System level test selection based on combinatorial dependency matrix

doi:10.23919/JSEE.2021.000084

Abstract

Abstract:

Test selection is to select the test set with the least total cost or the least total number from the alternative test set on the premise of meeting the required testability indicators. The existing models and methods are not suitable for system level test selection. The first problem is the lack of detailed data of the units’ fault set and the test set, which makes it impossible to establish a traditional dependency matrix for the system level. The second problem is that the system level fault detection rate and the fault isolation rate (referred to as "two rates") are not enough to describe the fault diagnostic ability of the system level tests. An innovative dependency matrix (called combinatorial dependency matrix) composed of three submatrices is presented. The first problem is solved by simplifying the submatrix between the units’ fault and the test, and the second problem is solved by establishing the system level fault detection rate, the fault isolation rate and the integrated fault detection rate (referred to as "three rates") based on the new matrix. The mathematical model of the system level test selection problem is constructed, and the binary genetic algorithm is applied to solve the problem, which achieves the goal of system level test selection.

Key words: test selection, dependency matrix, fault detection rate, testability prediction, binary genetic algorithm

Peng YANG, Haoyu XIE, Jing QIU. System level test selection based on combinatorial dependency matrix[J]. Journal of Systems Engineering and Electronics, 2021, 32(4): 984-994.

Figures/Tables 11

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References 31

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	${t_{\rm{1}}}$	${t_{\rm{2}}}$	${t_{\rm{3}}}$	···	${t_n}$
${f_{\rm{1}}}$	${b_{{\rm{1,1}}}}$	${b_{{\rm{1,2}}}}$	${b_{{\rm{1,3}}}}$	···	${b_{{\rm{1,}}n}}$
${f_{\rm{2}}}$	${b_{{\rm{2,1}}}}$	${b_{{\rm{2,2}}}}$	${b_{{\rm{2,3}}}}$	···	${b_{{\rm{2,}}n}}$
$\vdots $	$\vdots $	$\vdots $	$\vdots $	$\ddots $	$\vdots $
${f_m}$	${b_{m{\rm{,1}}}}$	${b_{m{\rm{,2}}}}$	${b_{m{\rm{,3}}}}$	···	${b_{m{\rm{,}}n}}$

	${t_{\rm{1}}}$	···	${t_N}$	${t_{N{\rm{ + 1}}}}$	···	${t_{N + W}}$
${f_{\rm{1}}}$	${b_{{\rm{1,1}}}}$	···	${b_{{\rm{1,}}N}}$	${b_{{\rm{1,}}N{\rm{ + 1}}}}$	···	${b_{{\rm{1,}}N + W}}$
···	···	···	···	···	···	···
${f_N}$	${b_{N{\rm{,1}}}}$	···	${b_{N{\rm{,}}N}}$	${b_{N{\rm{,}}N{\rm{ + 1}}}}$	···	${b_{N{\rm{,}}N + W}}$
${f_{N{\rm{ + 1}}}}$	${b_{N + 1{\rm{,1}}}}$	···	${b_{N{\rm{,}}N + 1}}$	${b_{N{\rm{ + 1,}}N{\rm{ + 1}}}}$	···	${b_{N{\rm{ + 1,}}N + W}}$
$\vdots $	$\vdots $	$\ddots $	$\vdots $	$\vdots $	$\ddots $	$\vdots $
${f_{N + M}}$	${b_{N + M{\rm{,1}}}}$	···	${b_{N + M{\rm{,}}N}}$	${b_{N + M{\rm{,}}N{\rm{ + 1}}}}$	···	${b_{N + M{\rm{,}}N + W}}$

	${t_1}$	${t_2}$	${t_3}$	${t_4}$	${t_5}$	${t_6}$	${t_7}$
${f_1}$	0.9	0	0	0	0	1	1
${f_2}$	0	0.9	0	0	0	1	1
${f_3}$	0	0	0.85	0	0	0	1
${f_4}$	0	0	0	0.95	0	0	1
${f_5}$	0	0	0	0	1	1	1
${f_6}$	0	0	0	0	0	1	1
${f_7}$	0	0	0	0	0	0	1

	${t_1}$	${t_2}$	${t_3}$	${t_4}$	${t_5}$	${t_6}$	${t_7}$	${t_8}$	${t_9}$	${t_{10}}$	${t_{11}}$	${t_{12}}$	${t_{13}}$	${t_{14}}$	${t_{15}}$	${t_{16}}$	${t_{17}}$	${t_{18}}$	Fault rate
${f_1}$	0.9	0	0	0	0	0	0	0	0	1	1	1	1	1	1	0	0	0	40
${f_2}$	0	0.8	0	0	0	0	0	0	0	0	1	1	1	1	1	1	0	0	50
${f_3}$	0	0	0.75	0	0	0	0	0	0	0	0	1	1	1	0	1	1	0	100
${f_4}$	0	0	0	0.85	0	0	0	0	0	0	0	0	1	1	0	0	1	1	60
${f_5}$	0	0	0	0	0.95	0	0	0	0	0	0	0	0	1	0	0	0	1	50
${f_6}$	0	0	0	0	0	1	0	0	0	0	1	1	1	1	1	0	0	0	70
${f_7}$	0	0	0	0	0	0	1	0	0	0	0	1	1	1	1	1	0	0	200
${f_8}$	0	0	0	0	0	0	0	1	0	0	0	0	1	1	0	1	1	1	150
${f_9}$	0	0	0	0	0	0	0	0	1	0	0	0	0	1	0	0	1	1	30
Test cost	12	14	11	10	19	10	17	19	11	18	18	18	11	16	16	12	11	15	—

Result	Constraint	Unit level test set	System level test set	${\gamma _{{\rm{FDs}}}}$	${\gamma _{{\rm{FIs}}}}$	${\gamma _{{\rm{FDx}}}}$	$C$
1	${\gamma _{{\rm{FDs}}}}{\rm{ = 0}}{\rm{.95}}$ , ${\gamma _{{\rm{FIs}}}}{\rm{ = 0}}{\rm{.9}}$ , ${\gamma _{{\rm{FDx}}}}{\rm{ = 0}}{\rm{.95}}$	$\left\{ {{t_1},{t_{\rm{2}}},{t_3},{t_4},{t_5}} \right\}$	$\left\{ {{t_{12}},{t_{17}}} \right\}$	0.9567	0.9389	1.0000	97
2	${\gamma _{{\rm{FDs}}}}{\rm{ = 0}}{\rm{.95}}$	$\left\{ {{t_1},{t_{\rm{2}}},{t_3},{t_4},{t_5}} \right\}$	$\left\{ {{t_{14}}} \right\}$	1.0000	0.3327	1.0000	82
3	${\gamma _{{\rm{FDs}}}}{\rm{ = 0}}{\rm{.95}}$ , ${\gamma _{{\rm{FIs}}}}{\rm{ = 0}}{\rm{.9}}$	$\left\{ {{t_1},{t_{\rm{2}}},{t_3},{t_4},{t_5}} \right\}$	$\left\{ {{t_{16}},{t_{17}}} \right\}$	0.8980	0.8901	0.8444	89
4	${\gamma _{{\rm{FDs}}}}{\rm{ = 0}}{\rm{.95}}$ , ${\gamma _{{\rm{FIs}}}}{\rm{ = 0}}{\rm{.9}}$ , ${\gamma _{{\rm{FDx}}}}{\rm{ = 0}}{\rm{.95}}$	?	$\left\{ {{t_{\rm{6}}},{t_{\rm{7}}},{t_{\rm{8}}},{t_{\rm{9}}},{t_{10}},{t_{11}},{t_{{\rm{12}}}},{t_{13}},{t_{14}}} \right\}$	1.0000	1.0000	1.0000	138
5	${\gamma _{{\rm{FDs}}}}{\rm{ = 0}}{\rm{.95}}$ , ${\gamma _{{\rm{FIs}}}}{\rm{ = 0}}{\rm{.9}}$ , ${\gamma _{{\rm{FDx}}}}{\rm{ = 0}}{\rm{.95}}$	$\left\{ {{t_1},{t_{\rm{2}}},{t_3},{t_4},{t_5}} \right\}$	?	0.3327	1.0000	0.0000	66