

“What language thing?” Andy asked.

“My mother is gaga over you because you speak Spanish and French,” she said, then sighed. “After all, she teaches both at Hanover High. I always struggled with Spanish and never took French.”

“For me, it was a gift,” Andy started to explain. “I played with a group of friends that were of Hispanic heritage and I asked them to only speak Spanish when we played. Also, my grandmother was French-Canadian and she babysat for me when I was young. She spoke to me only in French.”

They continued to discuss this situation and the plans for their Williamsburg vacation.

“Oh, there is one more thing,” Sue mentioned. “PDA.”

“Yikes, I have never even touched you in front of your parents,” Andy groaned.

“That’s the problem,” she replied. “They can’t understand why you never hold my hand, etc.”

“That is a problem I can solve,” he said, leaning over for a kiss.

Later, after their pre-calculus class, the couple went to the ice cream shop and began preparing for their next SMT 101 workshop.

The workshop was on component placement. Both were comfortable discussing how the component placement machines work as well as ancillary equipment, like feeders. But Andy had a concern.

“Ugh, line balancing,” he groaned.

“Well, what is usually the ‘gate’ in electronic assembly?” Sue asked, as Andy responded, “Component placement.”

“So, say we have two component placement machines, a chip shooter and a flexible placer,” Sue began. “The chip shooter takes 35 seconds to place all of the passive ‘chips’ and the flexible placer takes 25 seconds to place the simple integrated circuits (SICs) and the complex integrated circuits (CICs). What should we do?”

“Move passives to the flexible placer,” Andy responded. “But how many passives?” Sue teased.

“That’s where I get stuck,” he admitted.

“Well, we want the time on each placement machine to be the same, right?” Sue queried.

“Okay, so we take the passives off the chip shooter and that speeds it up and adds the passives to the flexible placer that slows it down,” Andy said, his voice rising in excitement. “We want to do this so that the times are the same. Now we need a math equation. Let me see if I can set it up.”

Sue commented, “Well, we need to know the numbers of components and placement speeds. Let’s assume there are 350 passives, 28 SICs, and six CICs. Also, that the chip shooter places passives at 30,000 per hour, and the flexible placer places passives and SICs at 8,000 per hour and complex ICs at 3,000 per hour.”

“Okay, so the chip shooter takes 350/30,000 = 0.01667 hours to place the passives and the flexible placer takes 28/8000 + 6/3000 = 0.0035 + 0.002 = 0.0055 hours,” Andy added. “So, we are waiting on the chip shooter.”

“Can you set up the equation to determine how many passives need to go to the flexible placer to time balance the line?” Sue asked.

Andy responded: “I think so. It would be: (350 – x)/30,000 = 0.0055 + x/8000. The left side of the equation is the time that the chip shooter takes with x less passives and the right side of the equation is the time the flexible placer takes to place the integrated circuits and x passives. To be time balanced, the times must be equal. All we have to do is solve for x.”

With a little manipulation of the equation and their calculators, they solved the equation that x must be equal to 39 passives. So, the time for each machine is (350 – 39)/30,000 = 0.01037 hours or 37.3 seconds.

They discussed a few more things about the workshop on component placement and called it an evening.

Epilogue:

Andy Connors and his dad, Frank, were never very close. Let’s listen in on them while they have a little chat.

“You know, son, I have never really talked to you much about life or your plans, but I have to tell you, Mom and I are extremely impressed with the change that has come over you recently,” Frank said proudly. “Even your boss, Maggie Benson, called us to tell us how proud of you we should be.”

“Wow, thanks, dad,” Andy said. “I think a lot of my motivation has come from knowing Sue March. She is so smart, especially at math.”

“Well, you know a guy could live 100 lifetimes and never meet a gal like her—don’t lose her,” Frank replied.

Both Andy and his dad felt a closeness like never before.

This column originally appeared in the September 2022 issue of SMT007 Magazine.