The model of the influence of the available time on the tension of operators and the infallibility of their activity is considered. The productions and methods of solving possible optimization problems are developed to search for ergonomic reserves to increase the efficiency of critical systems.
Modern technological, transport, aerospace and energy systems are inherently critical
[
The analysis of the real operators’ activity made it possible to determine the
following failure conditions for most cases [
Scientists working within the framework of the functional structural theory of
ergotechnical systems of Prof. A.I. Gubinsky, have traditionally paid much attention to
the study of optimization problems for operators [
The task is to identify current problems and develop appropriate models that allow solving the problems of optimizing the discrete activity of operators by varying the values of parameters that characterize time resources, i.e. by means of regulation of operational-tempo intensity. 3 3.1
Quality of Activities. Professor P.P. Chabanenko [
Tension, as a psychological fee for achieving the goal of activity, includes several
components, the main ones being the tempo, determined by the time deficit to solve
the problem, and the operational one, determined by the nature of the operations of
the activity algorithm. The joint operational-tempo tension is determined by the
simultaneous influence of two noted factors: The tension H defines the probability P0 of
switching on the self-monitoring of the current operation by the operator [
Optimal tension of the operator’s activity: Hopt = 0.262. The area H < Hopt corresponds to an insufficient load on the operator, and the area H > Hopt corresponds to an excessive load on the operator.
When H = Hopt, there is a probability to start a self-monitoring function P0 = 1, which corresponds to the case of setting error-free operation.
When H = 1, the probability P0 = 0, which corresponds to the speed setting. An illustration of settings types in the operator’s activity is shown in Fig. 1.
Tempo Tensity. Time limitations are determined by the characteristics of the flows of incoming signals or orders, or various organizational decisions (including the number of operators in the shift and distribution of functions among them). They may be set instructively by the managing operator or they can be established by software and technical means of activity management.
Depending on the nature of the activity and the level of optimization (function, complex of functions, etc.) we distinguish 2 classes of possible tasks.
Choosing the optimal time constraint for the implementation of activities (1st class of tasks). Task 1.1 (single criterion):
There are given: The structure of the activity algorithm; characteristics of reliability and execution time of operations, permissible time limits for the implementation of the activity algorithm in the form of the lower limit of Tmin and the upper limit of Tmax (may not be available); and the maximum permissible activity tensity H0. It is necessary to choose the limit value T, imposed on the implementation time, which provides the maximum probability of the error-free execution:
B(T ) max H (T ) H0
Tmin T Tmax where T is the allowable time for activity implementation; B (T) is a probability of error-free execution; H(T) is an intensity of the activity; H0 is a maximum permissible intensity; Tmin, Tmax are minimum and maximum times to implement activity.
Task 1.2 (multiple criterion):
The criterion for minimizing the intensity is added to the formulation of the Task 1.1. (2) – (4) instead of, or in addition to the restriction on the intensity (3).
H (T ) min Task 1.3 (optimization of income from activities): (2) (3) (4) (5)
The statement appears due to the need to solve the problem of the type "what is better: a greater number of implementations of activity algorithm with low infallibility or high infallibility with fewer implementations". The economic consequences of correct (incorrect) implementations of activities can be evaluated in various ways, for example, "income from correct implementation" and "damage from improper implementation".
Consider one of the possible formulations of the problem, taking into account the economic consequences of the activity. The following statements are given in addition to the initial data of tasks 1.1 and 1.2, where C1 is an income from a single errorfree implementation of the activity; C2 is a damage from a single implementation of the algorithm with an error; T’ is a total time during which the activity algorithm should be repeated (taking into account the deduction of time for various breaks: technological, for leisure, etc.). If we consider that the number of applications realized in time is determined by the time allocated for a single implementation n=T’/T, the target function will have the form
T ' T
(C1B(T ) C2 (1 B(T ))) max under the constraint (3)-(4).
Task 1.4 (multiple criterion analogue of task 1.3): The criterion of intensity minimization (5) is added to the statement of task 1.3, instead of, or in addition to the constraint (3).
In the formulations of tasks 1.1-1.4, there is no explicit restriction on the timely implementation of the activity algorithm, since, as follows from the initial assumptions, the activity is pre-configured and the operator provides (at Tmax not less than the minimum required time for implementation of the activities) timely execution (by enabling or disabling the self-monitoring of operations).
The way to solve the tasks of choosing the optimal time limitations for activity implementation:
Since the analytic dependence for B(T) cannot be defined in principle, and the
mathematical model, algorithm and program for calculation of the probability of
error-free execution at a given point (for a given T) are developed (see [
Optimization algorithms based on one-step or multi-step choice are possible. The one-step choice consists of determining the number of points N, calculating values Ti Ti1 Tmax Tmin ,
N
(6)
(7)
where i=1,…,N, T0=Tmin, computing B(Ti), H(Ti) (using algorithms and programs [
A multi-step search is implemented in a coherent strategy related to the following actions:
1) The use of the selection rule for the first few points T1,T2,…,Ts ϵ [Tmin,Tmax], and localization of the minimum point on the segment [T’min,T’max];
2) Choosing points TS+1,…,TK on the localized segment and determining the next segment;
3) The analysis of the solution that was obtained for an admissible approximation to the optimal one, and the optimal sequential search, carried out by one of the known methods, for example, "Fibonacci search", "Golden section" method, etc.
Distribution of the directive time for realization of activities between their fragments (2nd class of tasks):
Task 2: The statement makes sense in the case when the algorithm of the
operator's actions is divided into several parts (fragments): each part is executed in the
interval between two events. And the first event (signal) is synchronized with the
beginning of the implementation of the algorithm corresponding to the activity
fragment, and before the second event (signal) arrives, the algorithm must be completed.
Such a situation usually occurs when fragments of system operation algorithms are
realized in parallel by a human operator and a machine (with a starter and a
functionary of type "AND"[
The fact that it is not always expedient to operate the automation machine with the
maximum possible speed is noted in a number of ergonomic studies: For example, in
some cases it is recommended to introduce a delay in the "computer response" in
order to ensure the comfort of the operator [
However, there is no way to determine the optimal reaction time in each particular case. We assume that for technological or economic reasons the maximum permissible time T for the implementation of the algorithm of functioning (AF) of the entire system is set. The task is to determine the directive times for the operator to perform individual fragments performed between the signals of automatic means, ensuring the maximum probability of error-free realization of the entire AF. At the same time, restrictions on the intensity of activity on each of the fragments can be introduced. Here is the definition of vector (T1,T2,…,Tn) that provides:
F (B1(T1), B2 (T2 ),..., Bn (Tn )) max
B
FT (T1,T2,...,Tn ) T
Hi (Ti ) Hi0 ,i 1,..., n
(8)
(9)
(10)
where FB is a dependence of the probability of error-free execution of AF from Bi(Ti),
i=1,…,n, determined by the structure of AF; Ti is a directive execution time of the i-th
fragment of AF; Bi(Ti) is a probability of error-free execution of the i-th fragment of
AF; Hi(Ti) is strength of the i-th fragment; H0i is maximum permissible tension for the
i-th fragment; FT(T1,T2,…,Tn) is a dependence of AF execution time on the execution
time of its individual fragments, determined by the structure of AF; n is a number of
AF fragments. FB and FT are determined by the models developed for the typical
operational structures [
In the particular case, when AF fragments are sequentially performed, the statement (7)-(9) takes the form:
The way of solving the task of directive time distribution to realize the activity between their fragments:
Step 1: Generation of a set of directive time values of the fragment implementation for each i-th fragment of i=1,…,n, for example, as follows:
1a. Definition of the range of research [Timin,Timax], where Timin is the time required to implement the AF fragment without performing functional control for all operations (for example, for a sequential chain of operations, n Bi (Ti ) max i1 n Ti T
i ni Tmin TPij , j 1 where i=1,…,n and Ti,0=Timin.
Ti,k Ti,k 1
i i Tmax Tmin ,
Ni where ni is the number of basic work operations in the i-th fragment, TPij is the mathematical expectation of the execution time of the j-th operation in the i-th fragment);
Timax is the maximum time value for the AF fragment implementation, provided that all operations are performed with self-monitoring and taking into account the variance of the execution time, for example, for a sequential chain of operations where TPKij and DPKij are the mathematical expectation and a variance of the execution time in the i-th fragment of AF of the j-th self-monitoring operation.
1b. Definition of the number of investigated values of the directive execution time Ni for each i-th fragment i=1,…,n, and generation of the following values: Ti,1,Ti,2,…,Ti,Ni ϵ [Timin,Timax], in the simplest case
Tmi ax ni TPKij 3( ni DPKij ) j 1 j 1 1/ 2 , (11) (12) (13) (14) (15) (16)
Step 2. Evaluation of error-free and activity intensity values on each i-th fragment, i=1,…,n, with all the generated values of the directive time: Bi(Ti,j), Hi(Ti,j), i=1,…,n, and j=1,…,Ni. The evaluation is carried out by using models and programs developed in [3–5, 9 and 10].
Step 3. An exception for each i-th activity fragment of Ti,j(i=1,…,n, j=1,…,Ni) those values that do not satisfy the constraints on the activity tensity Hi(Ti,j)≤H0i.
Step 4. Choosing the best option. With the generated variants of the execution of fragments with available estimates of the quality indicators, the task is reduced to the standard problem of maximizing the probability of error-free execution of AF under the constraint on the mathematical expectation of the execution time [6,7 and 10].
Step 5. Investigation of the vector obtained as a result of the solution of the optimization problem. (T*1,T*2,…,T*n); generation of directive time values for each i-th fragment in the range [T*i – ∆i, T*i + ∆i], (Δi can be determined, for example i
i i Tmax Tmin
Ni (17) (see 1b)), and transition to step 2 (steps 2-5 should be repeated until the solution with required accuracy is obtained).
The convenience of the approach is that one of the steps reduces the task to the
known problem of optimizing a human machine system and can be solved by any
known method [
The models were used in the development of the following systems ensuring
ergonomic quality:
Automated processing plants for various purposes [
Operational-tempo tension is determined by time constraints on the activity of operators of critical systems and significantly affects the indicators of error-free functioning. It is convenient to evaluate the influence of time resources on the efficiency of ergotechnical systems by using models based on formalisms introduced by Prof. P.P. Chabanenko.
Solving the tasks of choosing temporal constraints for the implementation of activities and the distribution of directive time for the execution of work between its fragments makes it possible to ensure the fulfillment of specified requirements for the operation of critical systems while observing the normative indicators of the intensity of the operators’ activities. Solving the problems of choosing a temporary restriction on the implementation of activities and the distribution of directive time for the implementation of activities between its fragments can provide specified requirements for the effectiveness of critical systems, while observing the normative values of the activity intensity of operators.
The models should be used as elements of mathematical support of DSS for operators-managers of critical systems.