New Excel Software Tools to Practice for SMTA Certification #2: Reflow Profiling

Folks,

In my last post, I shared about an Excelbased software tool called Line Balancer to help candidates for SMTA Certification prepare for the line balancing part of the program. They can use Line Balancer to check the correctness of practice line balancing problems. This post will discuss another Excel-based software tool, Reflow Profiler, to help candidates prep for the reflow profiling part of the certification.

Typically, the reflow profiling goal is to determine if the reflow profile matches the requirements of the solder paste specification.

As an example, let’s consider a reflow profile as shown in Figure 1. The solder paste specification is shown in Figure 2. We will first solve the problem by hand and then use the software.

Figure 1. A ramp-to-peak reflow profile.
Figure 2. The solder paste reflow specification

The first task is to determine if the ramp-to-peak rate matches the solder paste specification outlined in red in the specification shown in Figure 3. By measuring the change in temperature in Figure 4 from point A to B and dividing it by the change in time from those points, we see in Figure 4 that the ramp-to peak-rate is 0.857°C/sec., and is within the recommended specifications 0.5 to 1.0°C/sec.

Figure 3. The solder paste specification with the ramp-to-peak rate highlighted.
Figure 4. The reflow profile with the ramp-to-peak rate calculated.

Figure 5 shows the solder paste specification with the time above liquidus (TAL) with the peak temperature highlighted. While Figure 6 shows the reflow profile, where the TAL is measured as 60 seconds and the peak temperature at 240°C, both are consistent with the recommended values.

Figure 5. The solder paste specification with the TAL and peak temperature highlighted.
Figure 6. The reflow profile with the TAL and peak temperature identified.

Lastly, Figure 7 shows the solder paste specification with the cooling ramp rate highlighted and Figure 8 shows the reflow profile with the cooling rate calculated as -2.8°C/s, again within the specification.

Figure 7. The solder paste specification with the cooling rate highlighted.
Figure 8. The reflow profile with the cooling rate calculated.
Figure 9 shows all of the calculations performed and matched to the specification with Reflow Profiler.

If you are interested in a copy of Reflow Profiler send me an email at [email protected]

Cheers,
Dr. Ron

New Excel Software Tools to Practice for SMTA Certification #1: Line Balancing

I recently developed some Excel-based software to help those who are planning to take the SMTA certification exam to practice. 

In this post, I will discuss the tool that performs line balancing. In a typical SMT assembly line, the placement machines are the “gate” in the cycle time of the line. To assure that their cycle time is the lowest, the placement machines must be time balanced. For example, suppose a simple SMT assembly line has one chip shooter and one flexible placer. Let’s say that the chip shooter takes longer to place all of the chips than the flexible placer takes to assemble the simple and complex integrated circuits. So, in this case, chips should be removed from the chip shooter and be placed on the flexible placer. But how many should be moved to the flexible placer? Determining the number requires algebra, and to understand how to do it, we need a numeric example.

Let’s do an example. In an assembly line, the “gate” in the cycle time is component placement.

  • The chipshooter (CS) places passives at 60,000/hr and Simple ICs (SICs) at 4,000/hr
  • The flexible placer (FP) places complex ICs (CICs) at 3,000/hr and SICs and passives at 8,000/hr
  • The bill of material (BOM) is 354 passives, 12 SICs, and 4 CICs
  • If the FP takes less time to place the CICs and SICs than the CS takes to place all of the passives, then move some of the passives to the FP to time balance the line
  • Let’s check the situation that the FP takes: (4 CICs / 3,000/hr) + (12 SICs / 8,000/hr) = 0.001333 + 0.0015 = 0.002833hrs
  • The CS takes: 354/60,000/hr = 0.0059hrs
  • So, move chips to the FP—but how many? Let’s call the number x. The times should be equal, so:
    • 0.002833+x/8000 = (354-x)/60,000.  Solve for x to time balance the line.
    • 0.002833+x/8000 = (354-x)/60,000, multiply each side by 60,000
    • (60,000*0.002833) + (60,000x/8000) = 354 – x
    • 170 + (60/8)x = 354 – x,  gather x terms
    • 170 + ((60/8) +1)x = 354, gather numbers
    • (68/8)x = 354-170 = 184, solve for x
    • x = (8/68)*184 = 21.65 or 22 passive moved to FP

Let’s see if the times on each machine are the same.

  • CTCS= 332 passives/60,000 passives/hr =0.005533 hrs or 19.92 secs

Is the FP the same?

  • CTFP = 0.002833 + 22/8,000 = 0.005583 hrs or 20.10 secs

Why the difference?

The times can’t be exactly the same as we rounded the number of passives moved to the FP.

Figure 1. The “Line Balancer” answer to the problem

Figure 1 shows the calculations from the Excel® software tool I developed called “Line Balancer.”  Note the answers are the same. If you would like a copy, send me an email at [email protected].

Here is a problem for you to solve:

  • The chip shooter (CS) places passives at 50,000/hr and Simple ICs (SICs) at 3,000/hr
  • The flexible placer (FP) places Complex ICs (CICs) at 4,000/hr and SICs and passives at 7,000/hr
  • The bill of material (BOM) is 390 passives, 14 SICs, and 6 CICs

How many components need to be moved, and to which placement machine? What is the cycle time?

To the first person that sends me the answer, I will send them a Dartmouth hat.

Why Square Apertures Provide More Solder Paste than Circular Apertures

Folks,

When comparing the volume of solder paste provided by a circular versus square aperture, consider that if the side of the square is D and the diameter of the circle is also D, the square has greater than 25% more area. (i.e., (1-0.785)/0.785 = 0.274). See Figure 1.

Figure 1. Square vs. circle areas.

However, the greater area of a square is not the only reason square apertures deposit more solder paste. The curving of the circular aperture enables more surface of the stencil to contact more of the solder particle’s area. See Figure 2. So, the solder particles will adhere to a cicular aperture more readily and not adhere to the pad, resulting in a smaller solder paste deposit. 

Figure 2. The curving of a circular aperture results in more contact area with solder particles than a square aperture

These two effects can result in dramatically different soldering results, as seen in Figure 3. Using the square aperture provides so much more solder paste; when compared to what a circular aperture provides, it is stunning in the soldering result.

Figure 3. Circular aperture/pad (left) and square aperture/pad (right), using the same Type 3 powder size, area ratio, flux chemistry (no-clean), and reflow profile (RTP)

Cheers,

Dr. Ron


Hypothesis and Confidence Interval Calculations for Cp and Cpks

Folks,

I am reposting an updated blog post on Cp and Cpk calculations with Excel, as I have improved the Excel spreadsheet. If you would like the new spreadsheet, send me an email at [email protected].

One of the best metrics to determine the quality of data is Cpk. So, I developed an Excel spreadsheet that calculates and compares Cps and Cpks.

———————————————————————————————————-

Folks,

It is accepted as fact by everyone that I know that 2/3 of all SMT defects can be traced back to the stencil printing process. A number of us have tried to find a reference for this posit, with no success. If any reader knows of one, please let me know. Assuming this adage is true, the right amount of solder paste, squarely printed on the pad, is a profoundly important metric.

In light of this perspective, some time ago, I wrote a post on calculating the confidence interval of the Cpk of the transfer efficiency in stencil printing. As a reminder, transfer efficiency is the ratio of the volume of the solder paste deposit divided by the volume of the stencil aperture. See Figure 1. Typically the goal would be 100% with upper and lower specs being 150% and 50% respectively.

Figure 1. The transfer efficiency in stencil printing is the volume of the solder paste deposit divided by the volume of the stencil aperture. Typically 100% is the goal.

I chose Cpk as the best metric to evaluate stencil printing transfer efficiency as it incorporates both the average and the standard deviation (i.e. the “spread”). Figure 2 shows the distribution for paste A, which has a good Cpk as its data are centered between the specifications and has a sharp distribution, whereas paste B’s distribution is not centered between the specs and the distribution is broad.

Figure 2. Paste A has the better transfer efficiency as its data are centered between the upper and lower specs, and it has a sharper distribution.

Recently, I decided to develop the math to produce an Excel® spreadsheet that would perform hypothesis tests of Cpks. As far as I know, this has never been done before.

A hypothesis test might look something like the following. The null hypothesis (Ho) would be that the Cpk of the transfer efficiency is 1.00. The alternative hypothesis, H1, could be that the Cpk is not equal to 1.00. H1 could also be that H1 was less than or greater than 1.00.

As an example, let’s say that you want the Cpk of the transfer efficiency to be 1.00. You analyze 1000 prints and get a Cpk of 0.98. Is all lost? Not necessarily. Since this was a statistical sampling, you should perform a hypothesis test. See Figure 3. In cell B16, the Cpk = 0.98 was entered; in cell B17, the sample size n = 1000 is entered; and in cell B18, the null hypothesis: Cpk = 1.00 is entered. Cell B21 shows that the null hypothesis cannot be rejected as false as the alternative hypothesis is false. So, we cannot say statistically that the Cpk is not equal to 1.00.

Figure 3. A Cpk = 0.98 is statistically the same as a Cpk of 1.00 as the null hypothesis, Ho, cannot be rejected.

How much different from 1.00 would the Cpk have to be in this 1000 sample example to say that it is statistically not equal to 1.00? Figure 4 shows us that the Cpk would have to be 0.95 (or 1.05) to be statistically different from 1.00.

Figure 4. If the Cpk is only 0.95, the Cpk is statistically different from a Cpk = 1.00.

The spreadsheet will also calculate Cps and Cpks from process data. See Figure 5. The user enters the upper and lower specification limits (USL, LSL) in the blue cells as shown. Typically the USL will be 150% and the LSL 50% for TEs. The average and standard deviation are also added in the blue cells as shown. The spreadsheet calculates the Cp, Cpk, number of defects, defects per million and the process sigma level as seen in the gray cells. By entering the defect level (see the blue cell), the Cpk and process sigma can also be calculated. 

Figure 5. Cps and Cpks calculated from process data.

The spreadsheet can also calculate 95% confidence intervals on Cpks and compare two Cpks to determine if they are statistically different at greater than 95% confidence. See Figure 6. The Cpks and sample sizes are entered into the blue cells and the confidence intervals are shown in the gray cells. Note that the statistical comparison of the two cells is shown to the right of Figure 6.

Figure 6. Cpk Confidence Intervals and Cpk comparisons can be calculated with the spreadsheet.

This spreadsheet should be useful to those who are interested in monitoring transfer efficiency Cpks to reduce end-of-line soldering defects. It is not limited to calculating Cps and Cpks of TE, but can be used for any Cps and Cpks. I will send a copy of this spreadsheet to readers who are interested. If you would like one, send me an email request at [email protected].

Cheers,

Dr. Ron

SMT Assembly is an Optimization Process

Folks,

SMT assembly is an optimization process. There is no single stencil printing process for all PWB designs. The stencil printing parameters of stencil design, squeegee speed, snap off speed, stencil wipe frequency, and solder paste for assembling all PWBs will not be the same; just as there is no single reflow oven profile for all PWBs. Fortunately, most solder paste specifications give good boundaries for all of these parameters, but typically some trial and error experiments will be needed when assembling a new PWB design that is not similar to past assemblies.

The need for optimization is most obvious when trying to minimize defects. As an example, minimizing graping is often facilitated by using a ramp to peak reflow profile. However, the ramp to peak profile may acerbate voiding. See Figure 1.

Figure 1. The ramp to peak reflow profile may minimize graping, but acerbate voiding.

Figure 1. The ramp to peak reflow profile may minimize graping, but acerbate voiding.

Thankfully your SMT soldering materials and equipment suppliers deal with these optimization issues on a daily basis. So if you are ever stuck with some challenging SMT assembly process, contact these solder materials and equipment experts first.

Cheers,

Dr. Ron

Answers to the SMT IQ Test

Folks,

Here are the answers to the SMT IQ Test of a short while ago.

  1. What does the “A” in SAC305 stand for?
    ANSWER: 
    SAC stands for tin (Sn), silver (Ag), and copper (Cu). The “305” indicates 3.0 percent by weight silver, 0.5% copper, and the balance (96.5%) tin.
     
  2. The belt speed on a reflow oven is 2 cm/s. The PCB with spacing is 36 cm. What is the maximum time that the placement machines must finish placing the components on the PCB to keep up with the reflow oven?
    ANSWER: 
    Time (s) = product length (cm)/belt speed (cm/s) = 36 cm/2 cm/s = 18 sec.
     
  3. In mils, what is a typical stencil thickness?
    ANSWER
    : In range of 4 to 8 mils.
     
  4. BTCs are one of the most common components today; a subset of BTCs is the QFN package.
    1. What does BTC stand for? ANSWER: Bottom terminated component
    1. What does QFN stand for? ANSWER: Quad Flat Pack No Leads.
       
  5. What is the melting temperature of tin-lead eutectic solder?
    ANSWER:
     183° C.
     
  6. In mm, what is the finest lead spacing for a PQFP?
    ANSWER:
     Most common is 0.4 mm. A few have 0.3 mm, but these smaller spacings are hard to process.
     
  7. Are solder pastes thixotropic or dilatant?
    ANSWER:
     Thixotropic; the viscosity of solder paste drops when it is sheared (i.e forced through a stencil). Dilatant materials stiffen when sheared.
  8. In stencil printing, what is response to pause?
    ANSWER:
     When stencil printing is paused, the viscosity of the solder paste can increase; this situation would be considered a poor response to pause. Pastes that have stable viscosities during pausing are considered to have good response to pause.
     
  9. For a circular stencil aperture for BGAs or CSPs, what is the minimum area ratio that is acceptable?
    ANSWER:
     Typically greater than 0.66, although some solder pastes can print well a little lower than this.
     
  10. What are the approximate dimensions of a 0201 passive in mils?
    ANSWER: Approximately 20 by 10 mils.

Test Your SMT IQ

Folks,

Mary had worked at a small SMT “mom and pop” shop for 12 years. Business was always good and she moved up to CFO of the 60 person company. Revenue had been over $12 million for a few years with profits north of $1 million each year. She marveled how well Fred, the owner,  managed the small firm. As CFO, she was well aware of the strong financial strength of the company.

Mary was stunned when 18 months ago, Fred said he wanted to retire in less than two years, and he wanted her to “buy him out.” Fred was fit and spunky, but 75 years old was now in the rear view mirror.

Mary was more than stunned by the price Fred wanted; it was way, way too low. She even “complained” about this. But, Fred considered her more as a daughter and insisted on the low price. However, one of the concerns they both had was that Fred was really also the chief engineer. They had many loyal workers, as Fred paid 50% over the local rate and provided great benefits, but no one could fill in for Fred in the technical aspects of running the shop.

Fred had been trying to coach Mary for the past 18 months so that she would understand the technical aspects of SMT assembly better. Mary was a fast learner, but with only 6 months left before Fred’s retirement, they both agreed they needed to hire a chief engineer.

So, Fred developed an SMT IQ Test for the candidates. If they could not get at least 80%, they would not be considered. Fred argued that if you were really good enough, you had to know 80% of these questions. Here they are:

  1. What does the “A” in SAC305 stand for?
  2. The belt speed on a reflow oven is 2 cm/s. The PCB with spacing is 36 cm. What is the maximum time that the placement machines must finish placing the components on the PCB to keep up with the reflow oven?
  3. In mils, what is a typical stencil thickness?
  4. BTCs are one of the most common components today. A subset of BTCs is the QFN package.
    • What does BTC stand for?
    • What does QFN stand for?
  5. What is the melting temperature of tin-lead eutectic solder?
  6. In mm, what is the finest lead spacing for a PQFP?
  7. Are solder pastes thixotropic or dilatant?
  8. In stencil printing, what is response to pause?
  9. For a circular stencil aperture for BGAs or CSPs, what is the minimum area ratio that is acceptable?
  10. What are the approximate dimensions of a 0201 passive in mils?

Try the test. Stay tuned for the answers.

Cheers,

Dr. Ron

Thixotropy: An Important Solder Paste Property

Folks,

To the SMT process engineer, the second most important thixotropic material in their lives is solder paste. If solder paste was not thixotropic, it would be difficult to print and would likely slump after printing the paste. What is a thixotropic material? It is a material that has a low viscosity when it is shear stressed and a high viscosity when it is not shear stressed. So, when the solder paste is forced through the stencil aperture by a squeegee, its viscosity plummets and allows it to fill the aperture. See Figure 1.

Figure 1. The viscosity of solder paste dramatically decreases as it is forced through the stencil aperatures.

When the stencil is removed, the resulting solder paste deposit experiences no shear stress so the deposit maintains the shape of a “brick.” See Figure 2. So thixotropy is a very helpful property of solder pastes.

Figure 2. After printing, the solder paste viscosity is high, enabling the depost to maintain the brick shape. Figure courtesy of Ron Lasky, Jim Hall, and Phil Zarrow.

If solder paste was dilatant, it would be a disaster. These materials are the opposite of thixotropic materials. They have a low viscosity when not shear stressed and a high viscosity when shear stressed. So they could not be forced through the stencil aperture and, if they could, they would flow all over the board. Cornstarch and water is an example of a dilatant material.

Oh, yes, what is the most important thixotropic material to the SMT process engineer? Their blood. When getting up from lying down, our heart automatically makes a strong “pump” to rush the flow of blood to our head. Since blood is thixotropic, it shear thins and makes it easier for our heart to get the needed blood up to our head. If blood was not thixotropic, we might faint every time we rise from reclining!

Cheers,

Dr. Ron

SMT Workshop Pre-Test

Folks,

Six months ago …

Patty had just finished an all day workshop on “Common Defects in SMT Assembly and How to Minimize Them.” The workshop seemed to go really well, and many of the 35 or so attendees thanked her for a great learning experience.

After most of the people filed out of the room, two approached her as she was disconnecting and packing her laptop.

“Dr. Coleman, that was a great workshop. But, I do have one question. You used a term all day that I wasn’t familiar with, ‘SAC’,” a 35-year-old process engineer commented to her.

While saying this, he presented his business card that referred to him as a “Senior Process Engineer.”

Patty was trying to recover from this shock, when the second similar looking fellow asked, “And what are ‘OSP’ and ‘eutectic’.”

After explaining these three terms and exchanging a few pleasantries, the two senior process engineers walked out of the room and bade Patty farewell. As the room became empty, Patty settled into a chair.

“How can this be?” she thought. She was stunned that people with enough experience to be called “senior process engineers” would not know these terms.

Today 6 AM …

Patty was jogging back to her house in Woodstock, VT, when she spied a beautiful red fox. Neighbors had reported seeing the fox numerous times. People believed that the fox was nesting. In addition, a black bear had been sighted by everyone in her family over the past few weeks. Add all of this to the family of deer and the rafter of turkeys in her neighborhood and it was quite an experience for Patty, Rob, and their sons.

The fox, however, created a new problem. Patty and Rob had bought their twin sons a Yorkshire puppy, Ellie, about a year ago. At 6 pounds she could be dinner for the fox, so, unfortunately, they could no longer let Ellie out by herself.

Figure 1. Ellie the Yorkie after a big day. Sadly she has to be watched when she goes outside of Patty’s house, due to the local predators.

By 7:30AM Patty was in her office. She was giving a workshop in two weeks at a local chapter meeting in Boston and decided to create a pre-test to give to the attendees so that she could assess their current knowledge. Patty planned on having the students grade each other’s exams and on working the exam in as a leaning experience at the start of the workshop. By assessing the results of the pre-test, she wanted to make sure she didn’t use acronyms they don’t understand, and to also explain topics that the students might not be familiar with. As she was working on the questions for the pre-test, Pete walked in.

“Hey, Professor C, how goes it?” Pete asked.

“I’m preparing a pre-test for the workshop I’m giving in a few weeks,” Patty replied nonchalantly.

“I remember you talking about doing it a month or so ago. Seems like a good idea to me,” Pete responded.

“I’m ,glad you approve,” Patty said wryly. “I just finished it. Do you want to take a look at it?” she continued.

Patty printed out a few copies and handed one to Pete. They both looked at it for a few minutes, in silence.

Finally, Pete commented sheepishly, “Aaa, Patty your joking, right?”

“Why do you say that?” Patty asked, a little annoyed.

“It’s just too easy. Everyone will get 100% and you won’t get any information,” Pete opined.

Patty then reminded Pete of her experience 6 months ago.

“OK. Maybe you have a point. But, I still think it’s too easy,” Pete concluded.

“I’ll tell you what. How about a bet? If the average pre-test grade is above 70%, Rob and I will take you and your new crush, Mary, out to Simon Pearce. If it is 70% or less, you treat us,” Patty teased.

“It’s a bet,” replied Pete quickly.

The Pretest:

  1. What does the letter “S” in SAC stand for?
  2. How much silver is in SAC305?
  3. What is the approximate melting point for SAC305 solder (+/- 4oC)?
  4. Solder paste is approximately how much (by weight) metal (+/- 5%)?
  5. What is not a current common defect in SMT?
    1. Head-in-pillow
    1. Pad cratering
    1. BGA Ball Matting
    1. Graping
  6. Which is a closest to typical stencil thickness?
    1. 5 microns
    1. 20 mils
    1. 5 mils
    1. 20 microns
  7. Which is closest to a typical lead spacing for a plastic quad flat pack (PQFP)?
    1. 0.1mm
    1. 0.1mil
    1. 0.4mm
    1. 0.4mils
  8. Which has finer solder particles, a Type 3 or 4 solder paste?
  9. What does OSP stand for?
  10. Place an arrow at the eutectic point of the tin-lead phase diagram below.

Epilogue (two days after the workshop)

Patty arrived at Ivy U and couldn’t wait to see Pete. She went to his office but he wasn’t there. Finally, she found him in the machine shop helping four students with a project that required some additive manufacturing.

“Hey, Pete! When are you and Mary going to treat us to our dinner?” Patty teased.

“Don’t tell me the average was less than 70%,” Pete grumbled.

“Forty-three point zero eight to be exact,” Patty punctuated.

Figure 2. The Pretest Scores

“Yikes!” Pete exclaimed, rubbing the back of his neck. “I guess you were right.”

“It really helped me to take things slowly and explain all the terms. I think I helped the students much more than usual,” Patty explained.

“Rob and I both agreed, we are ordering the most expensive meal that Simon Pearce has,” Patty joked.

At that Pete let out a deep groan.

Dr. Ron note: All of the events in this post are true. How would you do on the pretest?


The Return of Patty and the Professor: Uptime Part 2

Folks,

For the next few weeks I plan to repost some of the first Patty and the Professor episodes. As I visited several facilities, some of them in other industries, I found that uptime is as vital a topic as ever. Although these facilities were tracking a few metrics, uptime was not one of them.  I estimated they were little better than ACME in the following vignette. Let’s all be committed to measuring and improving our processes uptimes. Now on to Patty and the Professor.

Two weeks passed quickly and The Professor returned to ACME. Patty met him at the door. “Professor, it’s great to see you,” Patty said with enthusiasm. “We collected the uptime data in real time on a laptop, no one has seen that results yet. We wanted it to be a surprise,” said Patty. The Professor suggested that he go out on the shop floor to observe the manufacturing activities until shortly after lunch. He pointed out  that his observations may help to understand the uptime results.

The morning seemed to drag for Patty, she was very anxious to see the resets of the uptime data. She bet Pete a dinner for two that the uptime would not be more than 50%. If she wins, Pete and his wife will treat her and her boyfriend Jason to dinner at the restaurant of her choice.

Around 1:30 p.m. The Professor suggested that he was ready for the meeting. Patty had written a simple Excel macro to perform the calculations for the uptime. She only had to push a button and he whole room would see the result in a moment, as Patty connected her laptop to a projector. There was tension in the air, friendly wagers had been made, but the entire process team realized that their reputation was on the line.

When the number emerged on the screen, John, the manager’s face became ashen. Pete’s visage was redder than two weeks ago. John thought, “I should be fired. How could I manage this team for five years and not know that our uptime was only 9.7%.” Patty was thinking about her choice of restaurants.

“How can we be so bad?” John asked The Professor. The Professor responded, “The good news is that there are tremendous opportunities for improvement. After observing the operations out on the floor this morning, I think we can get the uptime to greater than 40%.” Pete shot back, “You’re kidding, only 40%?”

“I’ve only seen two operations that have greater than 45% uptime, and I’ve been to over 150 facilities worldwide,” answered The Professor.

“Where do we start?,” asked John.

“How about lunch?” beamed The Professor.

“We just had lunch!” Pete groaned.

“No, no Pete,” The Professor chuckled, “I mean how lunch is handled out on the line. Lunch costs the company more than 1½ hours of production in an eight hour shift. That’s nearly 20% of the entire shift.”

Now John was a little agitated. “Professor, lunch is only 30 minutes. We purposely have a short lunch period to avoid the line being down for a long time,” John said with a note of annoyance.

“John, this is true, but I watched what the operators did. Lunch is supposed to start at 12 noon, but the operators turn the line off at 11:40 a.m. They don’t get back to the line until 12:40 p.m. and it takes them more than 30 minutes to get the line running again. Today, the line was not running until 1:15 p.m. It was down for 1 hour and 35 minutes,” stated The Professor.

John thought again, “Yes, I should really be fired.”

Will John keep his job? What restaurant will Patty choose for dinner? What should be done about lunch? Where are all of the other hours lost? Stay tuned for the answers to these and other questions.

Cheers,

Dr. Ron