All the processes in nature are unfortunately far from "perfect"; variations around the desired output value of a process or a product are always present and they can have different causes, such as manufacturing tolerances, material properties variations, human errors or uncertainties of many kind.

Real-world variables always fall within a range, that can be usually controlled under certain limits, determining the final product quality.

For example, when cutting a metal sheet to obtain a given piece, many factors can compromise the quality of the final product; the sheet thickness and the material properties can vary according to the supplier, the operator, even the maximum care is used, always places the sheet in a different way on the working machine, which operates within a tolerance, and so on.

As a result, the obtained piece could not satisfy some technical requirements (it is too thick, too thin, unacceptable permanent deformations are present...), the customer could be not satisfied (the piece is not sufficiently reliable, too many cracks...), but also some "look-and-feel" expectations (it seems to be too heavy, it does not look sufficiently safe...) could be disappointed, and more, leading to a low quality level, with a consequent increase of costs.

The aim of the Six Sigma methodology, originally developed by Motorola in the mid of the 80s, is to eliminate defects and waste, measuring and reducing variations.

The statistical control tools, the data analyses and a continuous and systematic training inside the company are compulsory for a complete success of Six Sigma. However, Six Sigma has not to be confused with a mere application of complicated statistical tools, as one could think at the beginning, but it has to be considered as a well-structured data-driven methodology, which needs a large participation through all the company.

As often reported by the practitioners, some of the most important ingredients for the success and a good implementation of the Six Sigma are the persuasion, the co-operation and the contribution of all the personnel involved in a project. Shortly, it can be said that the "human factor" has a fundamental role.

This is usually obtained with a strict definition of the people roles inside the organization when performing a Six Sigma project. Four different figures are usually established;

• the "Sponsor", (also called "Champion") is the project owner and leader: he/she has to support the team, to make all the resources available and to organise different projects inside the company,
• the "Master Black Belt", he/she usually is an experienced employed with a deep knowledge of the company, profitably uses the statistical and quality control tools, he/she is also often involved in the personnel training,
• the "Black Belt", who probably has the most critical role, has to manage and organise the team activity from an operating point of view: he/she has strong problem solving capabilities, collects and organises all the relevant data,
• the "Green Belt", applies the Six Sigma in the everyday activity according to the directives given by the Black Belt.

The need of a large participation and also a "breakthrough" with the past needed by the Six Sigma, are the reasons why, sometimes, the Six Sigma is addresses to as a "philosophy" rather than simply to as a "methodology".

In these last years the Six Sigma has gained a wide popularity because it has shown to be very effective in the reduction of defects. Many companies have applied this methodology in different fields, with considerable results in money and time saving.

The most known and interesting experiences, which have been taken as a reference for the extraordinary results, are those developed in Motorola, Bank of America, General Electric, Toyota and many other companies operating all over the world.

The name Six Sigma has been used for the first time by Bill Smith and it indicates the level of quality that should be achieved by a process or a product. Sigma is the Greek letter used in statistics to describe the standard deviation or, in other words, the variability of a phenomenon around a mean value. The sigma quality level (6 in the case of Six Sigma methodology) indicates how often defects are likely to occur; this quality level is also expressed as "Defects Per Million of Opportunities" (DPMO) defining in this way the probability that the process output does not satisfy the required limits.

If the Gaussian distribution describes the probability density function of an output process variable, the mean value should coincide with the desired value, to which the process has to tend to. The standard deviation controls the probability of a given output to be inside or outside a fixed range and therefore its level of acceptability (see Figure 1). Therefore, a given level of quality can be obtained working on the variability of the process, driving the output variable towards a fixed number of standard deviations between the mean and the nearest specification limit (the upper or the lower specification limits, ULS and LSL respectively, see Figure 2).

Figure 1: The Gaussian distribution and the confidence interval. The probability to fall inside the confidence interval is expressed in percentage and DPMO terms, taking into account the normal distribution and a shift ("drill") of 1.5 of the standard deviation.

The aim of the Six Sigma is to reduce the process variation in order to have 3.4 defects as a maximum for 1 million of generated outputs.

This quality level is actually reached with a standard deviation of 4.5 sigma, but the Six Sigma approach allows a 1.5 sigma shift around the mean (originally called in Motorola as "long-term dynamic mean variation", but also referred to as "drift"), leading to the well known "six sigma level".

Figure 2: Graphical definition of the Lower Specification Limit (LSL), the Upper Specification Limit (USL) and consequently the acceptability interval. The process characterised by the green Gaussian probability density curve meets the Six Sigma standard (a generated output has a DPMO less than 3.4) while the red process is not able to satisfy the Six Sigma level since the points whose distance from the mean value is six standard deviations fall outside the acceptability interval.

It is important to note that this "±1.5 sigma shift" of the process mean is absolutely arbitrary; it was introduced by Mikel Harry at the beginning of the Six Sigma, basing his assumption onto some empirical observations. The need of this shift has been mainly justified over the years with two reasons. Firstly, that the accuracy of an assembly depends on the quality of the components, as suggests the variance propagation law; in this way, if the output of the Six Sigma projects are the components, also the assembly could consequently satisfy a Six Sigma quality level. Secondly, that there are always unpredictable events and phenomena that influence the process under study, which move the process mean independently to the effort of the process owner to stabilise it.

Some quality consultants moved criticisms to this "sigma shift"; also Mikel Harry tried to explain that the choice of 1.5 was absolutely arbitrary and based on some data he had at that time, but the industry had already taken this value as a reference in the everyday practice of the Six Sigma.

Another important observation is that the choice of a Six Sigma quality level could be not appropriate in some cases (for example when safety of human beings is involved), but it could be not necessary in some other cases (for example when an information campaign is to be organised).

DMAIC

In the case of the metal piece described above, the Six Sigma methodology should firstly drive to the classification of the defects, identifying some measurable quantities that determine the quality level (the right question to answer to, could be "what does defect exactly mean?"). Secondly the process has to be measured, studied and understood in detail. Then, the main causes of the defects (the too high variability of the metal sheet thickness, the way used to cut the sheet,...) should be identified and finally fixed.

Obviously, the increased quality level should be maintained in the future, better if increased, reaching the customer expectations. The project owner has to periodically check the obtained results and eventually organise a new activity to establish the desired quality level.

The traditional Six Sigma includes five steps: Define, Measure, Analyse, Improve and Control (shortly and commonly known as DMAIC).

1. Define: the main objective of this first phase is to define the project goals, the customer needs, the quality levels to be achieved, the most important variables and the quantities to be monitored. For the example described above, in this phase the metal sheet thickness, the material strength and the piece weight maximum variability should be identified as process variables and desired output respectively.
2. Measure: in this phase all the available data concerning the product or process under study have to be collected and categorized to obtain a reliable view of the actual situation. The metal sheet thickness and the metal strength have to be measured and related to the supplier, the period, the stock and so on. The final products have to weighted and the data have to be collected in a profitable way.
3. Analyse: the intent of this phase is to provide a deep insight of the process allowing the identification of the problems and the causes that generates them. Analysing the data it seems that a supplier provides sheets of worst quality, that a working machine tolerances are going to deteriorate and so on.
4. Improve: during this step solutions are developed and changes are done to improve the quality level. The maintenance frequency for a given machine has to be changed, some process operations have to be re-organized or some personnel has to opportunely trained.
5. Control: the goal of this last step is to monitor and control the results produced by the previous steps. Obviously, the expected result is an improvement of the quality level. If so, it has to be improved and maintained in the future, otherwise a new improve phase has to be performed. In the worst case a new project, starting from the analyse phase has to be planned.

During all this phases graphical, statistical and data control tools can be effectively used. The most known are the:

• time table, where the timing of all the project phases is defined,
• work flow diagrams, by means of which the process can be described and controlled. They are very useful especially in the first phase when defining the process,
• worksheets and data bases, where all the data are collected and organized making them available in a profitable way,
• cause-and-effect diagrams (the fishbone or Ishikawa diagram) which allow to identify the causes of a given phenomenon, FMEA (Failure Mode and Effects Analysis) to identify failure modes and their possible causes, etc.,
• Pareto diagrams, which allow to identify the main causes, according to the 80/20 empirical law,
• control charts of different nature (histograms, apple-pie diagram, graphs, etc.) which are used to visualize and interpret distributions,
• time history charts, which are essentially used to monitor the evolution of a variable,
• statistical tools able to highlight relations between variables (the regression analysis for example), T-Student analysis, etc.,
• design of experiment techniques (DOE), used to eventually plan an optimal campaign of experiments (obtain the maximum information from a system with the minimum number of experiments).

Obviously, all these instruments have to be used in a profitable way to obtain the maximum result. To this aim, one appreciable aspect for the practitioner is to have all them under a unique environment where the data can be shared and easily treated once loaded.

The presence of a "wizard" is also an interesting feature; it can suggest the best way to operate and it can allow to discover not evident (for a human being) relations between data. Another remarkable aspect is the possibility to monitor "real-time" the evolution of the process parameters during the last phase of a project, allowing a continuous control of the process.

DFSS

Another emerging discipline pertaining to the Six Sigma is the so-called "Design For Six Sigma" (DFSS). It is a methodology used to design new products or processes as early in the life cycle as possible, in order to satisfy the Six Sigma quality level. The main advantages of the application of the DFSS approach in the design chain, are mainly the relatively small cost to perform a design change and the possibility to meet all the customer needs in advance, with evident consequences on the market.

A correct application of the DFSS should seek to avoid possible process or product problems leading to a very high quality level, reducing to the minimum the subsequent DMAIC related activities. The DFSS is simply based on the idea that a good design leads to a good product or process with a low defect rate, reducing the need to correct errors when it is difficult, costly or at least impossible (see Figure 3).

Figure 3: The relative cost for a product/process change versus the cycle life. The DFSS tries to focus the attention as earlier as possible, in order to minimise the cost of possible design variations. The traditional Six Sigma operates later, when the product or process has been already designed.

The DFSS can be split into two different approaches according to their focuses. Specifically, the "Define, Measure, Analyse, Design and Verify" (DMADV) and the "Identify, Design, Optimise and Validate" (IDOV) approaches, which are quite well established. The former is used when designing a new product, the latter when designing a new process.

Even the letter used in the acronyms reported above stand for the same words as previously argued for the DMAIC, the DFSS approach has important differences with the traditional Six Sigma. Also the instruments which are typically used are different, as it can be easily understood.

IDOV

The "Identify, Design, Optimise and Validate" (IDOV) approach is adopted when a new product has to be designed. The prescribed four phases an be descried as follows:

• Identify the customer and its expectations. With more technical words it could be said that the Voice Of Customer (VOC) have to be identified. They can be very heterogeneous, coming from technical considerations, commercial aspects, usability (maximum weight, dimensions, costs, look, etc.) and also in contrast one to another (consumption, maintenance and cost, etc.).
• Design transforms the customer needs in design variable, which have to be measurable, through a reduction process, which leads from the VOCs to the VOPs ("Voice Of Process") passing through the definition of the "Key Functions".
• Optimise uses advanced simulation tools and techniques to find out the best solution. It is important to note that the robustness of the design has to be considered, being the key aspect for the success of the product. Robustness is an appreciable aspect of a solution, representing the insensitivity of a particular design to small variations of the design variables.
• Verify, or Validate, that the adopted design is able to satisfy the customer needs.

During the first phase the "Voice Of Customer" has to be identified, organised and understood. All the customer needs and requests have to be transformed into "Critical To Quality" (CTQ) or, in other words, the most critical aspects which determine the quality level have to be identified.

Obviously, this operation is fundamental for the success of the subsequent phases, since it determines the goals that have to be reached. For this reason it should be entrusted to a group of persons, avoiding in this way personal interpretations of the VOCs. There are many ways to collect information: usually customer interviews, market-researches and old databases are the most used to identify the customer needs.

The project timing has also to be planned together with the strategies that will be used further on.

The design phase is concerned with the translation of the CTQs into Key Functions (KFs), then into Design Elements (DEs) and finally with the identification of the Process Variables (PVs); the detail level is progressively increased, starting from high level design concepts down to a more precise definition of measurable engineering quantities. The most important tool used in this phase is the so-called "house of quality", coupled with the function analysis: they both help the practitioner to decouple, decompose and simplify very complex phenomena into simpler and easier-to-tackle sub-problems, increasing the problem knowledge.

During the optimise phase a detailed design has to be performed taking into account some important issues, such as the robustness and the reliability. Very often a multi-objective and multi-disciplinary optimisation has to be considered, making the success of this part of the project a very challenging task.

Of course, the chosen design has to be optimal, in the sense that it has to satisfy all the constraints and lead to the best performance, but it has also to be robust; this means that the performance has not to vary significantly when a given variation of the design parameters occurs. This aspect is not marginal at all, if a Six Sigma quality level has to be finally reached.

Moreover, the reliability of the design has to be checked, estimating in advance the bathtub curve for example; the design has to statistically guarantee a fixed level of robustness and performance for a given life cycle, avoiding premature problems.

The execution of this phase is usually done by the technical personnel, with a deep knowledge of optimisation and design.

The last phase has to verify that all the previous phases have given the desired output, leading to a good product design. It has to be validated that the design meets the customer needs and consequently the production ramp-up has to be launched.

To efficiently perform an IDOV problem it is necessary to use different kinds of instruments; As mentioned above the design time and the possibility to commit errors can be dramatically reduced if all these tools are integrated under just one, or at least few, environment.

The peculiarity of an IDOV process is the need to use tools of completely different kinds and complexities, as it can be easily understood from the following list:

• timetable, to manage the DFSS project,
• graphical tools, to collect the customer needs, to translate the VOCs into VOPs, etc.
• workflows and trees, to describe the process and organise ideas, etc.
• an optimisation software, able to seek for a optimal and robust solution,
• simulation software, able to reproduce the product behaviour, modelling very often the different physics involved,
• control charts, used to validate and control the goodness of the design

An IDOV project usually involves many people, with different backgrounds, who have to interact and share knowledge. Also in this case, as for the DMAIC, the human factor has a relevant role for the success and it has to be never disregarded nor neglected.

References

1. K. Yang, B. S. El-Haik, Design For Six Sigma, Mc-Graw Hill, 2003
2. Breyfogle, Implementing Six Sigma: Smarter Solutions Using Statistical Methods, Second Edition