Multi-Criteria Decision-Making Approach for an Efﬁcient

Postproduction Test of Reconﬁgurable Hardware System

Asma Ben Ahmed, Fadwa Oukhay and Olfa Mosbahi

Universit

e de Carthage, Institut National des Sciences Appliqu

ees et de Technologie, LR11ES26,

Laboratoire d’Informatique pour les Syst

emes Industriels (LISI), 1080, Tunis, Tunisia

Keywords:

Postproduction Test, Multi-Criteria Decision-Making, AHP, Choquet Integral.

Abstract:

This paper proposes a multi-criteria decision-making approach for guiding the postproduction test of reconﬁg-

urable hardware system (RHS). The latter is a hardware device that allows to change the hardware resources

at runtime in order to modify the system functions and dynamically adapt the system to its environment. The

optimization of the RHS postproduction test process is a matter of concern for manufacturers since the testing

activities have a signiﬁcant impact on achieving manufacturing objectives in relation to quality, cost and, time

control. Taking into account the fact that testing all potential faults is infeasible in practice, the testing process

hence needs to be optimized by prioritizing faults according to a well-deﬁned set of criteria. Accordingly,

multi-criteria decision-making tools prove their effectiveness in selecting faults to be tested. The proposed

method consists in targeting a limited number of faults that require more attention during the testing process.

Two strategies are investigated through the recourse to analytic hierarchy process and Choquet Integral. This

study helps to determine the most critical faults that have the highest risk priority score. A case study is pro-

vided to illustrate the application of the proposed approach and to support the discussion.

1 INTRODUCTION

Over the last decade, embedded systems have wit-

nessed an outstanding growth to meet technological

advancements. Due to the fact that the new generation

of embedded systems is addressing new criteria such

as ﬂexibility and agility, reconﬁgurability has become

an evolving approach in real-world applications and

scientiﬁc research. Therefore, a new class of systems,

which is fundamentally based on the ability to change

has emerged. An RHS is a hardware device that per-

mits to change the hardware resources at runtime in

order to modify the system functions and therefore

to dynamically adapt the system to its environment

(Ben Ahmed et al., 2018b). As the hardware system

manufacturing process is imperfect, several defects

including open circuits, bridging and stuck-at faults

may occur. Taking into account that these systems are

increasingly fragile and safety-critical and that the ac-

tual industrial world is facing the challenge of zero

defect, testing becomes an essential step for acquir-

ing fault-free and high-quality devices (Eggersgl

uß,

2019). The postproduction test is a crucial phase of

the hardware development process. It ensures that the

system is defect-free before it is released to the cus-

tomers. In industry, the most popular model is the

single stuck-at line (SSL) model (Pomeranz, 2020).

Given a device under test (DUT) and a fault model,

it is possible to construct the initial fault set which

contains all possible faults in the DUT. As the cost

of the testing process is intensely inﬂuenced by the

number of faults to be tested as well as the number

of test vectors to be applied, many interesting aca-

demic and industrial techniques have been carried out

to tackle this issue. In this context, the authors in (Eg-

gersgl

uß et al., 2023) introduce a method that aims

to reduce the number of automatic test pattern gen-

eration (ATPG). This issue is addressed by produc-

ing compact test sets and hence minimizing the vol-

ume of test data , test application time, and automat-

ically the cost of testing. The study in (Yang et al.,

2021) concentrates on the generation of high-speed

digital test vector to accelerate the testing process and

therefore allowing the detection of fault rapidly. Fur-

ther approaches, so far, investigate a machine learn-

ing based fault diagnosis (Higami et al., 2022). The

method does not require the performance of fault sim-

ulation or needs fault dictionaries storage for ﬁguring

out the candidate faults. The work in (Kung et al.,

2018) presents a new test pattern generation ﬂow to

Ben Ahmed, A., Oukhay, F. and Mosbahi, O.

Multi-Criteria Decision-Making Approach for an Efﬁcient Postproduction Test of Reconﬁgurable Hardware System.

DOI: 10.5220/0012862300003753

Paper published under CC license (CC BY-NC-ND 4.0)

In Proceedings of the 19th International Conference on Software Technologies (ICSOFT 2024), pages 511-518

ISBN: 978-989-758-706-1; ISSN: 2184-2833

511

target both stuck-at and transition faults at the same

time in one ATPG run without recourse to changing

the ATPG tool. A compact pattern set can hence

be obtained. It needs less volume of test data and

shorter time of test application without affecting the

fault coverage for both types of faults. The above-

cited works focus in the optimization of the testing

process through the reduction of the number of test

vectors.

As already mentioned, the optimization of the

number of faults is also worth considering. In fact,

testing all faults is practically infeasible as it strongly

increases the manufacturing costs and time delays.

Hence, the number of faults to be targeted during the

testing process crucially requires optimization. Con-

siderable work has focused on reducing the number of

faults particularly for RHS. The work in (Ben Ahmed

et al., 2018b) investigates a new testing methodol-

ogy using the inter-circuits relationships. Such a test-

ing method provides an optimal fault set that can be

efﬁciently used for testing purposes. The work in

(Ben Ahmed et al., 2019) presents a new extension

of the standardized boundary scan test method. The

endeavor is to work on a test approach that offers

the ﬂexibility and convenience needed to test RHS

based on combinational and sequential logic while

ensuring an optimal time and cost. The authors in

(Ben Ahmed et al., 2018a) introduce concepts of oc-

currence and severity ratings in the RHS testing pro-

cess as a means to target the minimal necessary set of

faults while ensuring an acceptable fault coverage rate

that meets manufacturing quality requirements. For

so doing, the authors propose an alternative for the

overall fault coverage that provides guidance for rank-

ing potential faults in terms of their occurrence and

severity. However, it is possible to take into account

other decision criteria such as controllability and ob-

servability. Multi-criteria decision-making (MCDM)

tools are therefore helpful when considering multiple

factors before making a ﬁnal choice.

In this research paper, we introduce a guiding

method for prioritizing potential faults according the

following set of criteria: occurrence, severity, control-

lability and observability. To put it differently, a fault

is weighted according to how frequently it can occur,

how serious its consequence on system functionality,

safety, etc. It is also about how controllable and ob-

servable it is. Taking into account that not all faults

are worth pursuing since they do not have the same

degree of the previously mentioned criteria, this pa-

per investigates the use of analytic hierarchy process

(AHP) and Choquet Integral (CI) to identify the most

critical faults. First, the AHP makes it possible to as-

sess the faults based on each criterion and therefore

to provide a global risk priority score (RPS). The lat-

ter enables selecting the subset of faults that need to

be targeted during the testing process. In the second

phase, the CI operator is employed for the aggregation

of the partial scores obtained for the different faults

according to each criterion in order to deal with the

preferential interactions between the criteria. There-

fore, the risk assessment will be more accurate. As

a consequence, targeting a limited number of faults

helps the industry to optimize test resources alloca-

tion without mitigating the correctness of the system.

The originality of this research, compared to ex-

isting works, lies in considering the risk-based cri-

teria needed for selecting faults to be targeted dur-

ing the testing process. This research also differs in

its use of MCDM tools allowing the reduction of the

targeted fault set without affecting the correctness of

the system. It is feasible to note that MCDM tools

are existing concepts in the literature that are used

for supporting complex decision-making processes in

various domains (Oukhay et al., 2021). However, in

this paper they have been coupled with hardware fault

techniques for reconﬁgurable systems.

The remainder of this paper is organized as fol-

lows: Section II presents the decision-making frame-

work based on risk optimization in the RHS test pro-

cess. Section III introduces the proposed MCDM

method for selecting the targeted faults. Section IV

deals with the suggested case study and highlights

some numerical results that prove the worth of the

contribution. Section V concludes this paper.

2 DECISION-MAKING

FRAMEWORK BASED ON RISK

FOR OPTIMIZING THE RHS

TEST PROCESS

Taking into account that testing all faults is infeasible

in the practice as it strongly increases the manufac-

turing time and cost, the testing process need to be

optimized. For a given DUT and with respect to SSL

fault model, an initial set of faults that includes all po-

tential faults is deﬁned. This fault set can be reduced

through intra-circuit fault collapsing which helps re-

ducing faults via equivalence and dominance relation-

ships (Prasad et al., 2002) (Venkatasubramanian et al.,

2015). The application of this technique minimizes to

some extent faults occurring within the same circuit.

The inter-circuits fault collapsing techniques is there-

fore processed generating a more important reduction

of faults.

As shown in Figure 1, faults generated using the

ICSOFT 2024 - 19th International Conference on Software Technologies

512

inter-circuit fault collapsing present the starting point

of our current approach. In fact, in order to assure ef-

ﬁciency, we propose in this work to focus the testing

process on the critical potential faults. The latter are

the faults that present the highest level of risk since

their appearance would engender signiﬁcant quality

degradation. This is supported by the argument that

pursuing faults having trivial impacts on system func-

tionality would be a waste of resources and time. Ac-

cordingly, identifying the faults to be addressed in

testing can be viewed as a decision-making task in

which assessing the risks associated with the candi-

date faults is needed. In this work, the risk degree of

a fault is assessed by calculating the RPS. The latter

includes multiple criteria: the likelihood of fault oc-

currence, the degree of severity of the effect, the de-

gree of controllability of the fault and, the degree of

its observability. The evaluation of the RPS is based

on the experts knowledge regarding the criticality of

the faults and it incorporates the decision-maker pref-

erences regarding the relative importance of the pre-

viously mentioned criteria. The experts deﬁne an ac-

ceptable level of risk (threshold) according to which

a decision about the fault is made. Potential faults

having RPS lower than the threshold do not need to

be tested. On the other hand, critical faults with RPS

that is higher than the threshold are included in the

testing process. In the following part, we provide an

MCDM approach for calculating the RPS.

3 PROPOSED MCDM METHOD

FOR SELECTING THE

TARGETED FAULTS

3.1 Method Description

The proposed MCDM method, consisting of ﬁve steps

is explained in the following:

Step1: Specify the objective. The goal deﬁned in this

study is to evaluate and prioritize the different faults

occurring within the RHS. The evaluation is done ac-

cording to a ﬁnite set of criteria in order to select

faults that require more attention during the testing

process and therefore to reduce testing workload and

allow better resource allocation.

Step 2: Specify the criteria. Let D be a ﬁnite set

of criteria denoted by D = {d

,...,d

}. To address

and test faults in a circuit, the concepts of occurrence,

severity controllability and observability play a major

role for so doing. Each criterion is deﬁned as follows:

• Occurrence: It gives us an idea about how often

faults can occur. Occurrence can provide informa-

DUT Fault Model

Initial

fault set

Intermediate fault set

Candidate faults

Minimal target fault set

Figure 1: Decision-making framework based on risk for

RHS test process optimization.

tion that help estimate or foreshadow future fre-

quency. Given that faults are not likely to occur

with the same frequency, they need to be weighted

by an occurrence rate. The latter estimates the

occurrence frequency of a fault. Faults with the

highest occurrence rate need to be addressed in

priority.

• Severity: It means the degree of seriousness of a

fault measured by its impact on system function-

ality, performance, safety, or other critical factors.

It is basically measured on a scale, with higher

levels determining more critical issues that need

immediate attention. Poor severity, however, indi-

cates that faults do not affect the functionality of

the system and therefore can be ignored.

• Controllability: It refers to the quickness of set-

ting 0 or 1 values at any point within a system

through its inputs. Good controllability is deﬁned

by the direct manipulation of the system allowing

to excitation of the fault as well as the observa-

tion of its effects. However, poor controllability

problematizes the quick isolation of the fault due

Multi-Criteria Decision-Making Approach for an Efﬁcient Postproduction Test of Reconﬁgurable Hardware System

513

to the fact that the application of inputs might not

activate it. Thus, faults having poor controllabil-

ity present high risk level and require the highest

attention during testing.

• Observability: It indicates the ability to determine

the value at any point within a system by observ-

ing its outputs. It permits the understanding of the

impact of the fault on the system outputs. Low

observability, on the contrary, makes it hard to

differentiate the fault from normal system behav-

ior which problematizes the pinpointing of faults.

Therefore, it is mandatory to focus on faults hav-

ing low observability during the testing process.

The faults are then assessed according to each crite-

rion based on the experts judgement using the AHP

method as described in details in the following steps.

Step 3: Specify the candidate faults set. Let F

be a ﬁnite set of potantial faults denoted by F =

{ f

, f 2,..., f

Step 4: Employ AHP method to assess and prioritize

faults. This step is explained in details in Subsection

3.2.

Step 5: Employ the CI to prioritize faults. This step

is explained in details in Subsection 3.3.

3.2 Prioritizing Faults Using the AHP

Technique

The AHP, also known as Saaty method, is a versa-

tile tool for MCDM that can be applied in different

contexts (Saaty, 1990). In this research paper, the re-

course to AHP is justiﬁed by the fact that this method

allows the organization of the problem of selecting

a limited number of faults which require more atten-

tion into a hierarchical structure of objective, crite-

ria, and alternatives. Furthermore, the AHP facilitates

the extraction of the relative performance scores of

the alternatives associated with each individual crite-

rion as well as the relevance weights of the criteria

through a series of pairwise comparisons. In addition,

it provides a mechanism for checking and improving

the evaluations consistency, which differentiate AHP

from other multi-criteria tools. The application of this

method for selecting a subset of faults is carried out

through ﬁve major steps:

1. Identify the problem and determine the main

objective: selecting a limited number of faults which

require more attention during the testing process.

2. Organize the problem into a hierarchy of lev-

els that comprise the objective, the criteria, the sub-

criteria, and the alternatives as described in Figure 2.

3. Make pairwise comparison matrices for each

element using the Saaty 9-point scale to determine the

relative weights of the criteria and alternatives (candi-

date faults).

4. Determine the weighted average for each can-

didate fault according to the following Equation.

∑

j=1

i j

) (1)

where w

is the weight of criterion j with w

>= 0,

sum(w

) = 1 and x

i j

is the partial score of the alterna-

tive i according to the criterion j.

5. Based on the obtained risk priority scores of the

faults represented by X

, the target faults are selected.

A risk threshold is deﬁned and the faults with RPS

higher than the threshold are chosen to be included in

the testing process.

Objective

Criteria

Alternatives

Figure 2: Hierarchy scheme for faults selection.

3.3 Prioritizing Faults Using the CI

As part of the AHP technique, the weighted aver-

age (equation (1)) is used to aggregate these partial

scores of the candidate faults in order to calculate the

global scores X

. Since it assumes the criteria’s in-

dependence, this operator cannot represent preferen-

tial relationships between the criteria. As a result, it

is unreliable because the interactions frequently oc-

cur (Mandic et al., 2015). We suggest utilizing the

CI to address the aggregation problem in order to be

able to consider interaction phenomena among crite-

ria. The CI operator allows to model not only the sig-

niﬁcance of each criterion but also the weighting of

each subset of criteria, based on a monotone set func-

tion known as the Choquet capacity or fuzzy measure

(Marichal, 2000). Fuzzy measurement can describe

three different kinds of criteria interactions (Grabisch

et al., 2008): (1) Negative synergy or negative inter-

action: When two criteria i and j are viewed by the

DM as redundant, they interact negatively; that is, the

signiﬁcance of the pair {i, j} is nearly equal to the

signiﬁcance of the individual criterion i and j. (2)

Positive interaction, also known as positive synergy, is

the presence of an interaction between criteria that are

deemed complementary, meaning that while the sig-

niﬁcance of a single criterion is negligible, the signif-

ICSOFT 2024 - 19th International Conference on Software Technologies

514

icance of the pair is considerable. (3) Independence:

When there is no interaction between two criteria, i

and j are said to be independent. The fuzzy measure

is additive in this instance: µ(i, j) = µ(i) + µ( j).

Some numerical indices, including the Shap-

ley value (Shapley, 1953) and the interaction index

(Murofushi and Soneda, 1993), can be computed to

help describe the interaction phenomena more fully.

A criterion’s overall relevance is measured by its

Shapley value, and the average interaction between

two criteria, i and j, is measured by its interaction in-

dex.

Let F be the set of faults and f

∈ S ,the global

score X

given by the CI according to a fuzzy measure

µ and a set C of criteria, is deﬁned by:

,··· , x

) =

∑

j=1

i( j)

[µ(A

( j)

− µ(A

( j−1)

]) (2)

Where the notation

(.)

indicates a permutation on C

such as x

i(1)

≤ ··· ≤ x

i(p)

. Also, A

( j)

= {(1)···(p)} ,

for all j ∈ {1,...n, p} and A

(p−1)

= φ.

The identiﬁcation of capacities is the main difﬁ-

culty while working with aggregation using the CI

based on fuzzy measurements. A survey of tech-

niques for capacity identiﬁcation in multi-attribute

utility theory based on CI is provided by the authors

in (Grabisch et al., 2008). The least squares approach,

which is the most popular optimization technique for

this purpose in the literature, is what we employ in our

work (Grabisch et al., 2008). Further understanding

of the intended overall evaluations Y

of the accessi-

ble items S

∈ S is necessary. Minimizing the overall

quadratic error E

between the global scores deter-

mined by the CI and the targeted scores Y

supplied

for each scenario is the aim of the least squares tech-

nique. To further enhance the outcomes, the heuris-

tic least squares approach may be applied. An initial

capacity must be deﬁned in order to use the heuris-

tic approach. The uniform capacity might be utilized

because it is challenging to determine the beginning

capacity (Grabisch et al., 2008). The deﬁnition of the

uniform capacity in this instance is as follows:

µ(1) = 0.333333 ; µ(2) = 0.333333;

µ(3) = 0.333333 ; µ(1,2) = 0.666667;

µ(1,3) = 0.666667 ; µ(2,3) = 0.666667;

µ(1,2,3) = 1.000000

4 CASE STUDY

In this section, we provide a case study using an RHS

circuit to demonstrate the proposed contribution.

4.1 Presentation

To further illustrate the proposed contribution, we

present a case study where hardware components can

be added, removed or updated to ensure the adequate

functionality of the system when needed. The system

presents two units that can perform addition and sub-

traction operations. These units are designed using

lower-level components such as logic gates, includ-

ing AND, OR, XOR gates and multiplexers and they

are also constructed using reconﬁgurable hardware as

shown in Figure 3. At a given time, the selection of

the unit is controlled by a multiplexer MUX as shown

in Figure 4.

a b

c e

d f

out

a- Addition operation (C

111

)

a b

c e

d f

c’

i’

b- Subtraction operation (C

211

)

1-Bit

Full adder

out

1-Bit

Full

subtractor

out

Figure 3: Different reconﬁgurations implementing the pro-

posed RHS.

MUX

out

1-bit

Full adder

out

1-bit

Full

subtractor

Figure 4: The proposed RHS.

Assumptions: Let’s assume that stuck-at 1 faults

occur more frequently than stuck-at 0 faults. Addi-

tionally, we assume that the faults in NOT gate are of

high occurrence and faults in AND gate are of a less

higher occurrence. However, faults in XOR and OR

gates are almost non-existent. The severity of faults

in OR gate is much higher than those in AND gate.

Faults in XOR and NOT gates are however of a very

low severity. Let’s assume also that a stuck-at fault, in

Multi-Criteria Decision-Making Approach for an Efﬁcient Postproduction Test of Reconﬁgurable Hardware System

515

a digital circuit, might be easily controllable only if an

input has a direct impact on the faulty node. Never-

theless, if the fault is hidden deep within the circuit,

controllability might be low. Moreover, determining

the observability of a faulty circuit output is less ap-

parent when the degree of similarity between a fault-

free circuit output and a faulty one is very high.

According to the case study, the application of

previous fault collapsing techniques (Ben Ahmed

et al., 2018b) reduces the number of faults from 34 to

11 faults. Therefore, the list of candidate faults are as

follows:

F={d/0 C111, d/1 C111, e/0 C111, e/1 C111,

e/1 C111, g/0 C111, g/1 C111, i/1 C111,

f/1 C211, i/1 C211, p/0 C211}

where d/0 C111 means that the signal d is stuck-at 0

in the circuit C111 (addition operation).

4.2 Numerical Results

The results of the AHP approach for ranking the

faults based on their risk priority score are shown

in Table 1. Based on the obtained AHP results, the

faults to be included in the test process are those

that have an RPS higher than the risk threshold

deﬁned by the expert. In this case, the threshold is

the mean between all the scores (threshold = 0.091).

Accordingly, the selected faults are;

p/0 C211 ; i/1 C211 ; d/1 C111 ; i/1 C111 ;

f/1 C211 ; f/1 C111

To enhance incorporating the expert’s preferences

into the decision process, the CI is employed in

the second part of the approach to calculate the

RPS instead of the weighted average used in AHP.

Initially, the decision maker is asked to provide a

preference order for a pertinent subset of faults,

meaning a subset that is thought to be especially

helpful in representing his preferences regarding the

criticality of faults:

p/0 C211 ≻ i/1 C211 ≻ f/1 C111 ≻ f/1 C211 ≻

e/0 C111 ≻ e/1 C111

The desired total scores that are associated with

this are Y

= [0.2230.1300.1040.1020.0260.025)].

Next, the heuristic least squares method is used to cal-

culate the Choquet capacity. Above are the capacities

attained:

µ({d

}) = 0.163;µ({d

}) = 0.267;µ({d

}) = 0;

µ({d

}) = 0.207;µ({d

}) = 0.527;

µ({d

}) = 0.488;µ({d

}) = 0.452;

µ({d

}) = 0.606;µ({d

}) = 0.548;

µ({d

}) = 0.400;µ({d

}) = 0.803 ;

µ({d

}) = 0.788,µ({d

}) = 0.697;

µ({d

}) = 0.606,µ({d

}) = 1

The obtained faults RPS using the CI are repre-

sented in Table 1. Accordingly, the faults that have

RPS higher than the threshold (threshold = 0.086)

are:

p/0

211;i/1

111; f /1

211; f /1

111

We notice that when using the weighted average the

faults to be tested are reduced to 6 faults. However,

when using the CI operator the faults are reduced to

5 faults. This result can be explained by taking into

account the decision maker’s preferences with regard

to the relative weight of the criteria, particularly

the way they interact. This can be analyzed more

thoroughly by computing the Shapley Values φ

and

the interactions indices I

parameters.

) = 0.283 ; φ

) = 0.323 ; φ

) = 0.173 ;

) = 0.221 ; I

) = 0.015 ; I

) =

0.157 ; I

) = 0.057 ; I

) = 0.071 ;

) = −0.05 ; I

) = −0.017 ;

The severity criterion d

in this instance is the

most important, followed by the occurrence, ob-

servability, and controllability criteria. The criteria

{severity, observability} and {observability, control-

lability} interact negatively, i.e., they present some re-

dundancy, whereas the criteria {occurrence, severity}

{occurrence, controllability }, {occurrence, observ-

ability }and, {severity, controllability} have positive

interactions.

To sum up, with respect to the proposed RHS the

application of this approach decreases the number of

faults from 11 to 6 and 5 (almost the half) using the

AHP technique and the AHP combined with CI, re-

spectively. The obtained fault set presents the critical

faults posing the greatest risk. These faults have to

be targeted during the testing process. The proposed

system can be part of a more complex digital circuit

such as the commonly used reconﬁgurable arithmetic

and logic unit (R-ALU) (Ben Ahmed et al., 2018b).

The n-bit R-ALU can be constructed by chaining n

1-bit R-ALU. For instance, in a 256 R-ALU, we ob-

tain 256*11=2816 candidate faults. The application

of AHP approach decreases drastically the number

of faults to 1536. This reduction reaches 1280 faults

when using AHP combined with CI.

For mass production, supposing that for each tar-

geted fault we need on average two test vectors, and

ICSOFT 2024 - 19th International Conference on Software Technologies

516

Table 1: Priority rankings derived using the AHP technique and CI.

Criteria d

: Occurrence d

: Severity d

: Controllability d

: Observability RPS RPS

Weights w

= 0.319 w

= 0.53 w

= 0.044 w

= 0.106 with AHP with CI

d/0 C111 0.117 0.072 0.021 0.026 0.0.79 0.057

d/1 C111 0.196 0.072 0.021 0.026 0.104 0.069

e/0 C111 0.016 0.026 0.032 0.041 0.025 0.026

e/1 C111 0.024 0.026 0.032 0.026 0.026 0.025

f/1 C111 0.066 0.109 0.032 0.203 0.102 0.102

g/0 C111 0.04 0.055 0.1 0.031 0.050 0.047

g/1 C111 0.052 0.055 0.1 0.045 0.055 0.052

i/1 C111 0.102 0.082 0.146 0.203 0.104 0.125

f/1 C211 0.057 0.118 0.032 0.203 0.104 0.103

i/1 C211 0.317 0.018 0.145 0.123 0.130 0.130

p/0 C211 0.014 0.37 0.34 0.075 0.223 0.220

that the test application time of a test vector takes

1s and one working hour costs $10, then for a 256-

bit R-ALU the total cost of 1000 256-bit R-ALU de-

vices will be about $15600 using the existing tech-

niques (Ben Ahmed et al., 2018b) (Prasad et al., 2002)

and about $8500 and $7100 using AHP approach and

AHP coupled with CI, respectively. We notice that

the difference between the costs is considered tremen-

dous in mass production industry.

This study is important in a way that (1) it guides

experts to identify faults that necessitate immediate

attention due to their criticality score (2) it supports

allocating resources and efforts more efﬁciently and

(3) it helps to save the scarcest resource in the indus-

try, which is time and cost.

5 CONCLUSIONS

This study presents a MCDM approach to prioritize

faults that require more attention during the testing

process. This approach is based on a well-deﬁned set

of criteria: occurrence, severity, controllability and

observability and is implemented using the AHP and

CI. The effectiveness of the proposed approach lies

in helping prioritize resources and efforts towards ad-

dressing the most critical faults posing the greatest

risk. It is feasible to note as a conclusion that two

major results of our study can be signaled. First, it in-

troduces a MCDM approach that allows the reduction

of the targeted fault set without affecting the correct-

ness of the system. Second, it implies that resources

are allocated in an efﬁcient manner. In future work,

we plan to add other criteria such as fault coverage

and to incorporate the proposed approach in the soft-

ware tool TnTest

https://lisi-lab-projects.wixsite.com/demo/demonstration

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