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Model-based Testing of Embedded Real-Time Systems in the Automotive Domain Eng. Sc. D. candidate: Justyna Zander-Nowicka Supervisor: Prof. Dr.–Ing. Ina Schieferdecker (TU Berlin) Supervisor: Prof. Dr. rer. nat. Ingolf Krüger (UC San Diego) Committee Chairman: Prof. Dr.–Ing. Clemens Gühmann (TU Berlin) Doctoral Thesis Defense: December, 19 th , 2008

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Page 1: Zander eng scd_final

Model-based Testing of Embedded Real-Time Systems in the Automotive Domain

Eng. Sc. D. candidate: Justyna Zander-Nowicka

Supervisor: Prof. Dr.–Ing. Ina Schieferdecker (TU Berlin) Supervisor: Prof. Dr. rer. nat. Ingolf Krüger (UC San Diego)Committee Chairman: Prof. Dr.–Ing. Clemens Gühmann (TU Berlin)

Doctoral Thesis Defense: December, 19th, 2008

Page 2: Zander eng scd_final

December, 19th, 2008 MBT of Embedded Systems Justyna Zander-Nowicka2

Motivation

Embedded systems in the automotive domain :

Addressed characteristics:

� Hybrid: continuous signal flows and discrete events

� Real-time

� Reactive

Testing :

� Demands 40-60% (EU, 2005) of development resources

� Systematic and automatic test approach starting at the earliest model phase ofsoftware development still missing

� Different companies use different technologies, methods, and tools

� The complexity of car softwaredramatically increases

� The functions are distributed� Demand to shorten time-to-market� Demand for quality assurance � safety

standards IEC 61508 and ISO 26262

Environment

Sensor Actuator

Embedded System

Embedded Software

Page 3: Zander eng scd_final

December, 19th, 2008 MBT of Embedded Systems Justyna Zander-Nowicka3

Outline

I. Model-based Testing (MBT)

II. Signal-feature Test Paradigm

– Test Development Process

– Signal-feature Detection for Test Evaluation

– Signal-feature Application for Test Data Generation

III. The Test System

IV. Case Study

V. Summary and Outlook

Page 4: Zander eng scd_final

December, 19th, 2008 MBT of Embedded Systems Justyna Zander-Nowicka4

Model-Based Testing

� Model-based testing is testing in which the entire test specification is derived inwhole or in part from both the system requirements and a model that describeselected functional aspects of the system under test (SUT).

� In this context, the term entire test specification covers the abstract testscenarios made concrete by the sets of test data and the expected SUT outputs.The test specification is organized in a set of test cases .

� Model-in-the-Loop for Embedded System Test (MiLEST ) proposed in this thesis.

I. Model-based Testing II. Signal-Feature Test Paradigm III. The Test System IV. Case Study V. Summary & Outlook

TEST MODEL

Test Objectives

SYSTEM MODEL Interfaces and Test Objectives

REQUIREMENTS

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December, 19th, 2008 MBT of Embedded Systems Justyna Zander-Nowicka5

MBT TaxonomyI. Model-based Testing II. Signal-Feature Test Paradigm III. The Test System IV. Case Study V. Summary & Outlook

Acknowledgement: M. Utting et al. (2006)

MiLEST

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December, 19th, 2008 MBT of Embedded Systems Justyna Zander-Nowicka6

Related Work Challenges and Thesis Contributions

Open Issues:

� Test data specification� automatic, but only for structural

test or state-based models� systematic for functional test, but

still only manual� Automatic test evaluation , but mainly

based on the reference signal flows

� Test process established, but not efficient enough in terms of cost, efforts, and reusability

Solutions :

� Automatic and systematic test data generation for functional test

� Automatic and online test evaluation based on reference signal partition

� Automation of MBT process jjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjj

Main goal � automatically created test design executable at the model level.

I. Model-based Testing II. Signal-Feature Test Paradigm III. The Test System IV. Case Study V. Summary & Outlook

� Signal-feature – based generation of test data

� Signal-feature – based test assessment by application of validation functions

� Application of automated hierarchical test patterns and transformations

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December, 19th, 2008 MBT of Embedded Systems Justyna Zander-Nowicka7

Signal Feature – DefinitionI. Model-based Testing II. Signal-Feature Test Paradigm III. The Test System IV. Case Study V. Summary & Outlook

� A signal feature , also called signal property, is a formal description of certainpredefined attributes of a signal. It is an identifiable , descriptive property of asignal.

� A feature can be composed of or predicated by other features, logicalconnectives , or timing expressions .

Acknowledgement: E. Lehmann (2003)

f(kT)

kT

decrease

constant

increase

local max

step response characteristics

time partitioning

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December, 19th, 2008 MBT of Embedded Systems Justyna Zander-Nowicka8

Proposed Test Development Process

SUT as a Model

automatic generation – step I

Test Harness Generation

manual refinement – step II

Test Specification

automatic generation – step III

Test Data & Test Control Generation

automatic execution – step IV

Verdicts Analysis

I. Model-based Testing II. Signal-Feature Test Paradigm III. The Test System IV. Case Study V. Summary & Outlook

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December, 19th, 2008 MBT of Embedded Systems Justyna Zander-Nowicka9

Test HarnessI. Model-based Testing II. Signal-Feature Test Paradigm III. The Test System IV. Case Study V. Summary & Outlook

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December, 19th, 2008 MBT of Embedded Systems Justyna Zander-Nowicka10

Signal-Feature Detection and Generation

transformation

I. Model-based Testing II. Signal-Feature Test Paradigm III. The Test System IV. Case Study V. Summary & Outlook

- temporal expressions (e.g., after(5ms))

- logical connectives(e.g., and)

transformation

DetectSignal Feature

GenerateSignal Feature

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December, 19th, 2008 MBT of Embedded Systems Justyna Zander-Nowicka11

Increase Detection and GenerationI. Model-based Testing II. Signal-Feature Test Paradigm III. The Test System IV. Case Study V. Summary & Outlook

� Detect Increase:The Increase feature can be detected by analyzing its derivative. This can beapproximated (simplified version of the algorithm!) where the actual signal valueand the past one (backward difference):

feature(kT) = sign [signal (kT) − signal ((k − 1) * T)]

feature(kT) is positive if the signal increases.

� Generate Increase:

� Example:

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December, 19th, 2008 MBT of Embedded Systems Justyna Zander-Nowicka12

Classification of Signal-Feature Detection Mechanis ms (1)

Tim

e-independent

Acknowledgement: A. Marrero-Pérez (2007)

I. Model-based Testing II. Signal-Feature Test Paradigm III. The Test System IV. Case Study V. Summary & Outlook

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December, 19th, 2008 MBT of Embedded Systems Justyna Zander-Nowicka13

Classification of Signal-Feature Detection Mechanis ms (2)

Acknowledgement: A. Marrero-Pérez (2007)

Triggered

I. Model-based Testing II. Signal-Feature Test Paradigm III. The Test System IV. Case Study V. Summary & Outlook

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December, 19th, 2008 MBT of Embedded Systems Justyna Zander-Nowicka14

Levels of Test Design in MiLEST

Feature Detection Level

Validation Function Level

Test Requirement Level

abstra

ctio

n

Test Harness Level

refinement

Feature Generation Level

Test Case Level

Test Requirement Level

Test Harness Level

Test Specification

designed manually

Test Data Generation

obtained automatically

Transformation

IF preconditions set THEN assertions set

IF preconditions set THEN generations set

Transformation

Transformation

Transformation

I. Model-based Testing II. Signal-Feature Test Paradigm III. The Test System IV. Case Study V. Summary & Outlook

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December, 19th, 2008 MBT of Embedded Systems Justyna Zander-Nowicka15

Test Patterns Classification� Test Specification Patterns

� Test Requirement Level

� Validation Function Level

- Signal-Feature Detection Level

Test activity Test pattern name Context Problem Solutio n instance

Test specificationDetect step response features

Test of an electronic control unit (ECU)

Assessment of an ECU behavior in terms of a selected signal feature

I. Model-based Testing II. Signal-Feature Test Paradigm III. The Test System IV. Case Study V. Summary & Outlook

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December, 19th, 2008 MBT of Embedded Systems Justyna Zander-Nowicka16

Pedal Interpretation Example

Interpretation of accelerator pedal position

Normalized accelerator pedal position (phi_Acc) should be interpreted asdesired driving torque (T_des_Drive). The desired driving torque is scaled inthe non-negative range in such a way that the higher the velocity (v) isgiven, the lower driving torque is obtained (Conrad, 2004).

IF v=const AND phi_Acc increasesTHEN T_des_Drive increases

IF v=const AND phi_Acc decreasesTHEN T_des_Drive decreases

IF v=const AND phi_Acc=constTHEN T_des_Drive=const

IF v increases AND phi_Acc=const AND T_des_Drive>=0

THEN T_des_Drive does not increase

I. Model-based Testing II. Signal-Feature Test Paradigm III. The Test System IV. Case Study V. Summary & Outlook

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December, 19th, 2008 MBT of Embedded Systems Justyna Zander-Nowicka17

MiLEST Quality Metrics – an Example

0102030405060708090

100

%

v phi_A

cc

phi_B

rake

I. Model-based Testing II. Signal-Feature Test Paradigm III. The Test System IV. Case Study V. Summary & Outlook

# of variants for a selected SigF applied in a test design

# of all possible variants for a selected SigFVariants coverage for a SigF =

Pedal Interpretation –manual generation

0102030405060708090

100

%

v phi_A

cc

phi_B

rake

Pedal Interpretation –automatic generation

� Consider MiLEST Quality Metricsin combination (weight-based approach), not in isolation!

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December, 19th, 2008 MBT of Embedded Systems Justyna Zander-Nowicka18

MiLEST SummaryI. Model-based Testing II. Signal-Feature Test Paradigm III. The Test System IV. Case Study V. Summary & Outlook

Contributions:

� Automatic and systematic test data generation for functional test based on signal-feature concept

� Automatic and online test evaluationbased mainly on signal-feature taxonomy

� Reusable test patterns constituting a test framework

� MBT methodology and automated test process

Achieved goals:

� Systematic and consistent functional test specification

� Automation of the test specification

� Novel manner of signal assessment� Continuous observation of the SUT� Automation of the test process

� Abstract and concrete views (i.e., abstract libraries concretized in the test system)

� Requirements- & model-based testing� Test execution starting at MiL level� System model and test model in

common execution environment

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December, 19th, 2008 MBT of Embedded Systems Justyna Zander-Nowicka19

Future Work

� Specific for current version of MiLEST:� Test stimuli generation algorithms and their optimization� Transposition of conditional rules (i.e., automation of the test specification)� Further test patterns (e.g., incl. different numerical integration methods)� Combination of the methods for verification or failure analysis purpose

� Automation for negative testing� More case studies (i.e., test approach scalability)� Further domains (e.g., aerospace, railway, space, earth, or military systems)� Further execution platforms� Mapping to TTCN-3 es� Further test quality metrics such as:

� Cost/effort needed for constructing a test data set � Relative number of found errors in relation to the number of test cases

needed to find them

I. Model-based Testing II. Signal-Feature Test Paradigm III. The Test System IV. Case Study V. Summary & Outlook

Page 20: Zander eng scd_final

Thank you so [email protected]

Page 21: Zander eng scd_final

Backup slides.

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December, 19th, 2008 MBT of Embedded Systems Justyna Zander-Nowicka22

Automotive Embedded System Test Dimensions

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December, 19th, 2008 MBT of Embedded Systems Justyna Zander-Nowicka23

Related Work – Tools

Criteria

Selected Test Methodologies, Technologies, Tools

Test Specification

TestPatterns Support

Transformation and

Automation Facilities

Manual Test Case / Test Data

Specification

Automatic Test Case / Test Data

Generation

Test EvaluationScenarios as Driving

Force

FormalVerification

EmbeddedValidator + + (15 patterns)

MTest with CTE/ES +

Reactis Tester + +

Reactis Validator + + –/+ (2 patterns)

Simulink® Verification and Validation™

+ + + (12 patterns)

Simulink® Design Verifier™ + + –/+ (4 patterns)

SystemTest™ +

TPT + +

T-VEC + +

TransformationsApproach (Dai,‘06) + +

Watchdogs (Conrad,‘98) +

MiLEST + + + (~50 patterns) +

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December, 19th, 2008 MBT of Embedded Systems Justyna Zander-Nowicka24

MiLEST with respect to MBT Taxonomy

TestApproach

Test Generation: Selection Criteria and Technology

Test Execution Options

Test Evaluation:Specificationand Technology

MiLEST

- data coverage- requirements coverage- test case specifications - automatic generation- offline generation

- MiL - reactive

- reference signal-feature – based- requirements coverage- test evaluation specifications- automatic- online evaluation

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December, 19th, 2008 MBT of Embedded Systems Justyna Zander-Nowicka25

Signal Features – a Descriptive Approach

u1(time) -step

timeq1(time)-

step response

time

Step response characteristics: rise time (tr), maximum overshoot (max), settling time (ts), steady state error (ess)

ts

max

tr

ess

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December, 19th, 2008 MBT of Embedded Systems Justyna Zander-Nowicka26

Signal-Features Generation

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December, 19th, 2008 MBT of Embedded Systems Justyna Zander-Nowicka27

Signal-Feature Generation for Test Data

transformation

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December, 19th, 2008 MBT of Embedded Systems Justyna Zander-Nowicka28

Signal-Features Generation and Evaluation

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December, 19th, 2008 MBT of Embedded Systems Justyna Zander-Nowicka29

From Signal Feature Detection to Signal Feature Gen eration

Signal feature detection

Trigger-independent

Immediately identifiable

� Detect signal value

� Detect increase / decrease

� …

Signal feature generation

Trigger-independent

Immediately identifiable

� Any curve coming through a given value within the permitted range of values , where duration time is default

� Any increasing/decreasing function with a default/given slope or other characteristicsin the permitted range of values , where duration time is default

� …

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December, 19th, 2008 MBT of Embedded Systems Justyna Zander-Nowicka30

Classification of Signal Features based on their De tection Type

Immediately identifiable

Identifiable with determinate delay

Identifiable with indeterminate delay

� Detect signal value� Detect increase / decrease /

constant� Detect continuous signal /

derivative� Detect linearity (w.r.t. 1st value)� Detect functional relation y = f(x)� Detect causal filter� Detect max-to-date / min-to-date

� Detect max / min / inflection� Detect peak� Detect impulse� Detect step

� Detect duration ofevery single delay

� Detect signal value @ time1

� Detect time stamp� Detect any time independent

features over a time interval� e.g., value @ time1

� e.g., value @ [time1, time2]

� Detect any timeindependent featuresover a time interval

� e.g., value @ time of max

� Detect step response characteristics(rise time, settlingtime, overshoot)

� Detect response delay� Detect complete step

Tim

e-in

depe

nden

tTr

igge

red

MSOffice8

Page 31: Zander eng scd_final

Slajd 30

MSOffice8 Complete Step Detection : das was die Preconditions von Step response machen: Step detektieren und dann triggern wenn die signale 'Step' und 'Step

response' sich stabilisiert haben.

Step detection : detektiert nur ein Step, triggert also direkt beim Step

max-to-date : speichert immer den maximalen Wert bislang. wenn ich z.B. die Wertefolge habe 0 1 2 3 5 6 10 9 54 6 7 3, max-to-date liefert: 0 1 2 3 4 6

10 10 54 54 54 54 Justyna Zander-Nowicka, 12/12/2006

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December, 19th, 2008 MBT of Embedded Systems Justyna Zander-Nowicka31

Signal-Features Classification (excerpt)

SigFEvaluation View Generation View

Time-independent

Imm

ediately identifiable

Signal value detection

Basic mathematical operations (e.g., zero detection)

Increase detection

Decrease detection

Constant detection

Signal continuity detection

Any curve crossing the value of interest in the permitted range of values, where duration time = default

Generation information: - value of interest

Any curve described by a basic mathematical operations (e.g., crossing zero value in the permitted range of values), where duration time = default

Generation information: - time of zero crossing

Any ramp increasing with a default/given slope in the permitted range of values, where duration time = default

Generation information: - slope - initial output- final output

Any ramp decreasing with a default/given slope in the permitted range of values, where duration time = default

Generation information: - slope - initial output- final output

Any constant in the permitted range of values, where duration time = default Generation information: - constant value

Any continuous curve in the permitted range of values, where duration time = default

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December, 19th, 2008 MBT of Embedded Systems Justyna Zander-Nowicka32

IF – THEN Rules

Logical connectives, e.g.:

IF constrained_inputsn AND constrained_outputsm THEN constrained_inputsn AND constrained_outputsm

IF constrained_inputsn AND constrained_outputsm THEN constrained_outputsm

IF constrained_inputsn THEN constrained_inputsn AND constrained_outputsm

IF constrained_inputsn THEN constrained_outputsm

IF true ^ any constraints THEN constrained_outputsm

Alternative, i.e.:

IF ATHEN B

OR C OR D

Temporal expressions, e.g.:

IF A THEN during(x)B AND after(y)C

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December, 19th, 2008 MBT of Embedded Systems Justyna Zander-Nowicka33

Test Patterns Classification (2)

Test activity Test pattern name Context Problem Solutio n instance

Test data generation

Generate signal feature

Evaluation of a step response function is intended

Generation of appropriate signal to stimulate an SUT

Test activity Test pattern name Context Problem Solutio n instance

Test control specification

Automatic sequencing of test cases

Test of an electronic control unit

Establishing of the starting point of the next test case

IF verdict=pass or verdict=fail or verdict=error of a test case THEN leave this test case at that time point & execute the next test case starting at that established time point

� Test Data Structure Pattern

� Test Requirement Level

� Test Case Level

- Signal-Feature Generators

� Test Control Patterns (e.g., for reactive testing)

� Test Harness Pattern

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December, 19th, 2008 MBT of Embedded Systems Justyna Zander-Nowicka34

Combination of Variants

� Combination techniques:

� Minimal combination

� One factor at a time

� N-wise combination

� Others:

� Complete combination

� Random combination

� etc...

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December, 19th, 2008 MBT of Embedded Systems Justyna Zander-Nowicka35

Pedal Interpretation Component

velocity (v)

acceleration pedal (phi_Acc)

driving torque (T_des_Drive)

System under Test

Page 37: Zander eng scd_final

December, 19th, 2008 MBT of Embedded Systems Justyna Zander-Nowicka36

Test Data Patterns Derivation

0,0

v,

phi_Acc

time

0,0

v,

phi_Acc

time

time0,0

v,

phi_Acc

0,0

v,

phi_Acc

time

Interpretation of accelerator pedal position

Normalized accelerator pedal position should be interpreted as desired driving torque. The desireddriving torque is scaled in the non-negative range in such a way that the higher the velocity is given,the lower driving torque is obtained.

Generate v=const

Generate phi_Acc increases

Generate v=const

Generate phi_Acc decreases

Generate v=const

Generate phi_Acc=const

IF T_des_Drive>=0

Generate v increases

Generate phi_Acc=const

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December, 19th, 2008 MBT of Embedded Systems Justyna Zander-Nowicka37

Concrete Test Data

0,0

phi_Acc

time

0,0

velocity

time

0,0

phi_Brake

time

Range constraints

Temporal constraints

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December, 19th, 2008 MBT of Embedded Systems Justyna Zander-Nowicka38

Variants for the Increase Generation – Concrete View

� Consider the velocity of a car < -10, 70 > with the partition point of 0.

� Then, using the classification tree method (Grochtmann & Grimm, 1993), and the formulas:

<pn, pn + 10% * (pn+1 – pn)> and <pn – 10% * (pn – pn-1), pn>

� Increase variants are: <-10, -9>, <-1, 0>, (0, 7>, <63, 70>.

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Concrete Test Data Variants

v phi_Acc

v1 v2 v3 v4 v5 phi_Acc1 phi_Acc2

{-10} {-5} {0} {35} {70} [0,10] [90,100]

t0

t1

t2

t3

phi_Acc v

SUT inputs

phi_Acc1

1

2

3

4

One factor at a time combination

tim

e [u

nit

s]

itera

tio

ns[

n]

phi_Acc2

5

6

t4

t5

v1 v2 v3 v4 v5

0

10

20

30

40

50

60

70

80

90

100

0 2 4 6 8 10 12

time [s]

phi_

Acc

-10

0

10

20

30

40

50

60

70

80

90

0 2 4 6 8 10 12

time [s]

v

phi_Acc1

phi_Acc2

v1v2

v3

iteration1 iteration 2 iteration3 iteration 4 iteration 5 iteration6

v1

v4

v5

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December, 19th, 2008 MBT of Embedded Systems Justyna Zander-Nowicka40

Set of Test Cases Sequenced in Test Suites

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December, 19th, 2008 MBT of Embedded Systems Justyna Zander-Nowicka41

Test Cases Sequenced in Test Suite

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December, 19th, 2008 MBT of Embedded Systems Justyna Zander-Nowicka42

MiLEST Test Quality Metrics

Test data related:

Signal range consistency

Constraint correctness

Variants coverage for a SigF

Variants coverage during test execution

Variants related preconditions coverage

Variants related assertions coverage

SUT output variants coverage

Minimal combination coverage

Test specification related:

Test requirements coverage

VFs activation coverage

VF specification quality

Preconditions coverage

Effective assertions coverage

Test control related:

Test cases coverage

Others:

Service activation coverage

System model coverage

Cost/effort needed for constructing a test data set

Relative number of found errors in relation to the number of test cases needed to find them

Coverage of signal variants combinations –CTCmax, CTCmin

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December, 19th, 2008 MBT of Embedded Systems Justyna Zander-Nowicka43

Summary and Future Work

� Three types of case studies :

� component level test

� component in the loop level test

� integration level test

Abst ract ion Test

Specification

Test Quality A

u to m

a ti o

n

Test E

val u

at i on, T

est

Oracl e, A

rbi t rat i o

n

S i gn a

l -F e a

t ur e

Ap p

r oa c

h

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December, 19th, 2008 MBT of Embedded Systems Justyna Zander-Nowicka44

Example: Ariane 5

� Ariane 5 Flight 501 on 4 June 1996 failed� Weight: 740 t, Payload: cluster satellites� Rocket self-destructing 37 seconds after launch

because of a malfunction in the control software� Most expensive computer bug in history:

370 Mio $

Causes:� Reused software from Ariane 4� Data conversion from 64-bit float to 16-bit

signed integer � overflow / not caught� ADA software with 2 channels (redundancy), but

identical implementation!� 1st channel had same problem 72ms before� Software handler got exceptions from both

channels, no Plan B for such situations� Main computer interpreted horizontal velocity

and sent strange control command� Self-destruction due to safety issues

...declarevertical_veloc_sensor: float;horizontal_veloc_sensor: float;vertical_veloc_bias: integer;horizontal_veloc_bias: integer;...

begindeclarepragma suppress(numeric_error, horizontal_veloc_bias);

beginsensor_get(vertical_veloc_sensor);sensor_get(horizontal_veloc_sensor);vertical_veloc_bias := integer(vertical_veloc_sensor);horizontal_veloc_bias :=

integer(horizontal_veloc_sensor);...

exceptionwhen numeric_error => calculate_vertical_veloc();when others => use_irs1();

end;end irs2;.

Horizontal velocity > 32786.0 internal unit

Unclassified Exception caught �Control transfer to 1 st channel

ADA Code of 2nd channel

* source: http://www-aix.gsi.de/~giese/swr/ariane5.html (retrieved 2008)

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December, 19th, 2008 MBT of Embedded Systems Justyna Zander-Nowicka45

MiLEST Realization

� MiLEST – Model-in-the-Loop for Embedded System TestingIt is a Simulink® add-on built on top of the MATLAB® engine.

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December, 19th, 2008 MBT of Embedded Systems Justyna Zander-Nowicka46

Integration of MiLEST in the Automotive-specific V -Modell ®

Acknowledgement: J. Großmann et al. (2008)

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December, 19th, 2008 MBT of Embedded Systems Justyna Zander-Nowicka47

Model- and Requirement-based Testing

Execution Environment

SYSTEM IMPLEMENTATION

TEST MODEL

TEST IMPLEMENTATION

Transformation Transformation

Test Objectives

SYSTEM MODELInterfaces and Test Objectives

REQUIREMENTS

� What is the role of a system model?� What is the role of a test model?� Is it possible to use a common language for both

system and test specifications?

� How can discrete and continuous signals be handled at the same time?

� How should a test framework be realized?

� How to automate the test process?

� How to assure the quality of tests?

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MiLEST Marketing

Features :� Systematic functional test specification� Signal -feature – oriented paradigm� Graphical test design� Test process automation

� systematic and automatic test datageneration

� online automatic test evaluation� Model-in-the-Loop test execution� Reusable test patterns� Abstract and concrete views

Benefits:� Testing in early design stages� Test of hybrid systems including temporal

and logical dependencies� Traceability of test cases to the

requirements� Traceability of verdicts to the root faults� Increased test coverage and test

completeness� Assured quality of the tests

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December, 19th, 2008 MBT of Embedded Systems Justyna Zander-Nowicka49

Discrete and Continuous Signal Interpretation in Si mulink

� Consider a second order Runge-Kutta numerical integration

21

12

1

)()(

)2

)(,2

(

)),((

atxtx

atx

htfha

ttxfha

kk

kk

kk

kkk

+=

++=

=

+