A.G.Kashkarov. Matrix method for identification of contradictions and secondary problems.


Matrix method for identification of contradictions and secondary problems
This paper presents results of studies conducted by the author with the aim to identify contradictions and secondary problems in the course of analysis and improvement of an engineering system (ES). The author proposes to identify contradictions and secondary problems based on a Table via correlating the hypothetic results of problem solving and their influence on main characteristics of ES. 
Key words: secondary problems, interrelated contradictions, matrix method,  cause-effect structure, substance-energy conversions.
Engineering systems are improved in the most efficient way through resolution of contradictions [1], but it is not always easy to identify physical contradictions retarding ES evolution. Usually contradiction formulation includes one variable parameter and two other parameters representing consequences of its variation (one parameter is improved, while another is worsened). However, in the majority of cases, an identified contradiction represents only a part of a problem. Resolution of contradiction often exerts influence on other parameters of the system (namely, worsens them), thus creating new contradictions [2]. Initially such parameters may seem to be independent. The proposed "Matrix method for identification of secondary problems" enables to identify such dependences, rank the problems, reconceive problems and find the best solutions.    
According to TRIZ methodology, elimination of key disadvantage inherent to ES, which was identified in the process of cause-effect analysis represents an efficient solution for a problem [3,4,5]. Key disadvantage could be represented by a root disadvantage or intermediate disadvantage in a cause-effect chain of disadvantages. However, sometimes solution of key problems couldn't be implemented unless the majority of secondary problems are solved. This could be explained, for instance, by the necessity of production technology modification requiring additional expenditures and solving arising problems or by disproportional increase in ES cost resulting from upgrading ES functionality or by worsening of secondary characteristics of ES in question or by unsolved latent problems that discredit the invention.
Inventors are of course not too happy when a beautiful and promising solution cannot be implemented in actual production process. One of the reasons for that consists in unilateral view on the problem. It is very seldom that a simple solution to a problem (aimed at improvement of one ES characteristic) does not exert negative influence on other characteristics of this ES. That's why one must consider ES problems as a complex set, solving not only one specific problem, but accompanying problems (arising both at different stages of ES life cycle and in the process of ES improvement). as well. Usually accompanying problems form several dependent contradictions. These dependent contradictions represent secondary problems, solving of which would allow increasing the probability of invention implementation.         
Each ES problem may have several different problems. Selection of the best solution (i.e. most efficient and inexpensive) represents an integral part of ES improvement. To identify a set of problems to be solved and outline the shortest ways for the accomplishment of required tasks, the author proposes to use a matrix method for secondary problem identification. The proposed method is based on Table-based comparison of hypothetic results of solving of key problems and their consequences (influence on ES characteristics at different stages of life cycle), which is accompanied by identification of dependent contradictions. This method was often used by the author when solving specific inventive problems. A description of matrix method intended for identification of contradictions and secondary problems is given below.
Refining the goals of ES improvement
The first stage of improving any ES consists in identification of goal for improvement. An image of ES or technology for ES manufacture free from identified target disadvantage represents a goal for ES improvement. A target disadvantage could be represented in the form of any inadequate characteristic (parameter) of ES or absence of any functional possibility of ES. Since elimination of ES disadvantage must not make other ES characteristics (parameters) worse or fall outside the improvement limits, it is necessary to identify important characteristics inherent to the ES in question. These characteristics represent factors of criteria of ES ideality [1] and can be selected, for instance, from the lists of characteristics (with specific parameters) given below.
Functional characteristics of ES:
·         Efficiency;
·         Dynamicity, productive capacity;
·         Accuracy, stability;
·         Controllability, adaptability;
·         Coordination in space;
·         Coordination in time;
·         Stability, durability;
·         Reliability, service life;
·         Convenience of use, ease of servicing/maintenance;
·         Aesthetic qualities;
·         Other.
Negative manifestations of ES:
·         Harmful processes in the system;
·         Harmful influence exerted by the supersystem;
·         Harmful influence exerted upon the supersystem;
·         Breakdowns, failures, malfunction, defective articles of manufacture;
·         Ageing, degradation;
·         Hazard for humans;
·         Harm to the environment;
·         Other.
·         Expenditures and losses of materials;
·         Expenditures and losses of energy;
·         Excessiveness of equipment;
·         Expenditures of labor and time;
·         Excessiveness of occupied space;
·         Wastes;
·         Disposal of defective articles of manufacture;
·         Costs for elimination of defects;
·         Transportation costs;
·         Other.
Estimate of the influence of hypothetic elimination of each target disadvantage (when evaluating the solutions in competing systems) on identified important characteristics of ES (what gets improved and what gets worse) enables to formulate engineering (technological) contradictions at the upper hierarchic level of ES. Subsequently, each engineering solution aimed to improve ES should be correlated with these factors - for instance, in the form of a Table of conflicts. :    
Table of conflicts

Actions on elimination
- of target disadvantage
- root disadvantage
-key problem
Important characteristics of ES
Functional parameters
Negative manifestations
Productive capacity
Toxic wastes

Identification of key and secondary problems
To find "strong" engineering solutions meeting the ES improvement goal, one should identify and resolve physical contradictions. To localize physical contradiction, one should analyze a system in question (or analyze the operative zone of ES). Function analysis [6] and flow analysis [7] or analysis of substance-and-energy conversions [5,8] allow to identify disadvantages inherent to ES in the form of inadequate parameters, while subsequent cause-effect analysis [3,4,5] enables to identify cause-effect relationships (chains) of these disadvantages with target disadvantages.
If it has been identified that one and the same parameter in one chain of disadvantages has insufficient significance, while in another chain - excessive significance, a physical contradiction could be formulated. However, it is not always that easy to identify physical contradiction.  
To identify physical contradiction, the author proposes:
- to identify root disadvantages (i.e. disadvantages that could be eliminated and that are located in the beginning of cause-effect chains of disadvantages)
- to compile a Table of conflicts. Actions aimed to eliminate root disadvantage represent headings of the Table in vertical direction, while ES characteristics (parameters) represent headings of the Table in horizontal direction (see previous section).    
- to make (in one mind) a parameter of each root disadvantage adequate and, while analyzing the ES operation, to estimate the influence of this change on important characteristics of ES. Results of this procedure should be put into the Table of conflicts - in particular, indicate worsening or improving of specific ES parameter at different stages of the life cycle in appropriate fields of the Table after improving the parameter of each root disadvantage.  
Analysis of results of the above-described steps will enable the researcher to identify a number of dependent engineering contradictions and secondary target disadvantages. Constructing cause-effect chains of these disadvantages further, one could quite easily identify new root disadvantages and specific parameters of ES with contradictory requirements that form physical contradictions (sometimes, multi-parametric). These physical contradictions and new root disadvantages (that does not form a contradiction) will represent a system of key and secondary problems that should be solved together.  
It needs to be pointed out that if a model of substance-and-energy conversions in ES is built for the analysis [5,8,9], the search for key and secondary problems is made much simpler because this model includes principles of action and cause-effect relationships of processes taking place in ES.  
According to author's opinion, the above-described methodological approach could be used as an individual tool for problems statement and a logical input fro ARIZ. Each goal of ES improvement could be achieved through different ways, solving different key problems. To chose the optimal way for achieving a specific goal, one can use the proposed Table and compare the lists of secondary problems for different key problems, after which he can assess expenses for implementation of one or another complex solution. Therefore, the proposed approach could be useful fro practical application not only at the stage of search for and refinement of problems, but also for comparing engineering solutions.     
List of References
1. G.S.Altshuller. ARIZ – Means Victory. ARIZ-85V. – In the book: Rules of Game without Rules. – Petrozavodsk: Karelia, 1989.
2. A.G.Kashkarov. "Trends of Engineering System Evolution - consequences of Laws of Dialectics" poster presentation and abstracts of paper in Collection of papers for the conference "Innovation Technologies of Designing at Present and Tomorrow", Saint Petersburg, 1999,  http://www.matriz.ru/4spec/4-2/kashkarov-ag/kag-works-1.html
3. S.S.Litvin, B.M.Akselrod. Method for Constructing Cause-Effect Chains of Undesirable Effects/Manuscript. – Saint Petersburg: IMICenter, 1996, 4 pages.
4. A.M.Pinyaev. Method for Analysis and Solving Inventive Problems with the Use of Cause-Effect Analysis and Functional Prompts. Author's abstract of the thesis for TRIZ Master Degree, July 2007. www.matriz.ru/4spec/4-1-4/pinyaev-autoref.doc
5. A.G.Kashkarov. Substance-and-Energy Conversions in ES. Method for Constructing and Analyzing Models./ Thesis for TRIZ Master Degree, July 2009.http://www.triz-summit.ru/redirect.php?id=204357
6. S.S.Litvin, V.M.Gerasimov. Conceptual Issues of Method for Conducting VEA / methodological recommendations, parts 4 and 5. – TRIZ Journal. - Obninsk: Protva-Prin, 1992, 3. 2 (No. 6).
8. A.G.Kashkarov. Relevant Models of ES. Algorithm of Construction and Analysis./Paper. Collection of papers for TRIZ-Fest 2009, Saint Petersburg, July 2009.
9. A.G.Kashkarov. Analysis of Principle of Action - tool for problems statement and ES improving./ Paper. Collection of papers for TRIZ-Summit 2011 "Principle of Action for System", Saint Petersburg, July 20 2011.