How much can a failure cost? The answer depends on the case. A failure in the production of low-value items is very different from a failure in an aircraft or on an oil platform. Following this reasoning, you are probably thinking that in some cases it makes sense to try to reduce failures to almost zero, while in others the cost of nearly eliminating failures may outweigh the gain. These ideas, which we studied when we discussed the "costs of quality", are worth revisiting for this lesson.We agree, then, that the pursuit of perfection, here understood as the elimination of failures, is worthwhile for some product and service companies. This is the context in which "Six Sigma" emerged: a set of practices that seeks to improve processes by eliminating failures or defects and, as a result, to increase companies' profitability.Six Sigma history and conceptsIn 1987, Motorola, in the United States, launched a new quality program called "Six Sigma". The methodology was formulated by engineer Bill Smith, known as the "father of Six Sigma", and it gained momentum because Bob Galvin, who led the company (then chairman of the board), adopted it and made it mandatory across the whole organization. The focus was to increase customer satisfaction and to reduce (or even eliminate) defects in the company's products and services.The program was designed for the entire organization, and the "Six Sigma" capability level was set as the target for approaching the "zero defects" standard. This standard was meant to apply to every area, that is, to products, processes and services.For Galvin, products and processes should be designed to be "Six Sigma": results with reduced variability and higher productivity. In its first years, Motorola reported savings in the billions of dollars from process improvement (a frequently quoted figure is US$ 2.2 billion, but the published numbers vary depending on the period considered), and in 1988 it received the Malcolm Baldrige National Quality Award in the United States. These results led many companies, in the United States and around the world, to adopt the program; General Electric under Jack Welch, from 1995 on, is the best-known case.We can therefore define "Six Sigma" as a disciplined and highly quantitative management strategy with a systemic approach, whose goal is to dramatically increase companies' profitability by optimizing products and processes, with a consequent increase in customer and consumer satisfaction.It is also a systematic way of managing the company's activities and reducing costs and process variability, through a methodology centered on statistical measurement and on improving efficiency and effectiveness.Let us recall the two concepts. Effectiveness means achieving the expected result, for example, delivering a product that meets all of the customer's requirements. Efficiency means achieving that result with the least possible use of resources. Now answer: is it possible to be effective without being 100% efficient? Surely your answer was yes. It is possible to deliver a product that meets 100% of the customer's requirements; however, if to do so we have to spend more resources than planned, we will compromise the projected profitability.A print shop delivered all 10,000 catalogs ordered, on time and without a single defect, but used 1,300 kg of paper when 1,000 kg had been planned. How should this result be classified?Answer: Effective, but not efficient — the result the customer asked for was delivered (effectiveness), but with 30% more paper than planned (efficiency of 1,000/1,300, about 77%). Six Sigma pursues both at the same time.Objectives of Six SigmaThe main objectives of the "Six Sigma" program are to reduce process variability and, consequently, the number of errors, whether in the manufacture of a part or in the delivery time of goods (in the case of a service). As a natural consequence, profitability and customer satisfaction increase. Imagine that your delivery company never delivered late. In that case there would be no "error", and the customer would always be satisfied with the service and willing to hire it again, which increases the company's profitability."Six Sigma" pursues both things: meeting customer requirements (effectiveness) and reducing the cost of delivering the product or service (efficiency). Another very important aspect of the program is the link between quality and financial indicators. Many executives of large companies were persuaded to implement it because they saw significant profitability gains in other companies. Gains this "convincing" rarely show up in models such as ISO 9001, TQM or PNQ (Prêmio Nacional da Qualidade, Brazil's National Quality Award). In "Six Sigma", quantifying the gains is the main indicator and the main argument for implementation.For this reason, priority Six Sigma projects are usually chosen based on financial indicators: the projects with the best financial return get priority in the allocation of resources.The program's very name shows its strong connection with statistics: sigma is the Greek letter (here, the lowercase σ) that represents the standard deviation, a measure of process variability that we studied in the lesson on statistical process control (SPC).In the case of a product, some characteristics are important or even critical to quality, such as the diameter of a part or the viscosity of an oil. We collect data and count the defects generated in the process, which occur when the monitored characteristic does not meet the specifications. The most widely used measure for this count is DPMO (defects per million opportunities):DPMO = number of defects ÷ (number of units × defect opportunities per unit) × 1,000,000Why Six Sigma matters: DPMO and the sigma scaleIf, in a production run of one million screws, 12,000 were rejected for not meeting the specification, and each screw has a single defect opportunity, we say that the process had 12,000 DPMO. The lower the DPMO, the better the process or product.The goal of "Six Sigma" is to get very close to zero defects: 3.4 defects per million opportunities. The methodology measures a process's quality level by converting the number of defects per million into a number on the sigma scale. It also serves as a measure of conformity, since the lower the DPMO, the more conforming the process or product.The sigma scale indicates how many standard deviations (σ) fit between the process mean and the nearest specification limit. The higher the sigma level, the lower the chance that a part falls outside the specification, and the greater the "perfection" of the process, whether it is a production process or a service.The chart above shows the sigma scale with the corresponding number of defects per million (ppm); its labels are in Portuguese ("Partes por milhão" means parts per million, and "Dois, Três, Quatro, Cinco, Seis Sigma" are Two to Six Sigma). Note that a "Two Sigma" process has about 308,500 defects per million opportunities (the chart shows 308,733, but the standard table value is 308,537). A "Three Sigma" process has 66,807 DPMO and a "Four Sigma" process about 6,200 DPMO. As the sigma level rises, the number of defects falls until it reaches the near perfection of "Six Sigma", with only 3.4 DPMO.Note an important detail: these values already include the so-called 1.5σ shift. Motorola observed that, in the long run, process means tend to drift by about 1.5 standard deviations; for this reason, the standard Six Sigma table calculates defects as if the mean were 1.5σ closer to one of the limits. Without this shift, a process with its limits at ±6σ from the mean would have only about 0.002 DPMO, and a process at ±3σ would have about 2,700 DPMO (99.73% conforming), not 66,807.Sigma levelDPMO (with 1.5σ shift)YieldDPMO without shift2σ308,53769.1%45,5003σ66,80793.32%2,7004σ6,21099.379%635σ23399.977%0.576σ3.499.99966%0.002You may be wondering why we argue over such a small difference: a process with 99% conformity looks excellent, and a "Six Sigma" process reaches 99.99966%. Look at the table below and decide which company you would rather be served by:99% conforming (about 3.8 sigma)Six Sigma (99.99966% conforming)7 hours without electricity per month1 hour without electricity every 34 years3,000 letters lost for every 300,000 letters mailed1 letter lost for every 300,000 letters mailed15 minutes of unsafe drinking water per day1 minute of unsafe drinking water every 7 monthsTV channel off the air 1.68 hours per weekTV channel off the air about 2 seconds per week1 emergency landing per day at São Paulo–Guarulhos airport1 emergency landing every 8 years at the same airportAn assembly process produced 2,000 circuit boards, each with 5 defect opportunities, and 50 defects were found. What is the DPMO?Answer: 5,000 — DPMO = 50 ÷ (2,000 × 5) × 1,000,000 = 5,000. The answer 25,000 comes from forgetting to multiply by the 5 opportunities and computing 50 ÷ 2,000. In the table with the shift, 5,000 DPMO is slightly above 4 sigma (about 4.1σ).In the standard Six Sigma table, a Three Sigma process has 66,807 DPMO, but the normal curve says only 0.27% (about 2,700 per million) falls outside ±3σ. Why do the numbers differ?Answer: Because the standard table assumes the mean drifts by 1.5σ in the long run — with the mean 1.5σ closer to one limit, only 1.5σ remains to it, and the tail beyond 1.5σ is 6.68%, or 66,807 per million. It is the same shift that makes Six Sigma equal 3.4 DPMO instead of 0.002.Applying Six SigmaIn industry it is common to have maximum and minimum specification limits for certain characteristics. In the manufacture of a screw, for example, it may be specified that it must be at most 2.1 cm and at least 1.9 cm long. These limits usually come from the customer's design or from technical standards.In this example, to meet the Six Sigma philosophy, the process must be centered at 2 cm and have a standard deviation of at most 0.1 cm ÷ 6 = 0.0167 cm. That way, the mean plus 6 standard deviations gives 2.1 cm and the mean minus 6 standard deviations gives 1.9 cm: the specification limits are six sigmas away from the mean. Even if the mean drifts by 1.5σ over time, the process still produces about 3.4 defects per million.If the screw factory operated with a standard deviation of 0.1 ÷ 3 = 0.0333 cm, it would be at Three Sigma: according to the standard table (with the 1.5σ shift), it would have a yield of about 93.3% and 6.7% errors, or 66,807 DPMO. With a perfectly centered process and no shift, it would be about 2,700 DPMO.After the "Six Sigma" program has been applied, the lower and upper limits are only reached at ±6σ from the mean. We then say that the company is at the 6σ level, with a yield of 99.99966% and about 3.4 DPMO.Note that this relationship is the same as the capability indices studied in SPC: with the limits at ±6σ of a centered process, Cp = (USL − LSL) ÷ 6σ = 0.2 ÷ (6 × 0.0167) = 2.0. A Six Sigma process therefore corresponds to Cp = 2.0; with the 1.5σ shift, Cpk = 4.5σ ÷ 3σ = 1.5.A shaft has a specification of 10.0 mm ± 0.3 mm and the process is centered at 10.0 mm. What is the largest standard deviation that still keeps the limits six sigmas away from the mean?Answer: 0.05 mm — the distance from the mean to the limit is 0.3 mm, and 0.3 ÷ 6 = 0.05 mm. The 0.10 mm option corresponds to Three Sigma (0.3 ÷ 3), and 0.03 mm would come from dividing the tolerance by 10.The DMAIC methodSix Sigma improvement projects usually follow the DMAIC roadmap: Define, Measure, Analyze, Improve and Control.Phase 1 – DefineThe "D" (Define) in DMAIC is about selecting high-impact projects and choosing the metrics that will show whether the project succeeded. In this stage the problems (or improvement opportunities, as some prefer to call them) linked to the processes are defined, along with the project's goals and scope, clearly.It is very important to describe the problems quantitatively. Indicators such as conformity, productivity, cost and customer satisfaction will be used throughout DMAIC. Therefore, in the first phase it is necessary to define which process problems will be studied, to understand the purpose of the process and what is expected from it, and to state what improvement in the indicator is intended.Quantitative goals must be tied to solving the problem and usually have a value (for example, increase production by 3%) and a deadline (for example, three months).Phase 2 – MeasureIn the measurement phase, we get to know and observe how the process is working today. We must make sure the data are reliable (the measurement system has to be adequate), establish the current level of the chosen indicator, which will serve as the baseline, and start listing the potential causes of the problem. This is done along two paths: one more quantitative and one more qualitative. On the quantitative path, we take the database, select an indicator and study its behavior with statistical tools such as control charts, histograms and capability indices.On the qualitative path, we study the process in more depth, trying to find out where the problem defined in the previous stage occurs. It is important to map the process and the information that will help identify the potential causes of the problem.Phase 3 – AnalyzeIn the measurement phase, the main process inputs and the possible causes and effects were identified. Now statistical cross-analyses and other analyses are carried out to confirm which cause-and-effect relationships really exist.The analysis usually goes through the following steps:root cause analysis;process analysis;data analysis;resource analysis;communication analysis;conclusion, with the confirmed causes that will be tackled in the next phase.Phase 4 – ImproveIn this DMAIC phase, the improvements that address the causes of the problems are implemented. To do this, it is important to work closely with the people who develop the product and run the processes.The most important document the team prepares in the improvement phase is the action plan. It must contain, at a minimum:a) the action to be taken (based on the sources of variation identified in the analysis phase);b) the person responsible for each action;c) the planned implementation date;d) the document's issue date and revision date;e) if possible, an indicator to track the action.A good recommendation is to use the tool known as 5W2H.Phase 5 – ControlIn the final phase of DMAIC, the improvements are evaluated: the team checks whether they are producing the expected effect and whether the results are sustained over time. To do so, the project team should:document and standardize the changes (procedures, work instructions, training);monitor the process continuously, for example with control charts;define what to do if the indicator gets worse again (reaction plan) and hand the process over to its owner.In which DMAIC phase does the team prepare the action plan, with action, owner and deadline, often using 5W2H?Answer: Improve — this is where solutions to the causes confirmed in the Analyze phase are implemented. Control is the most tempting option, but that phase is for standardizing and monitoring what has already been improved.Six Sigma case studiesApplying Six Sigma at MotorolaApplying Six Sigma in a gymApplying Six Sigma in a hospital to improve patient meals
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