A method for evaluation of seakeeping performance in ship design based on mission effectiveness concept

3 SEP. 1984

ARCH IEF

To be presented at the 2nd Iternationa1 symposium on Practical Design

in Shipbuilding [PRADS 83],, in Tokyo, October 16-22, 1983.

A Method for Evaluation of Seakeepirtg Performancé in Ship Design Based on

1. mooucrio&

Progress in deterministic and

non-deterministic theories for predicting responses

of ships

in waves have made it possthle for

naval architects

to estimate the seakeeping

quality of ships

in a seaway (1] [2 J. Many

excellent results have been reported so

far,

and some of them have been used in estimating

the sea margin and the wave loads acting on a ship hUll; however, they have not been fully

utilized at the initial design stage of ships

for the overall evaluation of ship performance

in a seaway.

We may mentioñ here that traditionally the evaluation of seakeeping performance has not held a steady position in the

initial

ship design process for various reasons. For

example, a guaranteed speed

in calm sea has

been considered the nst important factor

in

ship design. Moreover, it may be said that no

practical method which enables us to evaluate the seakeeping performance of ships at sea

quantitatively and synthetically has been

established.

In the case of initial design of naval ships or patrol bòats,

it

is i.inderstood that designers pay special attention to the

motion-induced performance, degradation of ship hull, onboard equipment and personnel, which is strongly associated with the execution of

missions even in rough seas (3 J

- (5].

Some

seakeeping criteria are reflected on the design

of hull form, structUre and equipment onboard. Even . in such cases, effects of performance

degradation of equipment on the ship's misaion

at sea are not necessarily evaluated as a whole.

In the present study, the authors propose a

method for the overall and" quantitative

__

t

Mission Effectiveness Concept

-1-Lab.

y. Scheepsbouwkunde

Technische Hogeschoól

Deift

evaluation of seakeeping performance by

introducing a concept of mission effectiveness

which gives a quantitative measure of - the

effects of seakeeping performance on the ship

system capability.

In order to evaluate the mission effectiveness, a ship under a specified mission is assumed to be a ship system, which consists

of various subsystems such as ship hull,

onboard equipment, personnel, etc.

Since each subsystem is considered to be

associated separately with the execution of the ship's mission, the mission effectiveness can

be evaluated by synthesizing the

effects of

seakeeping performance on the function of each

subsystem.

In order to get the quantitative

indices of the mission effectiveness, simple

formulations, commonly used in

reliability

engineering, are introduced.

In this paper, the authors present a method for evaluating the mission effectiveness

in a

narrow sense,

i.e.,

performance effectiveness

of ships at sea.

Examples for evaluating the

mission effectiveness of patrol boats operated

for salvage of ships

in distress at sea are

presented to examine the

availability of

the

present method.

2. SS ION EFFECTIVENESS

2.1 Concept of Mission Effectiveness

The mission effectiveness introduced here is defined as follows:

Let us assume

first

that a ship system provided with a specified mission is completely

effective in calm sea. This abIlity is defined as ship system capability, but when the ship

moves into waves, the ship system no longer has

Ryusüke R(ODP: Prof.e College of Engineering, Univ. of Osaka Prefecture, 4-804 Mozu-umemächi,

-

Sakai, Osaka 591, 7apan.

yoshikuni ZUNITA: Manager, Ship and Ocean Project Read Quarters, Mitsui Engineering and

Shipbuilding Co., Ltd., 5-6-4 Tsukiji, Quo-ku, Tokyo 104, Japan. ifatsumi Z4A: Manager, Ships Technological Department, Maritime Safety Agency, 2-l-3

Kasurnigaseki, Chiyoda-ku, Tokyo 100, Japan.

Hiroshi NAMURA: Assistant Manager, Ship and Ocean Project Head Quarters, Mitsui Engineering and

the same capability because the performance of subsystems onboard may be necessarily degraded due to waves and induced responses of the ship.

Bere, we can define the performance

effectiveness,

the mission effectiveness in a

narrow sense in the present study, which measures what rate of the ship's mission can be

accomplished in rough seas. The mission

effectiveness in calm sea is identically equal

to 100%, indicating the ship system

full

capability, while the mission effectiveness in

rough seas is indicated as the rate of the full

capability.

En

Fig.l,

the concept of mission

effectiveness is shown schematically.

c

I

Fig.l Shematic Representation of Ship's

Mission, Ship System and

Seakeeping Performance

It

is understood that the evaluation of

mission effectiveness is to be done based on

several factors, such as ship's mission, ship

system which includes various onboard subsystems and their own performance, and

causes of performance degradation due to ship

responses in waves.

In evaluating the mission effctiveness

quantitatively, we must (1) clarify the ship's

mission, (2) compose a ship system and relevant subsystems corresponding to the ship's mission, and (3) understand the motion-induced performance degradation of each subsystem onboard.

The mission effectiveness has to be

considered both in short-term and long-term periods because the short-term mission

effectiveness represents the ship's proper

capability in performing the imposed mission

under a specific sea condition while the

long-term mission effectiveness indicates the degree of performing the mission dur ing long time operation in a specified route or sea area.

2.2 Ship System

Since ships usually have necessary

subsystems to perform various missons, we Shalt have to choose suitable subsystems and their combinations for making up the ship system

-2-according to a given mission.

Fig.2 shows the structure of the ship system for the salvage mission by a patrol boat. The

salvage mission consists of (I)

travel to the

position or estimated position of

a wrecked

ship, (2) surveillance of the ship

if

necessary, (3)

saving lives and the ship, and

(4) towing the ship to

a port

if. necessary.

Since the nature of these actions differ, the

ship system shall be composed of necessary

subsystems such as ship hull, main engine,

radar, communication, personnel, etc., for each

action, as shown in Figs.2 (b) (e). In order

to make up the ship system, we introduce two types of system structure

series structure

and parallel structure as shown in the

figure. By iñt±oducing these two types of

system structure, evaluation of the ship system performance can be made quantitatively, as

mentioned in the next section. c.. mw- OF SlIP'S MlSS( ('L'le * .3 I fsiaycIu.Ai

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Cc) Plt1flSl S5Vt1U.* 4ucOFT'l ,.1

t.:

(s) 'l(SSISl aiim ILL & 3I .iTSfl%OUlf-. 3-o '.3

Fig.2 Breakdown of Ship's Mission and

Structure of Ship System

Corresponding to Ship's Mission 2.3 Method for Evaluating Performance

Effectiveness

The method for evaluating mission

effectiveness will be explained by

taking a

surveillance mission as an example. For other missions, the same procedure can be applied.

In order to perform the surveillance, it is

imperative to secure one subsystem or ship hull & structure against capsize or fatal damage due to violent ship motions, and to avoid emergency

halt of one other subsystem or main engine.

If

either. subsystem

fails,

the- ship system

(b) N(S5I _i lOi, ¡ .4 1.1 t.

I.'

* _C plU. & STOIT(JSO t .2

t.,

£

so \ longer has the capability

of

tformiflg surveillance. Provided that

:jnctioflS of these two subsystems are

Independents the system structure is called

2erieS structure in the reliabilitY engineering

f Leid. Here, the performance of each subsystem

jg assumed to be affected independently by sea

envirOflmeflt and resultant ship responses.

Let US suppose the number of the system

component of series structure to be n, and the performance effectiveness of each component to "be ei (i1,2, ...., n); then the performance

effectiveness of the series system e5 can be

given as

n (1)

e5 = flej

j=l

by using the expression cited from reliability engineering (6 1. The suffix i is indicated

i-th component of series structure as shown in

Fig. 2. Thus we can understand that the

series structure in the ship system plays a

significant role in executing the mission.

If navigation is ensured, the patrol boat

must get into action of surveillance by using necessary subsystems onboard. As shown in

Fig.2 (C), the third component of the series

structure, which indicates the function of

search for a wrecked ship and her personnel,

consists of subsystems in parallel. In case of

the parallel structure, components are

complementary to each other to execute the

mission. In other words, the system fails to

execute the mission only when the performance

of every subsystem decreases under a prescribed level simultaneously.

Given the number of the component n and the

performance effectiveness of each component ej

..., rn), we can calculate the

performance effectiveness of a parallel system by

ep = L

-iDi

ej). (2)

In evaluating the mission effectiveness of

the ship system, which is composed of series

and parallel subsystems, we can apply equations (L) and (2), and their combinations.

Since most of the equipment onboard is to be

operated by crew, we must take the. effect of

the human performance into account in

evaluating the performance of each subsystem.

This is the reason why the personnel system is

connected serially to other onboard subsystems. The propulsion system from which performance

is defined by nominal speed loss is allocated

separately from the main engine system, because

the nominal speed Loss is unavoidable for a ship sailing in rough seas and it must be considered as the performance degradation of

the ship system, separately from the emergency

halt of the main eng inc subsyh tern.

2.4 Estimation òf Mission Effectiveness

As mentioned in previous section, the

mission effectiveness is divided into two categories: short-term and long-term. We shall

have to illustrate how to estimate these two kinds of mission effectiveness. Fig.3 shows the block diagràm for estimating short-term and long-term mission effectiveness. As shown in

this figure, the fundámental flow of the

estimation procedure is the sama as that for the statistical estimation of seakeeping qualities of ships in a seaway (7], except for the parts related to mission effectiveness and performance degradation of subsystems. The parts, as indicated by heavier-lined blocks in Fig.3, are newly introduced to fit the present

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Fig.3 Block Diagram for EstimatiflgShOrtterm and Long-term Mission

Effectiveness of Ships

3. PEBF0R.NOE DEGRADATION 0V SUBSYSTEM ONSOARD

In order to estimate the performance effectiveness of subsystems onboard, it is of prime important to understand the correlations of the magnitude and severity of various

responses of a ship to the degradation of function and performance of onboard subsystems.

In this paper, those correlations are defined

as performanCe degradation. As far as the authors know, very few reports are available to specify the performance degradation of onboard equipment; consequently. the performance

degradation häs been estimated for some cases by reference to literature and advice of crewmen.

Several examples for the performance degradation" of ortboard subsystems of patrol boats are shown as follows:

(L) Human performance

The main causes which degrade the crew's workability are roll and pitch angle and vertical and lateral accelerations at locations

IL.Tt crIICTl.(SI?S L-Tt'a vaSI STA?!?T!C?

IL'a

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concerned. Fig.4 shows the human performance

degradation estimated on referring

te reports

by Cosistock et.al. [5], Aertssen [8] and ISO

Recommendation (9].

In the figure, light work

means work in the steering room, operation

room, etc., and heavy work means work oh deck and in the engine room, etc.

Effects of slamming and shipping water on deck are deleterious to human performance; however, these are not taken into account here

but are considered for the safety of ship hull

and structure.

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Fig.5 Estimated Attainable Speed of Ships in a Seaway

The estimation of nominal speed loss is carried out by considering added resistance due to

winds and waves [10], under assumptions that

the characteristics of main engine and

propulsIve performance are not influenced by waves (11]. Fig. 5 shows the examples of

estimated nominal speed loss of two different

ships.

Hull-Response Interaction

The safety of ship hull and structure including equipment onboard may be threatened by slamming, shipping water, excessive wave bending moment, undesirable bull vibration,

etc. Of these, slamming and shipping water (deck wetness) are the most important. They are deleterious to other subsystems indeed;

however,

it is quite difficult to distinguish

the effects clearly.

Therefore, slamming and

shipping water are considered to have

deleterious effects on the safety of ship hüll

and structure including effects on all other

subsys tens. After Aertssers (81 and comstock

et.al. [

5 1, the performance degradation due to

slamming and deck wetness is gIven as functions of numbers of oócurrence as shown in igs.6 and

7.

en

io is 20

mme e eAn once sTuu 90 ea

J

Fig.6 Effect of Deck-wetness on the

Performance of Hull and

Structure Su.bsystem

(SOC) e VJm,on eo ea

Fig.7 Effect of Slamming on the Performance of Hull and Structure Subsystem (5) Helicopter Operation Performance

Although the helicopter operation system might not be included in the ship system,

its

operational, effects on ship system capability

are obviously significant in performing the

surveillance mission. The effects include shortening the _{search time and enlarging} the search area, even though the endurance in one

flight is limited.

Fig.4 Euman Performance Degradation Due to Ship Responses in Waves

Radar Operation Performance

The function of radar is not so vulnerable

that its pérformance hardly decreases due to

ship motions. The function, is ensured to be fully effective under 25 degree inclination of the ship's body. Thug, the performance of a radar system depends on thé performance of the personnel who operate it.

The same treatméflt is applied for the

commun icat ion system.

Propulsion system performance

Due to winds, waves and resultant ship

motions, the speed of a ship necessarily

decreases. This speed drop is called nominal speed loss, which is proper to each ship and is

determined by sea conditions encountered.

However, the take-off/landing ability, whidh

is considered the measùre of the helicopter

operation performaflCei depends on relative wind

velocitY and motions of the ship. Fig. 8 shows

the helicopter operation capability in winds

and waves. These criteria are given for VTOL aircraft in accordance with Constock et.al.

1.5].

aóStsfl nh& tnLlIbl

4.2 Short-Term Mission EffectiveneSS

(1) PerformañCe Effectiveness of Subsystems Of all subsystems onboard, the personnel system is one of the most important subsystems.

vig.9 shows an example of the effect of roll

and vertical acceleration on human performance. The curves are thé contours of mission

effectiveness. This figure is basically the

sa expression as the seakeeping criteria

given by Kitazawa et.al. (13], because from the figure we can easily understand the effect of

1 4 5 7.5

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Fig.8 Relicoptér Operation Capability in Waves and Relative

Wind Envelope

4. SHOf-'EBM MISSION EFPECrIV4ESS OF PATROL BOATS

4.1 Patrol boats

In the present paper, seakeeping performançe of patrol boats engaged in salvage missions is

evaluated. Four typical existing patrol boats

of different size are chosen to compare the

seakeeping performance at sea. For further

comparisOfl two prospective patrol boats of

0mjSubmerged Catamaran (SSC) or

Small-Waterplafle.Aea Twin-Hull (STH) type are

selected. In Table 1, the main particulars of

patrol böats selected here are shown. In the

table, P indicates patrol boats and M denotes

mono-hull ships. SSC-1 is the existing semi-submerged catamaran ship (121 but SSC-2 is a

tatively_deSigned ship for the present

study.

Table 1 Main ParticulaçS of Ships

ship resflSe3

a seaway.

expression

the seakéepirtg

5

on the performance of a ship in

But, one weakness in this

that we are not able to evaluate performance on the whole.

etMT . E - VEOTOCM.

t Accac17A

Fig.9 An Example for the Effect of Ship

Responses on the Performance

Ef fectïverteSs of personnel System

pig.lO also shows personnel effectiveness from the. other standpoint of view in order to clarify the total effectiveness for the

personnel system as well as the separate effect of a certajn ship response on seakeeping performance at a constant ship speed. In this

f igure, the personnel effectiveness is

calculated by equation (1), so that we can

understand that even if individual effects are small, the integrated results are significant.

PI-1 PE!L ZÇRCT)Y0005S jruzc. 67)1% 66.E.

-Fig.lO An Example for the Performance Effectiveness of personnel System at Constant Ship Speed

(Fn0.3)

Figs.].]. (a) and (b) show examples of mission

effectiveness of PM-2 and sSC-2 for the surveillance mission in various conditions of beaufoct scalèo The ship speed corresponds to

MCR output of the main engine. In the figure.

the performance effectiveness of three principal subsystems and integrated missiofl

effectiveness are shown. As shown in the

figure, the mission effectiveness for

surveillance strongly dependS en the performance effectiveness of series structure

of the ship system, and the effect of the

parallel system is not so remarkable since components of the parallel structhre are PI.1 09.3 PI-3 06.4 312

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?ig.l1 Mission Effectiveness of Patro]. Baots

for Surveillance of Ship in Distress

at Sea

-6

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complementary tö each other as mentioned

previously. We also learn from these figures that the mission effectiveness can be improved

by changing the ship's heading to waves.

Fig.12 shows thé comparison of the

calculated mission effectiveness of each ship.

From this figure, we can understand that

performance of a small ship is less effective

than a large ship both in head and beam seas. In addition, the mission effectiveness is

greatly affected by ship type rather than ship

size. In the present study, however, differences of performance and economy in calm

sea between monohuils and SSCs are not discussed. The mission effectiveness in a

broad sense must be evaluated by using the

results of

the cost/performance trade-off in

addition to the authors' study on performance

effectiveness.

:. cAi.,SLA

Fig.12 Comparison of Short-term Mission

Effectiveness between Patrol Boats

of Various Sizes and Types

As indicated in Table 1, the patrol boats

PM-1, SSC-1 and SSC-2 are able to carry a helicopter on board. Although it is inferable

that the use of a helicopter is effectual in

the surveillance mission, the operational merit

of it is difficult to evaluate ist terms of the

short-term mission effectiveness. This is

caused by difficulties

in estimating quantity

of improvements by shortening the search time

and enlarging the search area when a helicopter

is used. Therefore, the authors should say

that the operational merit of a helicopter is

evaluated by a simulation study from the

operation research point of view. The

simulation study is briefly mentioned in the

next chapter.

5. LONG-TERM MISSION EFFECTIVENESS OF PATROL

BOATS

5.1 Statistically Predicted Long-Term Mission

Effectiveness

The long-term mission effectiveness can be

predicted by means of the

statistical

prediction method [7 J which is commonly used

for estimating the long-term responses of

ships. Im thé present study, the method is

modified slightly to be

fit

to the present

purpose. (4) PI3S3! (JI UR FFECTIVÙeS5 :50 50

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we can ca1ulate the short-term mission

'effectivenesh by applying the method outlined

in Chapter 2. The critical significant wave height with respect to threshold imwer level of the mission effectiveness can be determined from calculations of the short-term mission effectiveness for various combinations of significant wave height and mean wave period,

Long-term wave Statistics are necessary to carry out the prediction. Since, according to long-term wave data analyses, the probability

distribution of wave height and wave period

follows the log-normal probability law [141,

the log-normal distribution is assumed for wave height. The statistical values are obtained by 'analysing the waves described in the Area E06N

and EO6S, North Pacific Ocean.

Fig.13 shows an example of lcng-term

probability of operation for

the surveillance

mission. This example is obtained for the

ships speeds, Fn0 .3, except for the SSC-i.

The solid lines indicate the cases of uniform

heading from O to 21 while broken lines

indicate the cases of head seas.

It

is understood that the long-term rate of operation

decreases as the shOrt-term mission effectiveness increases and is also affected by

the size and type of the ship.

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Fig.l3 Long-term Probability of Performing

Surveillance as a Function of

Short-term Mission Effectiveness

Since every patrol boat is fully effective

in calm sea, the long-term probability obtained

here gives the index of the

possibility of

executing the surveillance mission for each

atroi

boat. Fig.13 does not show direct

comparison of mission effectiveness among these atròl boats provided.

.2 Long-Term Simulation of PatrOl Boat

Operation

In order to compare the overall performance

irectly from the operational point of view,

imulations of one year of operations were

arr ied Out for all patrol boats under the same

onditions.

7

The main features of the simulation studies

are briefly mentioned as follows:

The data regarding kindS and average time

interval'of sea casualty, kinds and sizes

of ship. in distress, were supplied by

Maritime :safety Agency.

By making use of the Maritime Safety

Agency's salvage manual, drift of wrecked ships, expected locations, effective

search areas, etc., were estimated. From many search techniques, a square search method was applied for patrol boats and a

sector seârch method for helicopters. Frequency'. of sea conditions as a function

of Beaufort Scale in each season was esitmated statistically according to the

long-term wind & wave

statistics.

Sea

conditions, were assumed

to be

unchanged

(a) on the way to the estimated place where a sea casualty occurred, (b) during

surveillance and rescue, and Cc) on the

way to thè home port.

The lower limit of mission effectiveness

for.all missions was considered to be 30%, and under this level, the missions were

not executed.

In order Ito evaluate the operational merit

of a hélicepter, the take-off/landing

operatioñ criteria are estimated for PM-I.

SSC-i and' SSC-2, by using the performance

degradátiòn..Shown in Fig.8. An example

showing . ':the operating envelope and performanée effectiveness on the

take-off/landing operation of a helicopter

is

shown in Fig.l4.

SOC-1

Fig.l4 Effect of Short-term Mission Effectiveness on Helicopter

Take-off/Landing Operation at Sea The simulàtion was repeated 50 times, namely, 50-year simulation was carried out

for each patrol boat to ensure the

reliability of the results.

Results of the simulation are briefly

summarized in Table 2, and the number of

salvages vs.' total operation time per year are plotted in Fig.15.

From thesà results, the following may be

stated:

Ç. 0.3 O.1 01 3C-l) PN.4

(1)

It is clear that, in the case of the

mono-hull type patrol boats,

the bigger ship

has the better seakeeping performance.

Table 2 ResultS of Long-term Simulation Studies

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Fig . 15 Annual Number of Salvages

as a Function of Annual

Operating Tns'e :

On the contrary, in the case Øf the SSC

type, the smaller SSC can salvage more

ships than the bigger SSC. This may be

due to

the

fact that

the service speed

of the SSC-1 is much faster than that of

the SSC-2.

Despite this difference, it is

interesting that the SSC-i, .the smallest

ship among the six patrol boats, has the

best seakeeping performance for the

salvage work of sea casualties.

The average times of a salvagé work for

the PM-i, SSC-i and SSC-2 are much shorter

than those of the other boats. One of the

reasons is obviously due to the

operatioñal merit in the use of a helicopter in the surveillance. Fig.l6

presented the operational merit of the SSC-2 with a helicopter indicating the

plots of the search time by the patrol

boat alone vs. that by the . boat with the

helicopter.

It is understoód, from this

figure, that the search time can be

drastically reduced by the use of the

helicopter, especially when a long

surveillance time _is required. On the

other hand, it is shown that the merit is

not significant when a wrecked ship is discovered within a short time. The same results were obtained for the cases of the PM-i and SSC-i.

r

I

Fig.l6 Operational Merit due to Helicopter Operation for the

Surveillance Mission

Although these results cannot be compared directly with those predicted by the

statistical

method, the simulation study is

very useful in evaluating the long-term overall performance in combinat ion with the predicted

results of the long-term mission effectiveness. 6. CON.UDrNC REMARKS

The authors proposed a method for quantitatively evaluating the overall seakeeping performance öf- ships at. the initial

stage of ship design.

Iñ order

to get the

quantitative measure of the effects of

seakeeping performance on the ship's capability under a specified mission, a concept of mission effectiveness was introduced.

The mission effectiveness was considered to be determined quantitatively by synthesizing the effects of motion-induced performance

degradation of onbOard equipment.

In order to

synthesize the effects, an idea of ship system

was introduced, which was composed of a

combination of series and parallel structure of

various orboard subsystems: hull structure,

onboard equipment, personnel, etc. Simple

formulations, which have been conly used in

evaluating the

reliability

of systems, were

applied to evaluate the performance

effectiveness of the ship system.

For the more effectual express ion -of the

concept, it was classified into two categories:

Short-term and long-term mission effectiveness. The former is estimated by synthesizing the effects of performance effectiveness of subsystems using the formulation introduced here while the latter is estimated by means of

non-deterministic methods under the condition of keeping short-term mission effectiveness

above a specified level, in a certain route and sea area. Another method, s imulat ion study, was proposed for evaluating the long-term mission effectiveness from the aperationa.1.

point of view. By this simulation study, the

ópera tional merit which is expected when another different system is used as an assistance of a ship system, such as -a

helicopter, was estimated.

Applying the present method to the salvage mission of patrol boats, the authors were sure :1

-i 05 05 05 0&Cfl

a a sa

(WI la a 22.0 0.7 0 (0. ¡01) (0.153)

4-)

of

the availability of the method and,

as a

result, are able to conclude as follows:

The concept of the mission effectiveness

and its evaluation method proposed in this 5. paper is remarkably useful for evaluating

the seakeeping performance of ships at the

early stage of ship design.

The idea of a ship system and the formulation to evaluate the performance

effectivess of

a ship system are quite

important.

The effects of the ship's inherent

seakeeping performance on ship's mission can be evaluated by calculating the

short-term mission effectiveness.

(4) In order to evaluate the overall

seakeeping performance of ships within a

long time period,

the statistical method

as well as

the simulation study for the

evaluation of the long-term mission effectiveness are useful.

Since information about the motion-induced

performance degradation are not necessarily avaIlable for the, estimation of performance effectiveness of subsystem onboard, the authors

should say it is necessary for us to accumulate

the adequate information for the more accurate 11. estimation. In the present study, the authors

concentrated on the mission effectiveness in a

narrow sense, i.e., peformance effectiveness;

however, the trade-off between costs and

performance is one of the most essential

processes of the

initial

ship design.

Therefore, a ship designer should consider it

in the evaluation of the mission effectiveness

in a broad sense.

Nevertheless, the authors are trustful that

the present method must be useful in evaluating the performance of marine systems at sea.

The authors would like to express . their thanks to Prof. K. Taguchi, University of Osaka

Prefecture and Dr. M. Takagi, Hitaàhi Zosen

Corporation for their helpful discussions.

They are also grateful. to Mr. M. Matsusbima,

Mr. H. Maruyama and Mr. S. Miyake for their cooperation and . considerable assistance. The present study was supported

in part by the

Science Reséarch Fund of Ministry of Education.

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