Computer System User’s Competency Influence on Reliability Factor Текст научной статьи по специальности «Компьютерные и информационные науки»

Computer System User’s Competency Influence

on Reliability Factor

G. Krivoulya, A. Shkil, D. Kucherenko, I. Filippenko, Y. Syrevitch

Kharkov National University of Radioelectronics, Kharkov, Ukraine

Abstract - Integral reliability characteristics of the monoergative computer system, one of the basic components of which is a human-operator, are examined. Mathematical models and analytical dependences of the restorable system dependability on the numeral values of the user’s competency are received. These dependences allow to define necessary expense on the improvement of the operator’s learning level, depending on the state of his current competence as an user of the technical system.

Index Terms - competency, operator, reliability factor, repairable system.

I. INTRODUCTION

The appearance of the complex organic ergative systems (ES) is associated with the rapid development of the computer information technology and the necessity for operators’ work with a control interface of the modern technical complexes, such as objects in the space and aviation engineering, power plants, process control systems, networks, internet, etc. ES found application in those objects where the intervention of an operator in the object operation is currently the requirement for error-free performance of these objects.

In most cases, ES is a complex computer-aided control system (CCS), a major component of which is a human-operator or group of operators, and depending on the number of operating staff the monoergative (one operator) and poliergative (several people) system are distinguished. By the operators hierarchy ES can be the first, second and higher order. For example, the second-order system has two levels of control, on the first of which an operator works with a technical device and on the second - the operator in addition to the work with a technical device to provide guidance of the first operator [1]. The research related to the development and improvement of the ES can be described

Manuscript received December 07, 2013.

G. Krivoulya is professor of computer aided design department, KhNURE, Kharkov, Ukraine, e-mail: krivoulya@i.ua.

A. Shkil is assistant professor of computer aided design department, KhNURE, Kharkov, Ukraine, e-mail: shkil@opentest.com.ua.

Y. Syrevitch ia assistant professor of electronic computers department, KhNURE, Kharkov, e-mail: syr jane@mail.ru.

I. Filippenko is assistant professor of computer aided design department, KhNURE, Kharkov Ukraine, e-maill: kiu@kture.kharkov.ua.

D. Kucherenko is postgraduate student of computer aided design department, KhNURE, Kharkov, Ukraine, e-mail: d zin@ukr.net.

by three stages. At the first stage, the goal of the ES improvement was a human adaptation to the technical device, at the second stage - the technical device to a human: his psychological, physiological, anthropometric and other characteristics. The third stage is characterized by a human factors analysis together with the characteristics of the technical object as a total integral character of the ES. But it isn’t a man is considered as an average link included to the technical system, but a technical device - as a tool included to the activity of a human-operator. That human generates and implements the goals of the ES operation by technical devices [2].

The mandatory components of the ES besides operating staff involved in control are computer hardware and software tools. The effectiveness of the ES operation considerably depends on the reliability (availability) of all three components. Subject to this the important task is to ensure their trouble-free operation during the operation. This task has three main components - the ES reliability, the availability to the system application and the qualitative characteristics of the service, in particular, the level of the diagnosability provision. These three components assume the diagnosis and elimination of the possible system problems, generated by faults and failures.

II. Problem definition

The reliability of the technical computer environment has been researched quite extensively and deeply. The reliability of the complex software systems is studied less and the reliability properties of the ES operators, the evaluation of their performance is currently research not well.

A human-operator is the basic link of the modern ES, statistics show that 20-30% of the accidents and disasters, directly or indirectly, related to the human error. Consequently, the overall assessment of the technical systems reliability and their integral characteristics must necessarily include the analysis of the human factor. In this connection, the development of the ES integral

characteristics evaluation procedure, taking into account the properties of all three components - the operating staff, hardware and software - is actual task. In the capacity of the basic integral ES characteristics the reliability factor of the restorable technical system taking into account the readiness of the operator based on his competence is proposed to use.

III. ES RELIABILITY SUBJECT TO THE HUMAN-OPERATOR ACTIVITY

Systematic approach of the ES reliability assessment provides the assessment of a human as one of the main components of the system. In the general case, this reliability is defined as the need of the successfully accomplish of the task on given stage of the system operation within a specified period of time under certain requirements to the activity time.

The ES reliability assessment is based on the following assumptions:

■ both hardware failures and operator errors are rare, random and independent events;

■ an appearance of more than one single-type event during the time of the system operation is almost impossible;

■ the ability of the operator to errors compensation and to the error-free operation - are independent properties of the operator.

Error (failure) of the human-operator is defined as the non-execution of the task (or perform forbidden acts) which can lead to violation of the scheduled operations.

The operator error can be divided into three groups:

■ the goal of the problem solving can’t be achieved due to the erroneous actions of an operator;

■ the operator seeks to achieve the erroneous goal;

■ the operator is inactive at the moment when his participation is necessary.

The criteria of the performance and reliability are used for evaluation of an operator activity [3].

The performance criterion is problem time, i.e. the time from the moment of an operator reaction on the signal to the moment of the stimulus end: Ton = a + bH = a + H / Von, where a - a hidden reaction time, i.e. period of the time from the signal appearance to the operator's response on it (0,2 ... 0,5 sec); b - the time of the one information unit processing (0,15-0,35 min); H - the amount of processed information; Von (2 ... 4 units/sec), or bandwidth, which characterizes the time during which the operator grasps the meaning of the information.

The reliability of the operator is characterized by his faultlessness, availability, accuracy, recoverability and timeliness. For each of these indicators the analytical dependences can be developed.

Let’s consider the case when the compensation of the operator error and hardware failure is impossible [2]. If hardware failure and human error - are independent events, the probability of the failure-free operation is: P(t0,t) = Pt(t0,t)P0(t), where Pt(t0,t)- the probability of

the no-failure operation of the hardware over a period t0 , t0 +1; P0 (t) - the probability of the error-free operator operation over a period t, subject to the hardware trouble-free operation, t0 - the total time of the system operation, t - the current period of the system operation.

The ES with noncompensible operator errors and hardware failures is occurring in practice relatively rare.

The reliability of such systems can be enhanced by the operators’ redundancy with periodic diagnosis of their activities results.

The technical systems with failures recovery and operator errors compensation are widespread. The operators can fix (compensate) the part of the admitted errors in proper time. The errors compensation is an important alternate way of the ES reliability improving. Bringing into the technical system the attachments facilitated the error correction, increases the ES reliability significantly.

The system with errors and failures compensation will work without failures during the time t0, t0 +1 under the following conditions:

1) the technical system didn’t fail and the operator didn’t make a mistake;

2) the technical system didn’t fail and the operator made a mistake, but fixed (compensated) it;

3) the operator didn’t make a mistake, the technical system failed, but through the operator intervention a system performed its functions;

4) the operator made a mistake, but fixed (compensated) it, the technical system failed but, trough the operator intervention, system and operator performed their functions.

IV. The reliability factor of the repairable system

For an approximate reliability indexed calculation of the repairable ES let’s accept the following assumptions. We consider the set of flows occurring in the system in case of the separate elements failure. The analysis of all the situations that lead to the system failure as a whole is conducted. As a result, the intensity of the events’ flow of this type and the length of the failed state by each of the reasons is computed. Then the procedure of the flows superposition of those situations, each of which leads to the system failure or flows’ depression for those situations that lead to the system failure during simultaneous implementation is consistently applied.

As a result, we obtain the resulting flow with two summary characteristics: average uptime and average recovery time.

Subject to the reliability of the systems uptime, as a rule, will be exponentially distributed, so these two parameters are sufficient for the evaluation of any other reliability indexes [2].

The process of the repairable object operation can be represented as a sequence of alternating periods of availability and recovery (standing idle) (fig. 1).

failure flow

failure_ Гі 12 Ln /

(recovery)

operation

Tl T2 T/ Тл \ recovery flow

Fig. 1. The repairable object operation, T...Tn - the periods of the availability; T • • • T - the periods of the recovery

The reliability factor - is the probability that an object will be in working order at any time, except for the scheduled periods during which intended application of the object isn’t provided. This index assesses at the same time the properties of the availability and maintainability of the object.

For restorable object on conditions that there is a simple flow of failures and recoveries the reliability factor equal

к = -L- =

T + _ х + ц 1 + ^ 1 + _ 1+Y

Ц T

(1)

where ц = —, X = — and y = — = _ _ T ц T

recoverability

index.

From the expression (1) it follows that the reliability factor of the object can be increased by increasing of the mean time between failures and reducing of the average time of recovery. On the other hand the reliability factor depends not on the absolute values of the variables T and _ , but of their relations, i.e. on value y .

Note that for the high-reliability systems Т >>_ or

Y=<< 1.

For high-reliability CCS 0,9 < KR < 0,999, i.e.

0,9 <—^- < 0,999.

1 + y

In other words

0,9(1 + y)< 1 < 0,999(1 + y) , 0,9 + 0,9y < 1 < 0,999 + 0,999y .

Solving the inequality, we obtain: 0,001 < y < 0,111.

For the practical calculations an approximate K calculations is used. For this let’s perform the following transformation:

K =

1+ Y - Y 1 + y

= 1 -Y. 1 + y

We assume that

Y

1 + y

: Y , so the conversion error will

be:

A =

Y

1 + y

■Y

Y-Y-Y

1 + y

Y

1 + y

as y << 1, A»f!.

Thereby, for computing K « 1 - y .

Together with the rise of the period under review an average reliability factor seeks to the reliability factor as to the limiting value, which with the increase of the interval time, i.e. K (t) = lim K (t), where K (t) - the probability

that at time t the product is up (in certain initial conditions

at t = 0), i.e. K(t) =—1— fP(t)dt, K(t)- the probability

T + _0

of the failure-free operation. For an exponential distribution Т and _ the dependency diagrams of the basic values

KR (t) = KR + кг <х+ц)‘ and the time for the corresponding values y are showed on figure 2.

V. The relationship of the reliability factor and

USER COMPETENCY

The high-reliability CCS is a set of the technical tools, dataware and software (SW), as well as operating staff that combined to perform control functions. it is assumed that failing of any three components leads to the system failing, which have to operate continuously over a preset time [3].

To simplify further discussion let’s introduce the following restrictions, which, in toto, don’t affect the calculation nature of the reliability factor:

- mean-time-between-failures Т and recovery time _ are random variables that obey an exponential distribution;

- CSS technical parameters which determine the value Т and _ , don’t change over time;

- Т and _ correlation doesn’t change over time (stationary process);

- staff qualification (training) affects the changes of the Т and _ as well.

The evaluation model of the human-operator activity in the capacity of the CCS component was proposed in [4]. The availability conservation property of the operator under appropriate functional activities on the assumption of training is represented by double exponential model:

-Xte-V_

Pi(t_) = г XXe , (2)

where t3 - the operator's time which required to perform task in the information system; X - the error intensity during work performance, _ - learning time, v - the error intensity during learning time.

A consequence of (2) is a formula of the conditional intensity of the operator failure (error) on the assumption of pretraining:

Л(Г) = P(t )X(t), (3)

where P(t ) - the conditional probability of the successful CCS operator activity under availability resource consumption which accumulated during training period,

A(t) - unconditional failure (errors) intensity of the operator. From (3) follows that the conditional failure intensity Л(ґ) comes to the minimization of the

unconditional failure (errors) intensity A(t) in P time. As

applied to systems with recovery, where Я = 1, it can be

assumed that the mean time to failure Ty increases in P time, i.e. Ty = T ■ p (actually, conditional mean time to failure decreases as 0 < p < 1). Applying the similar

reasoning to the restorations intensity p

1

—, we can

T

assume that the recovery time t will decrease in P2 time,

i.e.

T

У

T

P

(actually, the recovery time will increase, as

by-turn 0 < P2 < 1). On the assumption that the operator learning affect the Т and t as well, let’s assume that the conditional probability for them will be identical, i.e. P = P2 = P . For the operating CCS staff let’s define the

conditional reliability factor: Ky = —y—, that can also be

У Ty +Ty

referred as K P (operating personnel).

Taking into account Ty = T ■ P and Ty

—, we obtain:

P

K = -

T ■ P

T ■ P

T ■ P2

P2

— T ■P2 +t T ■P2 +t

T ■ P + —

P P P2 1

P2 +-

P

P2 + Y 1+Y P2

(4)

К =

If we accept that y = 0,01, we will get

P2 1

P2 + 0,01 1 + 0,01'

P2

The dependency diagram of the conditional reliability factor K P on the conditional probability in the range from 0 to 1 when у = 0,01 is showed on figure 3.

T

For approximate determination of the KP let’s define tolerance range for P :

T

T P T Y

К = 1 -y = 1---= 1----= 1----------- = 1--Lr. (5)

T T ■ P T ■ P2 P2

Y Y

On the basis of К = 1------ > 0 , we obtain —- < 1 or

P2 P2

P2 > y , i.e.

P >4Y. (6)

The dependence P on KP will be: y = (1 - К)■ P2;

P = J—Y— , which makes it possible

P2 =Y ;

1-к V1-к

calculate the increment AP depending on AK :

to

P + AP =

Y

AP =

1 -(K + AK)

- P .

Y

1 -(K + AK )

(7)

VI. The model of the operator learning

Operator learning C let’s define as the frequency of the correct task performance of the operating activities (learning outcome). At the same time (C -1) - the frequency of the incorrect task performance.

R

Then C = —, where R - the number of correct actions

V

of the operator in unit time, N -the total number of operations per unit time.

In terms of (2) and (3) the probability of failure-free operation is P(t) = ev, where v - the operator error intensity during learning time t . If we abstract from the random nature of the human error during the training period and from the learning time t , and consider only the training outcome C , then the operator error intensity during learning time can be replaced by the number of errors during learning time (C -1):

P = e-»-C> = e(C-1). (8)

For the transition from the conditional probability P to learning C let’s find the logarithm:

lnP = C -1; C = lnP +1.

Let’s define the tolerance range for P on the basis of

0 < C < 1:

0 < ln P +1 < 1,-1 < ln P < 0,

e-1 < P < e0,0.368 < P < 1.

(9)

Thus, then y = 0.01 the turndown KP will be

0,932 < K < 0,9901.

Based on a comparison of (6) and (9), we can conclude

that to compute the conditional reliability factor of the

personnel KP it's more than enough to use only approximate formula (5).

Let’s consider the extreme case. With the highest level of learning C = 1, P = e0 = 1 as well as KP is equal to the maximum value of the unconditional reliability factor, which corresponds to the objective nature of the learning process.

With minimal learning level C = 0, P = e0-1 = e-1 = 0.37 , as well KP = 0.932 . This value of the minimum KP due to the fact that the two-level exponential model takes into account other factors except the personnel learning, for example, learning time, ways of the personnel restorative function and others.

The dependency diagram of the conditional reliability factor KP on the personnel learning level C with y = 0.01 is showed on figure 4.

0 0,1 0,2 03 0,4 0,5 0,6 0,7 0.8 0,9 1 p

Fig. 4. The dependency diagram KP on P

Thus, the conditional reliability factor or staff reliability factor can be increased by increasing of the personnel learning level (competency) C, on AK = 0,01 in assumption of AP = 0,19, but the competency level has to be raised to C = 0,8 (i.e. AC = 0,25 ). For the competency assessment of the ES user we can use the method given in [5].

VII. Conclusion

The analysis of the integral reliability characteristics of the monoergative computer system showed that the availability of the repairable system appreciably depends on the functional availability level of the technical system user, which is determined by his learning (competency) as an operator. The received mathematical models and analytic dependences between system reliability factor and numerical values of user competency make possible to determine improvement costs of the operator learning level according to the state of his current competency.

References

[1] The reliability of technical systems: a guide / J. K. Belyaev, V. A. Bogatyrev, V. V. Bolotin et al. / By ed. I. A. Ushakov. - M.: Radio and Communication, 1985. - 608 p.

[2] The telecommunications infrastructure of data centers [electronic

resource] / Document SP-3-0092: (Standard TIA-942, Revision 7.0, February 2005). - Mode of the access: http://www.ups-

info.ru/etc/tia russkii.pdf. - 15.06.2011. - The title from the screen.

[3] Smagin V. A. Technical synergy. Issue 1. Probabilistic models of the complex systems elements / V. A. Smagin. - St. Petersburg: Military-Engineering Space University, 2003. - 66 p.

[4] Smagin V. A. The reliability model of a living organism (the operator). [Electronic resource]. - Mode of the access: http://sir35.narod.ru/Cmagin/index.htm. - 10.12.2010. - The title from the screen.

[5] Krivoulya G. F. Diagnosis of computer systems users competence / G. F. Krivoulya, A. S. Shkil, D. E. Kucherenko, E. V. Garkusha // ACS and automation devices. - 2010. - Issue 150. - p. 125-133.

Let’s show an example of the personnel learning level calculating in assumption of the reliability factor changes. Let’s suppose that there is a CCS with recoverability indices y = 0,01. The analysis results of the staff’s skill level showed that the learning level (competency) is equal to C = 0,55 . We have to determine how much personnel learning have to increase for the conditional reliability factor KP rose to 0.01 (AKP = 0,01).

Using (7) P = e(C-1), let’s calculate the conditional probability P = e0 55-1 = e-045 = 0,63, and base on it - the conditional reliability factor.

on the basis of (6) let’s calculate

AP =

0,01

1 - (0,975 + 0,01)

- 0,63 = 0,19 .

With reverse transition to the learning index (competency) C on the basis C = ln P +1 we will get: C = ln0,82 +1 = 0,801.