Model-Based Prediction of Human Performance with Respect to Monitoring and Failure Detection

Copyrigh t © IFA C Analysis. Design and E. . alu ati o n of Man-Machine Systems

Baden -Baden. Federal Repub(ic of Germany 1982

MODEL-BASED PREDICTION OF HUMAN PERFORMANCE WITH RESPECT TO MONITORING AND FAILURE DETECTION W. Stein* and P. H. Wewerinke** *Research instz'tute for Human Engz'neenng (FA T), Wachtberg- W erlhhoven, Federal Republz'c of Germany **Natz'onal Aerospace Laboratory (NLR), Amsterdam, The Netherlands Abstract. Human operator models for monitoring and failure detection are outlined. Corresponding experimental paradigms and extensive validation stud ies including eye movement results are explained . The state - space oriented models proceed with the information structure of the optimal control model (OCM) and conside r single - obse rv a tion as well as sequent i a l decisions. The broad coverage of th e models opens analysis and design applications in the area of supervisory control . The paradigm refers to multiple - process situations with optional dynamics, couplings and event characteristics and, thus, increases the practical utility of models. An outlook is give n on design theory and respective methodologies for man- machine systems . Keywords. Man-machine systems; mathematical analysis; human operator models; supervisory control; signa l detection; decision theory; model-bas e d desi gn methodology . INTRODUCTION This paper addresses possibilities of a de sign or synthesis methodology for certain areas of man-machine systems. Emerging de sign procedures based on human performance models are emphasized that have the predictive potential of evaluating systems on a pre liminary basis and to extrapolate into future concepts (Curry, Kleinman, Hoffman, 1977; Pew and others, 1977; Rouse, 19 8 1) . Certainly, analysis, design, and evaluation will be improved by satisfactory model-based methodologies in like manner, but the availabil it y of analyses is a prerequisite to any systematic design. Analysis procedures might be more elaborated than design within the field of man-mach ine systems, too. The design-methodological aspects of man-machine systems (Meister, 1971; Mc Cormick, 1976; Rouse, 1981; Topmiller, 1981) might be related to an arising and yet uncoherent design theory (Zwicky, 1967; Spillers, 1974, 1977; Director, 1981). Therein, so- called conventional approaches are regarded as fields of heuristics, i.e., decomposing a given problem to workable pieces (Himmelb lau, 19 73) and composing certain elements to a particular design al ternative originate in a primarily heuristic t axonomy. Analytical as contrasted with conven tional approaches impl y steps to a more systematic design by using data bases, opt imization procedures and specific metrics. Model-based approaches go beyond these by coherently inc orporating analy tical elements in human performance models. A prerequisite is a performance/workload metric. Experimental paradigms and appropriate validations may lead to predictive design tools and, furthermore, to a model-based task taxonomy. 221

The model - based approaches or i gi nate in dis play design for manual control situations (Clement, Jex, Graham, 1968; Clement, McRuer, Klein, 19 72) and utiliz e f r equency-domain models of the human operator comb in ed with a rationale of visual scanning and an empirical metric of workload. Therein proceeding, the optima l control model (OCM) of human response has provided design approaches with a more e l aborated formal structure (Curry, Kleinman, Hoffman, 1977; Baron, Levison, 1977; Hes s , 1977; Schmidt, 1979; Hess, 1981). Its pre dictive applicability is based on (1) the framework composed of modules for separate human functions (e . g ., pe r cept ion, central processing, decision making , motor response), (2) the f l exible info rmation structure suited for multivariable, multiple process and/or multitask situations, (3) the comparably high level of validation, and (4) the underlying, normative modeling perspective . Hence, our approach employs the in fo rma tion structure of the OCM. Our paper is purposed as a first step to extending model - based design procedures into the a re a of supervisory control. Correspond ingly we examine tasks a nd models of both tolerance-band monitoring (TBM) and failure detection (FD) and aspire at a taxonomy ori ginating in the modular framework of OCM-extensions. The experimental paradigm marks the area of validation and holds keyfactors of complex human operator tasks, that might be useful for a nalysis, design, and evaluation . The discussed results satisfy a high level of data/mode~ correspondence . Early OCM- extensions to TBM- and FD-tasks refer to Levison ( 197 1), Levison, Tanner (1971), and Gai,

W. Stein and P . H. Wewerinke

222

Curry (1976), whereas the presented models have been developed by Wewerinke ( 1976 , 1977a, 198 1a , 198 1b, 1982) .

rence t , whereas the fa l se - alarm probability f and miss probability PM describe the de F tection accuracy.

Tolerance - band monitoring (TBM) involves obse r ving a stochas t ic pr ocess Yi(t) (see Fig . 1) in r espect to exceeding the explicitly indicated to l erance band [b , b 1 that li ui are represented by the indicator variable

;

{":

if b

li ~ Yi (t)

- t ) denotes the interval be d f tween failure detection td and failu r e occur P

TASKS AND MODELS

h. (t) 1

time Td = (t

~

bui '

(1)

HI else. 1

The human has to duplicate the binary process h.(t) € { H~ , HI} , where the intervals of ex111 ceeding , H~ , and the intervals related to the depressed l keyboard, DI , have to be synchronized . In case of m variables , the response u(t) ; DI relates to the potentially up to m simultaneous exceedings of y.(t),i;l , .. . ,m. The TBM- performance metric ihvolves the deci sion error Pe = P + P and the error ratio fa ms Re Pfa/P ms where t he t ime fractions P and fa P , caused by the incorrect responses (H~ DI) ms 1 and (Hi DO) , denote the possibility of false alarm and missed exceed i ng, respectively . The binary var i ables hi(t) are generated by the Gau ss - Markov processes Yi(t) . Thus , hi(t) and u(t) are alternating renewal processes consti t u t ing a c l ass of the point processes (Cox, Lewis , 1966). The TBM- task requires single observa t ion decis i ons testing one pa i r of hypotheses (Sage , Melsa , 197 1) . Failure detection (FD) involves observing a stochast i c process y.(t) with respect to the potential occurrence1of abnormal events, where an event is defined as a change in the statistics of the displayed process that may be composed of c hanges i n mean , standa r d deviation , and dynamic properties. The FD- per formance metric contains speed and accuracy data with r e l ated trade - offs . The detection

We restrict the class of events to determi nistic time functions zxi(t) that are super imposed on stationary stochastic processes x. (t) (see Fig. 1) . The displ a y reference ihdications have a somewhat weak mean i ng in FD- t3sks, since the failure - related informa tion , e . g ., the ramp function, is corrupted by a stochastic process. Hence, failure detection requires sequential decisions, where the number of observations used as input to a decision is not fixed , but greater than one (Sage, Melsa, 1971) . Elementary failure detection is a binary task that consists in testing a pair of hypotheses . Situations with m displayed processes Yi(t),i= l , ... , m simultaneously admit m independent events or respectively composite events having redun dant information. We assume that the human observes an automatically controlled dynamic system, which is driven by white Gaussian processes wet) with covariance ~ , ~(t)

=

~ ~(t)

+

E wet).

The system is assumed linear and time - invari ant, with noise shaping states and automatic control system dynamics included in the sys tem state description . The displayed varia bles yet) involve combinations of the system states x(t) and , in case of failure detection , a superImposed deterministic time function , yet) = C x(t) + z (t) ,

(3)

z(t)=Cz(t), -y - -x

(4)

-

-

-

- y

where z (t) represents a specifiable abnormal -y event or a system failure to be detected . We assume that i f a quantity Yi (t) is displayed

1: (t)

L __ Fig . 1.

(2)

Human Operator

Mo del of to l erance - band monitoring a nd fa i lure detect i on

Model-based Prediction of Human Performance explicitly to the human, he can extract its rat e of change, Yi(t). Thus, Z(t) contains both position information y.(t),i=l, ... ,m a nd rate information 1

Yi (t)

= y m+ i

(5)

( t) ,i = 1 , ••• ,m,

where Yi(t) and Yi(t) are uncorrelated. The perceptual submodel reflects inherent limitations of time delay 1 and observation noise vi(t), ypi(t) = Yi(t-1) + v i (t-1),i=1, ... ,2m, (6) where y .(t) is the perceived information p1 upon which further pro cess ing is based. Frequently, the relatively invariant time delay 1 ; 0.2 s is negligible in observation tasks, so that the predictor part of the model may be dropped. The covariance Vi of white Gaussian noise v.(t) scales with variance of 2

.

1

o . of d1splay variable y;( t) and is given by y1 ~ 2 0 (7) V. = TI 0 . P ./f . , 1 y1 y1 y1 where po. is the reference value of the oby1 servation noise /s ignal ratio that relates to the level of full attention, f . = 1. Hence, y1 P . = Po ./f . = V./(TI 0 2 .), (8) y1 y1 y1 1 y1 is the effective noise/signal ratio associated with variable Yi(t). The attention sharing hypothesis of the OCM (Baron, Levison, 1977) assumes that the fractions 0 ~ f . ~ 1, y1 f . . = f ., applied to the variables Yi (t) , y1 y1 i=l, ... ,m obey the constraint m

L

i=l

f

.

y1

f

yo

~

(9)

1,

where f

denotes the effective level of atyo tent ion directed to the entire observation task. Losses due to visual scanning, for instance, cause f < 1. In a great deal of yo situations the reference ratio po. equals y1 P ; 0.01 = -20dB found in baseline studies yo (Kleinman, Baron, Levison, 1971), if specific physical conditions (i.e., zero-mean of Yi(t), high resolution displays with zero-reference indication) and idealized viewing conditions (i.e., fovea 1 viewing, full attention directed to Yi(t), negligible threshold and satura-

tion effects) are given. Some different po . have been found so far (Baron, Levison, y1 1980). Unlike the assumptions of Eq. (9), extensive studies indicate trade-offs within each pair of f ., f ... Hence, the attention y1 y1 sharing hypothesis of Wewerinke (1977b,1981a) assumes, regarding the above baseline studies,

223

that includes f.. ~ f . as a special case, y1 y1 where f . and P of Eqs. (7) a nd (10) differ y1 yo by a factor of 1/2 and 2, respectively. Accounting for thresholds associated with the perception of Yi (t) (Baron, Lev ison, 1977) the describing function gain N(.) of a thr es hold element is inserted in Eq. (7), so that the reference ratio po. is made a function of y1 the appropriate standard deviation 0 . and the threshold value a ., y1 y1 o 2 P. P /N (0 ., a .), (11) y1 yo y1 y1 N(o ., a .) = erfc (a ./(0 .

y1

y1

y1

y1

/2».

(12)

Perceptual thresholds are frequently not negligible for 0 . < 3 a ., i.e., in case of a y1 y1 low 0 . and, since 0 .. ~ W . ay;' a low bandy1 y1 01 ~ width w . Typical thr esho ld values are oi (Wewerinke, 1981a) a . y1

0.1 deg. visual arc,

( 13)

a. .

0.2 deg. visual arc/second.

(14)

y1

The above observation noise model fits to FDa nd not to TBM-situations, since it assumes continuously estimating an analogous quantity Yi(t) with respect to a zero-reference indication. Performing a TBM-task turns out to be rather reading an uncorrupt ed binary-valued quantity hi(t) than estimating Yi(t). The observation noise vi(t) might primarily relat e to the intermittent indifference associated with the moments, when Yi(t) ~ros:es the thresholds b and b . Stud1es 1nclud1ng li ui eye-movement recordings (Stein, 1981) let ass ume that the reference ratio po. is af y1 fected by P(H~), i.e., the probability of 1

Yi(t) exceeding the respective tol erance band [b

li

, b

ui

l. Thus,

o

p.. = P K(o . ,bl·,b .) y1 yo y1 1 U1

( 1 5)

is a reasonable expression, where K(.) is empirically approximated by (l-P(H~», so th at 1

o. « ! b . - bli l yields K(.) ; 1. Hence , y1 I U1 po. = -23dB is a typical value of TBM-tasks y1 having P(H~) 0.5. 1

Following the assumptions of the OCM (Kleinman, Baron, Levison, 1971), the perceived information y (t) is processed by an -p optimal observer (i.e., a Kalman-filter cascaded with an optimal predictor) that generates a best estimate x(t) related to x(t) of the observed system; I.e., if the err~r covariance matrix

m

L

i=l

(f . + f .. )

y1

y1

~

1, P

yo

-23dB

(10)

(16)

W. Stein and P. H. Wewerinke

224

then x(t) minimizes Tr {~} , where the trace Tr{.}-indicates the sum-of the diagonal elements of ~ . The optimal observer yields x(t) as well as ~ , so that estimate yet) and other variables can be derived, since-the matrices ~, ~, and C are defined by the experimental situation considered.

where E {.} indicates the ex pec t ed value in t respect of the ensemble an d the time. The moving average

The TBM-model assumes that the human generates the response process u(t) by maximizing the specifiable expected utility. Thus, applying an optimal Bayesian decision rule (Sage, Melsa, 1971), u(t) is defined as a process of required single-observa tion decisions,

has regard to the assumed span T

P(H1 Ia ) u(t) ={Dl if

P(HO I~:)

u

i: K '

(17)

t

n( t)

l /T

srn

J t-T

net) dt

( 21)

srn

=4s of sm short-term memory (Sheridan, Ferrell, 1974) and is affected by the fai lure z (t). The -y FD-metric includes the trainable speed/accu racy tradeof f Td(PF,P ). Detecting failures M of multiple-process situations in a minimal time T: presumes optimally a ll ocated f r ac tions of attention f* yi'

DO else, where P(Hi la ) is th e probability that hypo. -x thesis Hl is true, given information ~x = (i(t), by the observer. Ku denotes

I)

the decision threshold ( 18)

where u .. is the utility of responding lJ .

.

u(t) Dl, if het) = HJ is given. The reference ratio po., the a tt en tion indices f . and yl yl the dec ision thr es hold Ku are the adjustable model parameters. The decision e rror Pe=Pfa+Pms primarily dep e nds on th e parameters of th e experimental situations as well as po. and f . yl yl (i.e., the given information ~x)' whereas Ku affects the error ratio R =P /P first of all. e af r n s The FD- model assumes that the human's deci sions are based on the innova tions process net) of the Kalman filter given by net) = C x(t)+z (t)+v(t)-y(t), --

-y

-

-

( 19)

whereby time delay T ; 0.2 s is negli g ible in respect of detection time T . If no system d failure has occurred (i . e., z (t)=O), then -y net) is a zero-mean white Gaussian process having covariance N. If a failure occurs (e . g., a ramp function z (t)), then net) has -y a non-zero mean, but covariance N as before. Optimally detecting the system failure requires a numb e r of sequential observations or, correspondingly, an observation interva l Td=td-t that depend on the desired detection f accuracy (e.g., P =P =0.05). Regarding failF M ure situations having PM=O (e.g., ramp fail ures z (t)), the expected detection time is given-Yby

(20)

EXPERIMENTAL PARADICHS Two coherent experimen t a l paradigms are for mulated below covering six assumed keyfactors of tol erance -b a nd monitoring and failure de tection that are listed in Table 1. The paradigms can be rel ated to various multiple -pr ocess s itu ations (e.g ., control of fast and s lowly responding systems , vehicles , and industrial plants), since each factor i s varied within a broad range. TABLE

Experimental Factors

(indices i ,j r e f e r to Lhe processes) numb er of displ a yed processes

(1) N

a (2) w

bandwidth

01

P (H~) event prob a bility

(3)

1

(4) G a (5) r pij

field of Vlew

( 6)

l evel of fa ilure cou plings

P fij

level of process co uplings

Thus, questions concerning the a nalysis, de sign, and evaluation of man - machine systems can be considered on different levels of spe cification. 1 . Information leve l. 2. Display l eve l 3. Environmental and physical level. The information l evel r e l a tes to al l above factors except C , for the matrices A, E, C, a nd W include i~trinsic properties ~f thedynamic system under consideration. The display level primarily refers to the observa tion matrix C and the task-specific factors P(H~) and Pf~" Furthe r more, the perceptual 1

1J

thresholds a . and th e observation noi se v.(t) yl 1 are affected by the at tributes characterizing the actual display devices (e.g., e lectromechanical versus e l ectronic , level of sca ling versus level of integration, monochromat ic versus col or) . The physical level is connected with the workspace area and the control panel a nd, thus, relates to the field of view G that affects human attent i on shar ing. He con~ide r ed Ca runnin g up to 3" by 34

Mode l- ba sed Predi c ti on o f Human Performan ce

225

deg re e s of v i s ua l a r c . Tak ing int o a ccount th e s e fac t or s a nd l eve l s i s base d on th e pe rf o rma nce / wo r k l oad me tri c of th e a bove human o pe ra t o r mo de ls .

sys t em failures af f ec tin g mo re than a single di s pla ye d varia bl e , s o th a t r edund a nt informa ti on i s y i e lde d.

App l y i ng the pa r ad i gm t o a g i ve n dyna mic sys t em re quir e s app r oxima tin g Eqs. ( 2) and ( 3) by a se t of c oupled second- o r de r sy stems,

RES ULTS AND I NTERPRETATION

y ;( t) + 2s . w ~

~

.y. ( t )

o ~

~

2 + w .y .(t) o ~

~

( 22 ) wh e r e

Ij4s .w3 . ~

l ets equiva l e nt va ri a nces of

o~

wi(t) a nd Yi(t) . Ass uming a s t eady s t a t e , t he cova r i a n ce s~ , ~ ,

~( t), ~ ( t ) ,

a nd Y o f

a nd

obey

L (t)

0,

(23)

Huma n pe rforma nc e in s itua tions according to the experiment a l pa r adi gms is illustrated below, wh e reby th e high l e ve l of data / model co rrespondence ( St e in, 1981; Wewerinke, 1981a) ju s tifie s fo cu ss ing on mo de l results. Figure 2 summa ri ze s TBM-r e sults r ega rding the factors Na , wo i' a nd Ga · Th e dec i s i on e rr o r Pe=Pfa+Pms r ep r esent s a s ing l e -process s itua ti on and depends on th e bandwi dth woi a nd the as soc iated obse r va ti on no i se r a ti o P .=po./ f ., whe re yl yl yl O th e r efe r e nc e r a ti o p . =- 23 dB i s t ypical of a yl TBM-t a sk having eve nt proba bilit y P(H:)=0.5. 1

(2 4 )

Y

wh e r e t he di ago na l e l eme nts of Y e qu a l

0

2

.•

y~

Thu s , the d i s p l aye d pr oce s ses Yi(t ) ,i=1, ... , Na a r e a pp r ox i ma t e l y c ha r ac t e r ized by bandw i d t hs W . , fix e d da mpin g r a ti o s s . =s =1 / 12, va ri2

o~

a nces

0

~

a nd pr ocess coup l ings P .. be t wee n

.,

pq

y ~

y . (t ) a nd y . (t) , Pp ; J' ~

= Y .. /

IJ

/Y .. U

( 25)

Y ..

JJ

whe r e Y. . ,i,j =1 , ... , N de no t e th e e l eme nt s of a

~J

co va r i a nce ma t rix Y. Approxima ting th e bandwidth of y . ( t ) i s b ase d on eq ui va l e nt r ec t a ngul a r s of powe r sp ec t r a l dens it y f unction s a nd yi e ld s B.

= W

~

-:, ,'2/ 4

. o ~

(26)

[o r th e a bove second- o rd e r s ystem (Benda t, Pi e r s o l, 197 1) . Th e e ve n t pr obab ilit y P ( H l )=l - P( H ~ ) of pr oce ss y.(t) i s g i ve n by ~

~

Fu r th e rmo r e , Fig. 2 r efe r s t o mo nit oring N uncorrela t ed, homogeneou s va ri a bl es y. (t),a 1

i=1 , ... , N hav ing w =w = ... a nd P(H~)= a 0 1 02 1 P(H~) = ... , so that P(H ) =0 . 5 i s th e combined eve nt pro ba b i l i t y of Na processes . Ac cording O

J

~

Huma n time de l ay l i s f ixe d a t 0.2 s and pe rce ptu a l thr es ho l ds a r e neg l ec ted.

t o f . =f /N , f =1, a nd p .=- 23dB, the full y l yo a yo yl l eve l of a tt e nti on with out l o s ses is unif ormly a ll oca t ed t o N pr ocesses . Th e P -curves a ri se a t ze ro, a inc r ease mon o t o no~sly with W . 01

a nd P ., an d t e nd t owa rd s th e a s ymptotic maxiyl mum P( H: ) runnin g up t o 0 . 5 in th e gi ven ex1

amp l e . Pe a s a f un c t io n of wo i' be ing approxi mate l y linear a t P . =- 23dB , c ur ves with inyl c r eas ing no i se / signa l r a ti o P . . yl

~

th e r es pec t i ve probab il ity den s it y f un c ti on p(y i) a nd th e to l era nce ba nd [b ,b J. The li ui fa i l ur e c oup l ings P .. r e l ate t o th e system fq f a ilur e s z .(t) , z .(t) of Eq . (3) th a t a r e yl yJ ge ne r a t ed by ra mp f un c t i ons i n this parad i gm ,

{~

i f t
O.S -8dB

Pe 0.4

-14dB

03

-lOdB

( 27)

0.2

Th e FD - pe r fo r ma nces de pend on t h e s l ope r a t io c . / 0 ., so th a t c =0 .1 0 . pe r second I S ro y ~ rl y~ u se d t o defi ne t he st a nda r d fa i l u: e ro(t-t ). f Thu s , t he fai lu re coup li ngs a r e g I ve n by

01

t - t f ) c [1. i f t :i: t f .

o.s

2

1.S

Wo;

Pf;J' = z .(t) / z .( t ) = c . / c . , ~ y~ YJ r~ rJ

(28)

. a nd c ·rO; othe r wi se P ' ' i s fJI rl rJ rJ us ed i n s t ea d of P .. . Si mil ar coup ling meas f ~J ur es can be f ormul a t e d fo r o th e r fa ilure t ypes , too . Fai l u r e coup lings are cau sed by

whe r e c

. ~c

Py ;

Fig . 2.

2.5 [rad/s)

Dec isi on e rr or P as a function of ba ndw i dth W .e 01

The event probab ilit y P( H:) i s a n i mpo rtant 1

facto r of TBM-t as k s r ef l ec ting as pec ts of rare

226

W. Stein and P. H. Wewerinke

or frequent events in man-machine situations. The here not figured decision error Pe versus P(H~) arises at zero, increases within

20.--r-'~----------------'

Td[S)

~

o

~ P(H~) ~ 0.5, has the maximum at P(H~)=0.5, ~

1P

~

_17dB

and decreases within 0.5 ~ P(H~) ~ 1.0. A major outcome of TBM-investigations pertains to the effect of process couplings P .. that

Y1 -20dB

P~J

10

is paralleled by the failure-detection results (see Fig. 5). Hence, the effect of redundancy due to P .. seems to be negligible P~J

within the investigated range 0 ~ P .. ~ 1/12, pq

whereas p .. > 1/12 will hardly exist in acP~J

tual systems.

O+---~----~---.----.---~

Attentional losses, although neglected in Fig. 2, have to be considered, if the factors Na' woi' G , and, consequently, the frequency a of visual scanning exceed a certain level. Given a TBM-task with Na=2 homogeneous displayed processes, a field of view G having 34 degrees of visual arc, bandwidth~ w = 1 rad/s, and a combined event probabioi lity P(HI)=0.5, then the effective level of attention according to Eq. (9) is reduced to fYl + fY2 = fyO = 0.5, which has been sup-

Based on the assumption of ideal observation and signal reconstruction, monitoring a process y . (t) requires a fraction of attention, f ., sEaling with its bandwidth W • (Kleinman, o~

Curry, 1977). Thus, monitoring y.(t) with a fixed f . may result in an error~scaling with y~

W •• o~

Respecting Fig. 2, signal reconstruction

might be assumed, as far as Pe is approximately proportional to W .. Regarding the optimal allocation of attention, tolerance-band monitoring might parallel manual control (Kleinman, 1976; Wewerinke, 1977b) and failure detection tasks (Wewerinke, 1981a) in some respect. Details are given by monitoring multiple processes Yi(t) ,i=l , . .. ,N a that are inhomogeneous in bandwidth woi and

e~

the product of associated parameters, W .P(H~), ~

that scales with the dwell fraction fdi of foveally observing y.(t), as eye-movement data have shown. Hen~e, it is assumed that the optimal fractions of attention, f*., y~

i=l, ... ,N a , allocated to the displayed processes y.(t), i=l, ... , N minimize the cost function~l a N

a

a

L

i=l

f(P

./P(H~).

e~

~

15

2.0

2.5

Woi

Fig. 3.

[rod Is)

Detection time Td as a function of bandwidth W . o~

rized in Fi g s. 3, 4, and 5. Th e consider e d situations involve idealized condition s having the perceptual threshold s a .= a · .=0 y~

and the baseline ratio P

y~

=-20dB. Henc e , the

yo effective noise/signal ratio P . is giv e n by y~

/f ., where f

. is the fra c tion of

y~ y~ yo y~ y~ attention associated with th e displayed variable y. (t). Attentional losses due to scanning are ne~lected. Superimposed failures z . (t) y~

are generated by th e standard r a mp ro(t-t ) f with a slope of 0.10 . per second. Furthery~

more, a fixed FD-accuracy is assumed that includes the probabilities P F =0.05. (i. e ., false alarm) and PM=O.O (i.e., miss e d failure).

y.(t). The noise/signal ratio P .=-20dB r e ~

y~

fers to the level of full att e ntion, f .=f =1. Td versus W ., generally being y~ yo o~ non-monotonous, is approximately constant in the upper region o f bandwidth (i. e ., beyond W .~1 rad/s). The level of Td prima rily deo~

pends on the effective noise/signal ratio P . that is a function of the fraction of attenY~ tion, f ., and the perceptual threshold a ..

event probability P(H~). The process-related decision error P . is~highly correlated with

l/N

10

Figure 3 illustrates det e ction time Td versus bandwidth woi of observin g a singl e proc e ss

o~

o~

0.5

P .=P .. =P

ported by performance as well as eye-movement data.

y~

o

(29)

Results from failure detection relating to the factors woi' Na' P ' and P fij are summapij

y~

y~

In any case, Td is increased by a·.

y~

(i.e.,

the threshold of rate information Y.(t» ~n the lower region of bandwidth w ., ~ince o~

o .<3a·. is given there due to 0·. y~

y~

y~

~ ~

. 0 .

o~

y~

(see Eqs. (11) to (14». It is to be added that Td is sensitive to rate information rather in the lower than in the upper region of bandwidth. Consequently, Td of actual situations is approximately constant. Due to a .=a· . =0, Td reported in Fig. 3 is smaller yl yl than in actual situations, especially within the lower region of w . In sum, Td is only oi weakly dependent on w . oi

Model- based Pred iction of Human Performance

1.0

20

0.5

0.25

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,

/

Td [51 I /

,

/

/

/

/

I

I

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o

Fi g . 4.

2

4

6

8

10

De t ec tion time Td versus number o f proc e sses Na

Figure 4 r e pr ese nt s monitoring Na uncorrelate d homo gen eo us proc e ss e s Yi(t) ,i=l, ... ,N

a (i. e ., process c ouplings P .. =0), whereby a p1.J r a mp fa ilur e ro(t-t ) 1.S given on a single f proc e ss. Th e l e ve l o f full attention , f =1, yo is uni f ormly allocated resulting in f .=l/N y1. a and P . =P If ., wher e by a .=a·.=O. Certainly, y1 yo y1 y1. y1 Na increas es .the . det e ction time Td monotonous ly, but dupl1cat1n g N ef fe cts a less than duplicat~d T . UnlikeaFig. 4, a · .#0 of actual d y1 situations caus e s Td l e ss depending on w ' oi 15~------------------------~

Td [51 14 13 12 11

10

o

0.2

0.4

0.6

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Fig . 5.

Det e ction time Td as a function of couplings P .. and p .. f 1J P1J

Figure 5 describes detection time Td as a function of failure couplings P .. and proflJ cess couplings p ... The situation involves P1J the displayed proc e sses Y1 (t), Y2(t) corresponding with w l=w 2=0 .2 5 radls and P l=P 2= o 0 y Y =-1 4dB, whereby the two ramp failures ro(t-t ) f and P 12ro(t-tf) are superimposed . Thus, redundancy generated by P

reduces Td considerfij ably. The effects of P .. , paralleled by the p1.J

227

TBM-investigations, are weak and might be negligible in actual situations. These find ings are consistently supported by both data and model, whereas a potential effect of correlated processes is emphasized in the literature (Kleinman, Cu rry, 19 77; Pew and others, 1977) . Fur th er findings relate to eye- movement data, the optimal al l ocation of attention and the speed- accuracy trade-off at failure detection . Thus , tolerance-band monitoring and fai lur e detection are complementary tasks in respect of the information and decision structure . A TBM-d ecision presumes an appropria t e obser vation only, whilst making a FD- decision with a specified level of accuracy i s based on an amount of information that r equires multiple observa ti ons . An optimal FD-decision presumes a sample of n sequential observations, whereby n depends on the information in the samp l e and the specifi e d FD-accuracy (Sage, Melsa, 1971). An indication to ideal observation and signal reconstruction might be given by a task error sca ling with bandwidth w ' Consequently, oi signal reconstruction is li kely in case of TBM , bu t unlikely in case of FD .

CONCLUSIONS Partly new concepts have been presented to consider questions concerning analysis , design, and evaluation of man - machine systems. The concepts are rooted in the elaborated performance/workload me t ric .of human operator models that are based on the information structure of the optimal control model (OCM). The models pertain to fundamental multip l eprocess tasks in the area of supervisory control that are given by fast and slow l y responding systems. Thus , estimation, control , and decision theory in connection with state space techniques provide the basis for a multivariable system-theoretic approach to man - machine systems. The presented paradigms turn out to b e appropriate tools for reducing the complexity of man- machine problems in theoretical and experimental r e spect . Deve loping design methodologies is considered a problem of overwhe l ming size that presumes long-termed scientific p r ograms . The model based concepts discussed herein are viewed rather complementing than substituting the conventional design methodology .

W. Stein and P . H. Wewerinke

228 REFERENCES

Baron, S., and W.H . Levison ( 1977). Display analysis with the optimal control mod e l of the human operator. Human Fac tors, 19, 437-457 . -Baron, S., and W.H. Levison ( 1980) . The op timal control model. IEEE Conf. Cybern. & Soc., pp. 90-100. Bend~ J.S., and A. G. Piersol ( 197 1) . Random Data. Wiley, New York. Clement, W.F., H.R. Jex, a nd D. Graham (1968). A manual control - display theory applied t o instrument landings of a j e t tran spo rt. IEEE MMS, 9, 93-110 . Clement, W.F. ,-D.T. McRue r, and R. H. Kl ei n ( 1972). Systematic manual control di s play desi gn. In AGARD-CP96 , Gu idance and Control Displ ays . Cox, D.R., and P. Lewis ( 1966) . The Sta tistical Anal ys i s of Series of Even ts. Methuen l Wiley, London . Curry, R.E., D.L. Kleinman, and W. C. Hoffman (1977). A design procedure for controll display systems. Human Fac tors, 19, 42 1436. -Director, S.W. (Ed.) (1981) . Compu t e r- aided design. Proc. IEEE, 69 , 118 5-1 376. Gai, E.G., and R. E. CurrY-(1976) . A model of the human observer in fai lure det ec ti on tasks. IEEE SMC , 6, 85 -9 4 . Hess, R. A. ( 1977). Anal yt i ca l d ispl ay des i gn for fli gh t tasks conducted under instrument meteorological co nd iti ons. I EEE SMC, 7, 453 - 461. Hess~ R. A. (1981). Aircraft cont r ol - display analysis and design using th e optimal control model of the huma n pilot. IEEE SMC, 11, 465 - 480 . Himme lblau, D.M. ( 1973). Decomposition of Large Scale Problems. North-Holland, Amsterdam . Kleinman, D.L., S. Ba r on , and W.H. Lev i son (1971). A con tro l theoretic approach t o manned- vehicle systems ana l ysis . IEEE AC , 16, 824 - 832. Kl einman, D.L. (1976) . Solving t he op tima l attention allocation prob l em in manual control. IEEE AC , 2 1, 8 13- 821. Kleinman, D.L., and R . ~ Cu rr y (1977) . Some new control th eore tic models for human operator display monito ring. IEEE SMC, 7, 778 - 784 . Lev i son , W.H. (1971). A control th eo r y model for human decision making. Ann. Conf. Manua l Control, NASA SP 28 1. Levison, W.R., and R. B. Tanner ( 197 1). A Control-The ory Model fo r Human Decisio-n---Mak ing. NASA CR-1953 . McCormick, E.J . ( 1976). Human Fac t ors in Engi neering and Design. McGraw-Hill, New Yo rk. Meister, D. (197 1). Human Fac tors: Theory and Practice. Wiley, New York. Pew, R.W., and o th e r s (1977). Critical Review and Analysis of Performance Models Appli cable to Man-Machine Systems Eva luation. Report No . 3446, Bolt Be ranek and Newman, Cambridge, U. S. A. Rouse, W.B. (1981). Human-comput e r int e raction in the control of dynamic systems. Computing Surveys, ~, 72 -99.

Sage, A.P., and J.L. Melsa (1971) . Est i mation Theory . McGraw-Hill, New York. Schmidt, D.K. (1979). Optimal flight control synth es is via pi l ot modelling. AIAA J. Guid. & Cont., 2 , 308 - 312 . -----She ri dan, T.B., and- W. R. Fer r ell ( 1974) . Man-Machine Sys t ems . The MIT Press, Cambridge, U. S . A. Spillers, W.R. ( 1974) . Basic Questions of Design Theory. No rth- Ho ll and, Amsterdam . Spillers, W. R. (1977). De sign theory. I EEE SMC, 7, 20 1- 204 . Stein, w. (1981). A monitoring and decision ma king pa r a di gm . Eur. Conf . Hum. Dec. Mak . & Man. Cont . , Delft , The Netherlands. Topm iller, D.A. ( 198 1) . Methods. In J. Horaa l, K. F . Kr aiss (Eds.), Hanned Systems Design . Pl enum Press, New York. Wewerinke , P.H. ( 1976) . Human control and moni t orin g - models and expe ri ments . Ann. Conf . Manual Control , NASA TH X- 73 , 170. Wewerinke, P.H. (1977a). Human Monitoring and Control Behavior. TR 770 10 U, Nat . Aerosp . Lab . NLR, Amsterdam, The Netherlands. Wewerinke, P.H . (1977b). Perfo r mance and Work l oad Ana l ysis of In- Flight Helicopter Mi ss i on s. MP 77013 U, Nat. Aerosp. Lab . NLR , Amsterdam, The Nethe rl ands . Weweri nke , P.H. (198 1a) . A Model of the Human Observe r and Decision Maker. TR 8 1062 L, Na t. Ae r osp . Lab . NLR , Amsterdam , The Ne th e r lands. Wewerinke, P . H. ( 198 18) . A Model uf the Human Dec i sion Haker Observing a Dynamic System . TR 8 1062 L, Nat . Aerosp . Lab. NLR , Amste rd am , The Neth e rlands. Wewerinke, P . H. (1981b) . A model of t he human obse r ve r and decision maker . Ann . ConE . Manua l Control , JPL 8 1-95 , Calii . Inst . Tec hn., Pasad ena . Wewe rin ke , P.H . ( 1982). A model of the human observer and decision ma ke r - Theory and validation . This Con fe r e nce . Zw i cky , F ., and A. G. \.Jil so n (Eds.) (1967) . New Methods of Thou gh t and Procedure . Springer - Ver l ag , New York.