Design and Estimation of Education Quality in Engineering Education

TSOI, Evgene ¹, GRIF, Mikhail ² & DUBROVSKIKH, Alexey³

¹ Russia, Novosibirsk state technical university, ebcoi@nstu.nsk.su
² Russia, Novosibirsk state technical university, isr@first.nstu.ru
³ Russia, Novosibirsk state technical university, dalex@triton.net.ru.

Abstract: This report is dedicated to developing the optimal designing method of education process (EP) in engineer education. Two methods are offered for the EP quality estimation: a) without an evident description of the discrete exchange process of the EP state under the influence of lesson and educational effect; b) quality estimation based on the detailed expansion of EP in time, with indication of possible situations, checkpoints, and algorithms, etc. The first method depends on the theory of fuzzy multitude and linguistic variables. The second method uses the tool kit of object-oriented functional nets (OOFN). Optimization tasks of the EP are formulated with a vector task. Where indexes of the EP are taken as the local criteria. To consider these tasks, the method of successive optimization of the EP in OOFN is developed. It is based on the directed variant exchange method with the help of metaproducion system and logical conclusion mechanism.

Keywords: designing, optimization, index, criterion, estimation

1 Introduction

The main feature of modern manufacture is the requirement of specialist-engineers with ability to choice only required one from the large volume of information. And, the roles of the special knowledge and the individual training course are increased. The quality of engineer education is the integration (synthesis) of these qualities: educational program; regular and scientific potentials used in the EP; students; facilities of the EP; educational technologies; management of education. Consequently, the development of the mathematical tool for the EP optimal design method is strongly required.

Two methods to estimate the EP quality are offered: a) without an evident description of the discrete exchange process of the EP state under the influence of lessons and educational effect; b) quality estimation based on the detailed expansion of EP in time, with indication of possibly situations, checkpoints, and algorithms. The first method is easier, because, it is not required big volume of source data. But, the second method is potentially more precise than the first. The combined method is possible too.

The essence of the first method is:

• the EP quality is assigned by the linguistic variable with the meaning such as: "very high", "high", "middle", "below middle", "low", "very low", etc;
• factors influenced on the EP quality, are also assigned by the linguistic variables;
• the tree of the factors interference (production system using logical and arithmetic relations) with the root in EP quality is built;
• alternative EP execution variants are assigned;
• optimality criteria and restrictions on the EP are introduced;
• the most expected EP quality meaning as the linguistic variable to each alternative is found by the fuzzy conclusion algorithm;
• optimal execution variant of the EP is determined.

The EP may be defined as in the state space, as in the resolved task space. The EP examination is carried out as in the standpoint of a separate student, as in the average group. The separated EP state is defined by set of the significant characteristics, for example, examination marks, testing results, and teacher qualification, etc. The characteristics may be estimated as in the quality scales, as in the quantity scales. The relationship degree of the characteristics set to the state is estimated by using of the relation function or by the probability theory. An exchange process of the EP state may be described by the probability, and by the fuzzy production models, where exchange from one state to another is determined by a production with own relation function of the exchange.

The most important EP indexes are:

• the attainable probability (relation function) of the target EP state: B,
• the middle time of attainment: T,
• the middle cost of attainment: V,
• the probability of attainment:P (t<T).

The second method is based on the instrument of the OOFN and it uses an equivalent transformation of the typical algorithmic structure for EP quality estimation. The multitude of alternative EP execution variant is determined by the possible relations of the elemental and functional system structures, and the meanings of element characteristics. The basis of the OOFN is object-oriented description method. Its elements are composed of the classes, the objects, the relations, the productions, the predicates and the constructions. These constructions consist of object, attribute, value, sure extent, etc. This method describes elements, functions, states, relations, indexes, optimality criteria, optimization task restrictions, etc. When we choose mathematical instrument for the optimal EP designing, following two features must be taken into account:

1. EP is presented as a discrete purposeful (accidental) process;
2. Some operations of EP in most case can not be independent. The EP is therefore a process with the aftereffect.

Let's choose individual EP fragments, which consist of operations independent from each other. In this case, the instrument of mathematical description and quantity estimation of discrete purposeful processes without aftereffect is matched. It is frequently used for the description of ergatic systems (ES). Formulation and estimation of the human function are more complex than those in the ES. It is reduced to the aftereffect. But OOFN instrument is enough to describe the discrete purposeful processes for the system functioning and decision making. It can be the basis to the description and the estimation of the EP quality, the specific model of EP index calculation is designed to subject the EP aftereffect.

2 Task stage

The optimal ETS designing is based on selection of the best variant of the system execution. ETS with respect to processing objects may be presented as follows in matrix form [1]:

The multitude of alternative EP execution methods (AM) is defined by possible relations R(R_E, R_F, R_EF) as Q. In according to the new form of the ETS definition, the task (1) will be transformed to a task:

The data about E, F, R, Q, and AM are received as the result of a system analysis of E, F and R (as rule) and synthesis of Q. As the quality index of working product will be used the EQR probability indexes of functioning process (FP) in ETS. New indexes such as fuzzy ciphers (fuzzy probability right execution; B^~, fuzzy costs; V^~, and execution time; T^~) will be used too.

3 Method of successive EP optimization without taking into account of aftereffect

The common scheme of the successively-extended equivalent structure (SEES) method [2] for B, T and V criteria is described. The SEES method is similar to the successive variant analysis method [3] in the part of the functional-structural theory [1]. In this case, the multitude of the alternative procedure of ETS execution is defined by the integration of FN. The multitude of the alternative ETS execution is presented as the superposition of the finite set of the typical functional structures (TFS). The alternatives in structure and FN parameters are defined as possible (alternative) relations R. The possibility to define the alternative subnets is realized. The basic method in the SEES designing is a descending strategy.

1. Method to define the multitude of alternatives.

   An algorithmic method of the AM assignment is used. Alternative FN graphs (tree) and AM generation algorithm are introduced. An alternative FN graph (AG) is a graph like "AND-OR" with the nodes in the existent typical functional units (TFU). TFU included in a TFN is related with the logical function "AND". The "OR" function is interpreted as the alternative in the TFU execution method with the alternative nets. In order to form all AM in the SEES method, bypass of the alternative graph in "width" is used. The pending nodes are sequentially removed from bottom graph level to higher level with "OR" arcs. While consolidation is taken into account all combinations of the "OR" arcs, the intermediate nodes are become pendent. This process will be stopped after creating all TFU equivalent to the alternative FN.

2. Required conditions of optimality.

   The specific form of required optimization conditions is based on discovered property of monotonous recursiveness indexes of FN from the equivalent TFU indexes which is included in the superposition tree. It can be formulated by this way:

   Condition. In order to include the FN in the multitude of effective FN, any equivalent TFU in the superposition tree of this FN must be effective in respect to the alternative equivalent TFU. The effectivity index of FN is, therefore, inserted in this condition for the concrete combination of the indexes B, T and V.

3. Advantages of the method.

   • Optimization in the wide classes of the FN with different structure can be made;
   • A direct selection can be made on the base of one required optimality condition for the different optimization task;
   • High effectivity of the direct selection as the consequence of the low value of the optimality indexes.

   Required optimality criteria areas the following procedure:

   • the criteria B, T, P(t<T_d) and V;
   • in the case of influence of the controlling parameters to the indexes B, T, P(t<T_d) and V;
   • in the case of dependence between execution methods of the some TFU;
   • the criteria B^~, T^~ and V^~.

The technology for the design of alternative OOFN is based on the structural (descending and ascending) and object-oriented designing method. Several stages for making AM can be emphasized. On the basis of the ETS system analysis of the basic classes (system elements, functions, operations, etc.), the structure is specified. With the assist of relations between the classes, new classes are generated as derived from the basic classes. During descending design, the creation of AM is processed for the alternative graph description. But instead of the TFU, TFN and ETFU, the class objects (in the first order operations), their relations, and the special class; ALTERNATIVES are used. The next optimization can be used the inheritance preference, the monotonous recursiveness, and the restriction to the equivalent TFU (ETFU) execution method (objects). During the descending design, the creation of AG is processed through the stages of processing events in objects for making logical-temporal sequence operation execution. As a result, we have the similar AG to the source graph. In common case, the AG structure is depended on the consolidation algorithm. For the mixed design, descend and ascend stages are shifted in turns.

Because the OOFN is an integrated model, if the AM is defined on this model, an equivalent task staging on the OOFN can be transferred. The relations between TFU execution methods decrease the effectiveness of SEES method. The directed enumeration control scheme allows reducing this hardship. The choice of the optimal scheme of direct alternate OOFN for AG exchange allows controlling these factors:

1. The equivalent definitions for source AG.
2. Selection in "width" or "depth"; For selection on AG in "width" optimality conditions check is required after even step of TFN assimilation. But for selection in "depth" it is not required.
3. Usage of the required optimality conditions on the basis of EQR indexes multitude in the optimization task (for example, T(F) £ T_d ).
4. Usage of the required optimality conditions on the basis of boundary checking for EQR indexes of the optimization task. This verification can include the estimation of the checking index for the OOFN as a whole.
5. Usage of the required optimality conditions on the basis of boundary checking for the relations with the TFU execution methods.

The fundamental idea of the offered method of successive analysis of OOFN (SA OOFN) is concluded as follows:

• AG is changed into the equivalent production system;
• the control of the successive selection in "width" or "depth" is entrusted to the logical conclusion mechanism by the selection one possible production in each step (paths of the ascension on AG);
• selection of possible production is composed of the basis of the formal and expert metarules (included into the method SA OOFN), i.e. it is controlled by the expert system.

4 Method of EP designing with taking into account of aftereffect

The aftereffect in EP leads to change characteristics of the following TFU after the execution of current TFU. It is interlinked as with various results of some executions of an operation, as with peculiarity of humans (teachers and students). For example, in the cyclic process of the examination tests, we can not consider the fact that the operation characteristics of examination and result control will be the same in the each cycle.

The characteristics of the follows operation can be exchanged with the linear scheme of the operation execution. For example, it can be followed one by one operation of practical lessons or reading lecture. For the EP execution characterization, the achieving probability of one's purpose of the operation, mean time of the achieving, and the cost of the achieving are influenced by these EP factors such as qualification of the teachers, knowledge level of the students, quality of used technical means and others.

Principal differences of the designing EP with aftereffect registration are considered as:

1. The description methods are such as in the OOFN.
2. The requirements in the designing of "own" TFU may be appeared.
3. The formulas and methods for the calculation of the equivalent TFU in EP are principally changed.
4. With saving of the monotonous recursiveness of this characteristics can be used optimization methods.

Let's explain described above on example. Before optimization, the TFU like "Serial executed work operations" was used a converting formula B=B₁*B₂. But now, B₁ is a function depended on B₂ and other EP factors. With enough assurance we can surmise, that B₁ is a monotonous recursiveness function of B₂, consequently, B is a monotonous recursiveness function of B₁ and B₂. The method of SA OOFN can be used in this way.

The cyclic TFS is required to unroll into the linear sequence of working and control operation with the following synthesis of the ETFU characteristics by the expert and statistical methods. They have different characteristics as a result of aftereffect.

5 Conclusions

New approach to the optimal designing of educational process in the engineering education is offered. It is based on the complex application of the object-oriented and structural designing technologies. By applying a metaproduction system and a logical conclusion mechanism, the serial ETS optimization method is designed for the OOFN with direct variant selection.

References