Abstract   
As any system, TRIZ behaves according to the trends of the General Systems’ Theory. According to one of the trends, technological systems evolve in a general direction from mono-systems to bi- or poly-systems. Then the bi- and poly-systems convolute into mono-systems. TRIZ is not an exception to this trend. To date, TRIZ and a modified Value Engineering (VE) function analysis comprise a mono-system of contemporary TRIZ.
At a close review, TRIZ provides qualitative assessment and analysis of the system under consideration. Yet, in a technical system analysis a numerical representation of system’s features, functionalities and problems is very important as it provides a universal assessment of system’s parameters and provides foundation for comparative analysis of the system and its environment. Further, for TRIZ to become a true science it needs to be defined with mathematic precision using math formulas and logic. Therefore, it is imperative that TRIZ is equipped with necessary tools for quantitative assessment of system’s parameters.
In the last 8-10 years a number of attempts were made in combining TRIZ with some other methodologies. Most popular are attempts to combine TRIZ with Six Sigma. However, these attempts were made by Six Sigma experts, who are not very experienced with TRIZ and its tools. As a result, the most used TRIZ tool is the Contradiction Matrix and TRIZ is placed in a subordinate position to Six Sigma. Most notable is TRIZ application with DFSS – Design for Six Sigma, where some TRIZ tools are utilized for solution of design issues. 

TRIZ and Lean Sigma
A person, who is asked to describe the current state of the innovation tools, is immediately put into a difficult position. There is a great variety of techniques aimed at aiding an innovator with the development/improvement of products, processes and services.
Even a brief analysis of these methods shows that, despite the significant difference in the titles and stated purposes, they often duplicate each other, differing in minute details. Most of those are potent for situation analysis and problem formulation, while others – for design and implementation based on a selected concept. The middle of the innovation process, idea generation and concept synthesis, is not well covered. TRIZ and Lean Sigma stand apart from this filed. These two are recognized by many companies as two of the best innovation technologies.

In addition, the purveyors of each of these techniques often declare their comprehensive nature and extreme efficiency, while claims of self-sufficiency are followed by a demand that the technique must be “administered” by the purveyor.

The goal of any organization is to streamline its processes, thereby maximizing available resources to their fullest. One of the most visible results of this activity is the timely delivery of the high quality Value Proposition, the ultimate outcome of every business undertaking. Thus, we are looking at two very likely candidates for “Hybridization”: TRIZ offers qualitative analysis, Lean Sigma provides rigorous mathematical process for data collection and analysis. Both are used as innovation methodologies.

Melding TRIZ and Lean Sigma
Lean Sigma is a bi-system, organized along the lines of process improvement. TRIZ, on other hand, is focused on product improvement/development. 

Lean Sigma is about data collection and analysis, utilizing precise quantitative procedures. TRIZ is about qualitative assessment of the system/situation, utilizing a plethora of analytical tools, aimed at weakening mental inertia of an innovator. Lean Sigma is firmly embedded in corporate structure of many medium and large size companies. TRIZ is talked about a lot, but not as widely accepted. Lean Sigma consists of Lean Manufacturing + Six Sigma. Lean is based on Toyota Production System, Six Sigma started as a Quality Improvement methodology at Motorola. TRIZ was started in the late 1940s and in the 1970s it absorbed a large segment of Value Engineering. Thus, the contemporary TRIZ is a mono system, which grew out of bi-system consisting of TRIZ and Value Engineering.
• The main idea behind Lean Sigma is that quality of an offering should be improved based on evolutionary transformation, avoiding abrupt changes in product or service.
• The main idea behind TRIZ is that evolutionary transformations are effective up to appoint, then revolutionary transformations are in order through resolution of defined contradictions.

With all the differences, these methodologies have at least one thing in common – both are utilized in innovation process.
Lean Sigma, in use for many years, occupies a certain methodological niche. A lot of people in many companies are employed in the field of Lean Sigma application and training/certification. In other words, Lean Sigma is a flagship in the field of innovation.
However, the practice of applying TRIZ showed the following. If you overcome the initial reluctance of managers and specialists and engage in real work, the phenomenal performance of TRIZ quickly converts most of naysayers into believers. As a result, the management is puzzled by a situation where a small TRIZ team outperforms Lean Sigma establishment. Naturally, all sorts of ideas for reorganization of innovation process spring to life.
On the surface, the easiest way to accomplish such reorganization is by merging TRIZ tools into Lean Sigma process, notably into DFSS, which is often the case. The main idea of such a merger is to strengthen DFSS in its creative part, in the idea generation module. To date, this approach produces much better results than TRIZ-less DFSS in any rendition. TRIZ-DFSS union proved to be very effective for improving the quality of products.
However, the effectiveness of such union could be improved dramatically by negating the main obstacle of an effective merger between TRIZ and Lean Sigma – the difference in approaches.
Lean Sigma is obviously biased towards the evolutionary development of the product/process. Here, any idea that involves a radical change in any subsystem of a product or process is hardly accepted. A solution to a “mini-problem” (in the terminology of TRIZ), which provides minor changes in a system under consideration, optimizing its parameters and resolving minor conflicts that arise during the development of its subsystems. Application of TRIZ techniques can provide both an evolutionary change in the system,  optimization, and substantial transition to a new, improved system (i.e. – the solution of a “maxi-problem”). On a company level the second possibility is often overlooked, and Six Sigma experts persistently, but ineffectively struggle for the improvement of product quality, although higher level quality may be easily achieved by a qualitative change in the key subsystems of a system they are trying to improve. 
However, an attempt to mend these two is like an attempt to harness together a Shire horse and a race horse. One can pull a heavy cart, while another – to run much faster. How to reconcile these two?
Look at the situation from a TRIZ perspective the following contradiction emerges:
 

• DFSS, even reinforced with TRIZ, seeks to improve the existing situation without significant changes in the system or process;
• On the other hand, TRIZ enables evolutionary improvements of the system, as well as a transformation of the original system into a more sophisticated one.

To resolve this contradiction, let's look at the development of a real system.

Fig.1. The three dimensional dependency of an operational parameter on two selected parameters of a sub-system

Say, the operational parameter of the system, we are attempting to improve, depends on two chosen parameters of its subsystems, as shown in Figure 1 (in reality, the number of these parameters is much higher, but we consider the simplest case). Initially, the system is at some point, below the point of extreme maximum performance. Every improvement in a sub-system’s parameters is aimed at an increase in the value of the system's operating parameter.
And this is the main goal of Lean Sigma methodology. The optimization process is very complex, it requires large investments of time and effort. These investments grow exponentially when a system approaches optimal point. However, the current practice forces optimization efforts regardless of cost/benefit reality. This is true regardless of which optimization methodology is used. Still, the most effective here are TRIZ enhanced DFSS and other methodologies, based on TRIZ evolutionary tools.  

But ... what do we do if the system is at an intermediate optimum? Figure 2 shows that any change in the parameters of the subsystems now leads to deterioration of performance parameters. The evolutionary resources are completely exhausted. The law of diminishing returns dictates evolutionary stagnation. This condition is especially hard to overcome when there is an undetected, thus unresolved, contradiction, which prohibits continued improvement. This situation is not inherent in technical systems alone, it affects non-technical, i.e. business, systems as well.

Fig.2. If the system is at the intermediate optimum, its evolutionary recourses are completely exhausted

Under these conditions, the only way to improve is a qualitative transition (Fig. 3). That is, it is necessary to formulate one or more of the key contradictions, which prohibit the system’s ability to evolve. Then, exacerbate them to an extreme and resolve those contradictions to define a new version of the system, capable of continued improvement, based on newly found   resources for development. That’s where TRIZ is indispensable as its main strength is in formulating and resolving various contradictions. 

Fig.3. The transition to a new system that has additional resources for development

Obviously, the solution of the problem with breakthrough methods of TRIZ can not immediately produce a system with optimum operational parameters. Now, this task could be performed by using optimization techniques, primarily methods, which comprise DFSS (Fig. 4).

Fig.4. Selected system, obtained after the resolution of conflicts, needs further optimization

In fact, most of products and services evolve through alternation of optimization and “leap-frogging” activities (Figure 5).

Fig.5. A potential sequence of system’ development

Turns out that the contradiction between these requirements, optimization and “leap-frogging”,  is resolved by separation in time. 
1. During the optimization phase, system’ parameters are improving steadily through relentless efforts. Minor changes to the system are accompanied by optimization of its sub-systems. At this stage of development DFSS and evolutionary TRIZ tools work real good. Due to depletion of substance, information and field resources the development of the system slows down and eventually stops ...
2. This is the most opportune moment for the a breakthrough to a new and improved version of the system. As a rule, by this time the company's management is looking for a new ways of system’s development and is ready to accept the idea of a qualitative transformation of the system. Therefore, now is the time to use the “heavy artillery” of TRIZ tools, based on the concept of  contradiction.

We examined two approaches to innovation: Optimization and Disruption. How to select the one appropriate in a giving situation?
For a best answer to above question we need to remember that any problem solving process must start with some kind of analysis of the situation. The analysis should identify, among other things, the position of the system on the S-curve and the available resources. Here, one should utilize qualitative as well as quantitative analysis tools. Analysis of variations, a Lean Sigma tool, should be used along with TRIZ tools for identification of various resources.  
If the resources are available, the optimization may be in order. If the resources are exhausted, a disruptive approach is preferable. After all, the contradictions are most often result from lack of available resources. 
 
In conclusion:
1. Innovative methodologies, based on TRIZ and Lean Sigma, are not mutually exclusive, but may complement each other.
2. TRIZ enhanced Lean Sigma methodologies work effectively when we have the resources for system or process optimization.
3. TRIZ based tools for solving contradictions are effective when there are no available resources for system or process optimization.
4. The proper use of optimization and disruption techniques may increase the efficiency of both, Lean Sigma and TRIZ.

 References:
1. Altshuller G.S. To find an idea. M. Alpina Business Books. 2007.
2. Geoff Tennant. TRIZ for Six Sigma. ISBN 0 9546149 0 9
3. John Bicheno. Fishbone Flow: Integrating Lean, Six Sigma, TPM and TRIZ (Spiral-bound). ISBN-10: 095412443X
4. Altshuller G.S, Zlotin B.L, at al. The search for new ideas: from insight to technology. – Chisinau: Map Moldovenyaske, 1989.
5. Yu. Salamatov, I. Kondrakov. Idealization of technical systems. – Krasnoyarsk:, 1984.
6. Shpakovsky N.A. Trees of evolution. Analysis of technical information and generation of new ideas. M. Puls. 2006.