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Folks,
I posted this a while back. The solutions are in red.
Suppose you need to select a consultant or verify the qualifications of some of your staff to perform designed experiments (DOE), statistical process control (SPC) and statistical analysis. What are five questions you could ask to see if the folks you are interviewing have the right stuff to do the job? Try these?
1. What is the difference between common cause and special cause variation?
This was answered in a post a while ago.2. In designed experiments the f statistic is used to evaluate whether or not a factor is significant. How would you explain the f statistic to a layman? In a DOE, the f statistic is proportional to the difference between the average response values at the varying levels of the factor divided by the variation with response at the same level. An example may help. Suppose we want to see if temperature affects the volume of solder paste deposits. We measure 5 paste volumes at 20C and 5 at 30C. The 5 readings at 20C have an average of 1000 cubic mils with a standard deviation of 100 cubic mils. At 30C the deposits are 1400 cubic mils, also with a standard deviation 100 cubic mils. In this case the f statistic will be proportional to (1400-1000)/100 = 4, strongly suggesting that temperature affects solder paste deposit volume.
3. What do the Shewhart Rules tell us?
The Shewhart Rules tell us if it is likely that special cause variation is affecting a manufacturing process. As an example, let's assume we are measuring the average volume of 10 solder paste deposits on a PWB. The historic average for the deposits is 1200 cubic mils, and the 3 sigma control limits are +/- 300 cubic mils of this point. If the average of one of the set of 10 readings was 1650 cubic mils this would be about the control limit and would be a Shewhart Rule #1 violation. This violation would suggest that a special cause variation has entered the process. However, with 1000s of data points a Shewhart violation is possible even from common cause variation, since 3 sigma control limits will have 0.3% of their data outside of the control limits. However, if we got 4 Shewhart #1 violations in a row, we would surely have a special cause problem. All in all there are a total of 8 Shewhart Rules.
4. I would like to sample a large population and test whether or not I can claim that the population has zero defects with a 95% confidence. How can I do this?
I showed in a "Quiz" recently, that an infinite number of samples would be required.
5. What is Cpk? How does it differ from Cp?
Cp measure precision, Cpk measures precision and accuracy.
An extra: “Six Sigma” is widely claimed to be 3.4 ppm defects. Is this correct, if not why not?
3.4 ppm is wrong on two levels:
1. 3.4 ppm is 4.5 sigma for a one sided test. For a two sided test the defect rate would be 6.8 ppm.
2. True 6 sigma is about 2 ppb!
I’ll share the answers in a few days.
Cheers,
Dr. Ron
Click on this link to find the Shewhart Chart above
Patty's Sketch of The Professor
Folks, the adventures of The Professor continue.........
So far the meeting with The Professor had proven very valuable John thought. He was anxious to hear the other suggestions that The Professor had. The Professor began to speak.
“Change-overs are what really hurts ACME’s uptime and hence productivity,” The Professor commented. Pete was surprised. “Even you were impressed with our system of having a white board to document logistics status for each future job,” said Pete. “You are correct,” responded The Professor. “However, a change-over takes you about 2-3 hours and you have one or two change-overs per line per day,” The Professor added. “We have a high product mix business, it’s what we do,” said John. “The good news is, you can cut your change-over time to 30 minutes,” shared The Professor. “How?” asked John increduously. “By using feeder racks,” explained The Professor. “These racks allow you to setup the component reels for the next job while the current job is running. Admittedly they cost about $30,000, but they will pay for themselves in weeks. Right now you lose more than two hours per change-over loading the feeders on to the component placement machines. With the feeder racks, you just roll them and lock them in place,” said The Professor.
Pete moaned, “We already have feeder racks. We only used them once, because they stick on the carpet when we move them.” This comment caused The Professor to groan internally, but he hid it well. He had noticed the frayed carpet near the component placement machines. John was beside himself. “It’s a good thing we are not The Professor’s students……I don’t think we would be heading for an ‘A,’ “ he thought. John responded to Pete’s comment, “Pete, let’s get facilities to remove that rug and start using the feeder racks ASAP.”
Patty listened to all of this with comical fascination. She had harassed Pete about using the feeder racks several times. While the meeting was going on she drew a sketch of The Professor, who is notoriously camera shy. Oh, and she decided on the restaurant,
Aujourd’hui in nearby Boston. Maybe they can pick up a
Red Sox game while they’re there.
Epilogue: Six months later ACME’s uptime was a respectable 30.4%. John never had to buy another line. The improved productivity enabled ACME to increase their market share. Patty’s dinner and ball game were a complete success. She handled her victory modestly and she and Pete became best friends. Pete also joined the ranks of The Professor’s many admirers.
Dr. Ron’s note: I know that a story like this must seems too comical to be true. Every point and the associated uptime numbers, lost time etc, are all based on a real situation with no exaggeration. The Epilogue, however, is ficticious as is the Patty/Pete friendly (?) conflict. The names have been changed to protect the innocent (guilty?)
What is your uptime??
Cheers,
Dr. Ron
At ACME, there is such a thing as a free lunch
Folks,
The continuation of The Professor's second visit to ACME......
"Well what should we do Professor?" John said weakly. "Clearly, not shut the line down over the lunch hour," The Professor responded quickly. "We can't," said John, "the operators are all friends and they count on having lunch together." "How much are they paid per hour?" asked The Professor. "Ten dollars," replied John. "You can pay them $15 per hour and still make more profit if they keep the line running over the lunch hour," The Professor opined. "Fifteen dollars per hour for the lunch time or the 40 hour week?" John asked nervously. "For the whole week," was The Professor's reply. "I find that hard to believe," John shot back. "Consider this, said The Professor, your line is up only 9.7% of an 8 hour shift, that's only 47 minutes. Today you lost 95 minutes over the lunch hour. You may be able to increase your uptime to greater than 15%, by keeping the line running over lunch. I modeled your business with ProfitPro3.0 cost estimating software, your company will make millions more per year if you keep the lines running over lunch. I have worked with other companies to make this change, it is really easy with a 30 minute lunch hour. If 5 people normally run the line, you have just one stay back over lunch hour, that way each person only misses the lunch hour once a week."
John thought optimistically, "There is such a thing as a free lunch."
"Now let's talk about what we can do to double the uptime from the 15% we will get by running the lines over lunch," said the Professor.
Patty listened to all of this in amazement, The Professor was helping ACME more than she thought possible.
Yes, John will keep his job. What is The Professor's plan to get uptime to 30% or more? We still haven't learned where Patty will go to dinner. Stay tuned for the latest.
Cheers,
Dr. Ron
Dr. Ron note: As surprising as this may seem, this story is based on real events. The uptime numbers and improvements are from real examples. Any company that can acheive 35% or more uptime can compete with anyone in the world, even in low labor rate countries. Sadly, few companies know their uptime or have an urgency to improve it.
Folks,
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 1:30PM 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 5 years and not know that our up time was only 9.7%.” Patty was thinking about her choice of restaurants.
John asked The Professor, “How can we be so bad?” 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 it 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 world-wide,” 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 1 and ½ 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 11:40AM. They don’t get back to the line until 12: 40PM and it takes them more than 30 minutes to get the line running again. Today the line was not running until 1:15PM. 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 on May 30.
Cheers,
Dr. Ron
Goldratt's novel "The Goal" is about the Theory of Constraints
Folks,
Business was good at ACME. Even in these challenging times, the company's three assembly lines could not keep up with demand. John, the manger of the assembly lines, decided to request the funds for an additional assembly line. A member of his team, Patty, suggested he might want to consult "The Professor,*" before getting a new line. The Professor taught a course on line balancing that Patty took at the SMTAI conference last summer. Line balancing is an important part of optimizing productivity in electronic assembly. A balanced line ensures that the component placement process, usually the "constraint," is the fastest possible by assuring that each placement machine spends the same amount of time placing components. If any machine is waiting for the others, assembly time is being wasted. In a sense line balancing is an application of Goldratt's Theory of Constraints. John remembered that when Patty applied what she learned from The Professor, throughput increased 25%. Unfortunately, Patty did not attend The Professor's other class on "Increasing Line Uptime."
John decided to have a chat with Patty about The Professor. "Patty, why do you think I should consult with The Professor, about getting a new line?" "Well John, perhaps with some effort to improve our uptime , we wouldn't have to buy another line," said Patty. “Patty, that’s a good point,” said John.
Patty contacted The Professor and he agreed to fit ACME into his busy schedule. Upon his arrival, The Professor was given a tour. As part of the tour he was shown the process that ACME used to minimize changeover time between jobs. The Professor appeared to be impressed. After the tour, The Professor asked if a brief meeting could be held with the engineers and managers to discuss the situation.
“What is the average line uptime?” The Professor asked the assemblage. There was some hemming and hawing, finally Pete, the senior process engineer replied, “I’d say at least 95%, we work our fannies off out there.” There was a murmur of agreement from the 9 or 10 people in the room. Finally John spoke up, “Professor, what is your definition of uptime?” The Professor responded, “Simply the percent of time an assembly line is running.” Pete again responded that 95% was the right number.
The Professor asked for some production metrics and performed some calculations on his laptop. In a few moments he commented, “From the data you gave me, I estimate that your average line uptime is about 10%.” Upon hearing this, Pete became red in the face, especially after Patty whispered in his ear, “I told you so.” The noise in the room became so loud that John was concerned he might have a riot on his hands. The Professor asked to speak and John, in a booming voice, asked for calm.
“Let’s not become angry, perhaps my calculations are off. Why don’t we measure the uptime for a few weeks to be certain.” “How do we do that?” asked Pete, his face still crimson. “Each day one process engineer will go out to the lines every 30 minutes. If the line is running, he will put a 1 in an Excel® spreadsheet cell, if the line is not running a 0 will be entered,” responded the professor.” It was agreed that this will be done and The Professor will be back in two weeks.
Will Pete’s red face return to normal? Will the line uptime be 95%? Will Patty and Pete ever be on speaking terms again? Stay tuned on May 27 for the next episode.
Cheers,
Dr. Ron
* The Professor, as he is affectionately called by his many students, is a kindly older man who works at a famous university. Few know his real name. The Professor is an expert in process optimization.
Folks,
An effective process engineer will be good at statistically thinking. This skill will help her to quickly recognize and address changes in the manufacturing processes she is responsible for. One of the techniques I use to keep my statistical thinking tools sharp, is to look at what I would call “Statistics in the News” and see if they make sense. Recently such an article attracted my attention. It was in posted on the Boston Globe website. The article is about the concern for the high number of accidental deaths in the US military in Iraq. These and other deaths, by natural causes, are now greater than the number of combat deaths.
I would encourage you to read the
entire article, however the essence is that there are 130,000 US soldiers in Iraq and from September 2008 to April 2009, 72 soldiers have died from non-combat related causes. This perceived high rate death rate has caused the military to hire consultants to study ways to make the military safer. A question that is not asked in the article is: “What is the comparable death rate in the US.” A little searching on the web at the CEDC or Social Security will result in finding graphs such as the one above. If we assume a typical soldier is about 25 years old, from this graph, one would expect about 130/100,000 to die per year. Since there are 130,000 soldiers and the time period in which the 72 died is 8 months, we would expect about 115 to die in a group 130,000. Hence, save for combat, it is safer in Iraq than in the US!
It is hard to discourage efforts to improve safety, but unfortunately the act of living has its own risks.
Cheers,
Dr. Ron
Folks,
Suppose you need to select a consultant or verify the qualifications of some of your staff to perform designed experiments (DOE), statistical process control (SPC) and statistical analysis. What are five questions you could ask to see if the folks you are interviewing have the right stuff to do the job? Try these?
1. What is the difference between common cause and special cause variation?
2. In designed experiments the f statistic is used to evaluate whether or not a factor is significant. How would you explain the f statistic to a layman?
3. What do the Shewhart Rules tell us?
4. I would like to sample a large population and test whether or not I can claim that the population has zero defects with a 95% confidence. How can I do this?
5. What is Cpk? How does it differ from Cp?
An extra: “Six Sigma” is widely claimed to be 3.4 ppm defects. Is this correct, if not why not?
I’ll share the answers in a few days.
Cheers,
Dr. Ron
The photo is of Walter Shewhart of the Shewhart Rules fame. Click the link, his story is interesting!
Folks,
Ning-Cheng Lee: Distinguished Author and Distinguished Lecturer
Dr. Ning-Cheng Lee was recognized recently by two highly respected industry organizations as both a Distinguished Author and Distinguished Lecturer.
SMTA International has selected Dr. Lee as a Distinguished Author by “Special Invitation from the SMTA International Technical Committee”. Ning-Cheng was selected from authors of exceptional papers and “Best of Conference” award recipients from past events. This honor is part of the SMTA’s 25th Anniversary celebration.
In addition, the IEEE’s Components, Packaging, and Manufacturing Technology Society (CPMT) approved Dr. Lee to be a CPMT Distinguished Lecturer. According to the director for the CPMT Distinguished Lecturer Program, Dr. Lee was nominated and endorsed by several colleagues from the industry. The CPMT Distinguished Lecturer program includes “Fellow Caliber” technologists from all over the world who are available for any CPMT-sponsored venue. The CPMT is the leading international forum for scientists and engineers engaged in the research, design and development of revolutionary advances in microsystems packaging and manufacture.
Please join in offering your congratulations to Dr. Lee by adding your comment below.
Cheers,
Dr. Ron
Folks,
In teaching process optimization and failure analysis, one of the most helpful concepts is understanding he difference between common cause and special cause defects. A special cause defect, in a well tuned process, occurs when something unpredictable changes. As an example, let's say you get a batch of printed wiring boards (PWBs) that have oxidation on the pads. This is a defect and the boards shouldn't used, however we will assume that somehow they made it through the company's receiving inspection process. It should not be too surprising that when the boards are assembled that they have a poor first pass yield, say 35%. Typical first pass yield in this optimized process is 95%. It is obvious that the poor yield was due to this "special cause," the oxidized pads.
Common cause failures are a little more difficult to explain and comprehend. In a process, there are multiple entities that can vary, within the specifications, such as the solder paste viscosity, the temperature and humidity of the room, the reflow profile, the wettability of the component leads and PWB pads etc. Statistically, within the specifications, the variation can be such as to result in a small number of fails......say the 5% we get with this process when everything is as it should be. These types of fails are called common cause fails.
It is fundamentally crucial to understand the differences between special and common cause fails to successfully monitor and improve processes. One of the tragedies that I often see when the failure rate increases, due to special cause fails, is the process engineers changing the process parameters (e.g. raising the reflow temperatures when the pads in the special cause example above did not wet). In a well optimized process the process parameters are determined by designed experiments, any collapse of process yields is the result of a special cause. You can only fix special causes by identifying and rectifying them, not by changing the process!
Cheers,
Dr. Ron
Folks,
Recently someone asked me about reworking a SAC305 solder joint with a SnBi solder. The reason to consider SnBi was that the lower melting point of SnBi would make the rework process easier. The main concern the person had was what the properties of the reworked solder joint would be. Unfortunately no one can tell them. Note that I didn’t say that there would be a problem, I just said that the properties of the resulting solder would be unknown. Let’s see why.
Think about what is going on in reworking the solder joint with the above parameters. An unknown amount of SAC305 solder is being reworked with an uncontrolled amount Sn Bi solder. The resulting solder joint with be a mixture of the two solders with unknown percentages. So it is not possible to predict the properties of the reworked joint. I suppose if one knew the properties of all mixes of SAC305/SnBi from 0 to 100% you could at least bracket this performance. However, considering that the industry is crying out for more reliability data on SAC305 itself, it is unlikely that such data exists.
So the bottom line is to proceed with caution when mixing solders in rework. You will likely end up with a solder joint with unknown properties.
Cheers,
Dr. Ron
The photo above shows a SnBiPb ternary phase resulting from mixing leaded and Bi containing solders. This phase has very poor mechanical properties as can be seen in the photo, which is taken after thermal cycling. The photo is from Zequn Mei, Fay Hua, and Judy Glazer, “SN-BI-X SOLDERS”, SMTA International, San Jose, CA, Sept. 13-17, 1999.
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