YANG ET AL:ARE SLICE-BASED COHESION METRICS ACTUALLY USEFUL IN EFFORT-AWARE POST-RELEASE FAULT-PRONENESS.. 337 TABLE 4 Example Metrics Computations at the Data-Token Level Type Metric Computation Value End slice Coverage =1/3×(21/34+18/34+32/34) =0.696 MaxCoverage =32/34 =0.941 MinCoverage =18/34 =0.529 Overlap =1/3×(12/21+12/18+12/32) =0.538 Tightness =12/34 =0.353 SFC =12/34 =0.353 WFC =27/34 =0.794 A =(21+18+32)/(3×34) =0.696 SBFC =(12×3×2+15×2×1)/(34×3×2) =0.500 NHD =1-2/(3×34×33)×(21×13+18×16+32×2) =0.629 Metric slice Coverage =1/3×(25/34+30/34+32/34) =0.853 MaxCoverage =32/34 =0.941 MinCoverage =25/34 =0.735 Overlap =1/3×(24/25+24/30+24/32) =0.837 Tightness =24/34 =0.706 SFC =24/34 =0.706 WFC =31/34 =0.912 A =(25+30+32)/(3×34) =0.853 SBFC =(24×3×2+7×2×1)/(34×3×2) =0.775 NHD =1-2/(3×34×33)×(25×9+30×4+32×2) =0.757 excellent quantitative measure of function cohesion [5],[13]. fault-prone functions more accurately than the most com- In particular,for each of the investigated slice-based cohe- monly used code and process metrics do.From Table 5,we sion metrics,a large value indicates a high cohesion.From can see that the most commonly used code and process met- this reasoning,we set up the following null hypothesis H2o rics are based on either simple syntactic information or con- and alternative hypothesis H2A for RQ2: trol flow structure information among statements in a function.In contrast,slice-based cohesion metrics make H20.There is no significant correlation between slice-based cohe- use of the semantic dependence information among the state- sion metrics and post-release fault-proneness. ments in a function.In other words,they are based on pro- H2A.There is a significant correlation between slice-based cohe- gram behaviors as captured by program slices.In this sense, sion metrics and post-release fault-proneness. slice-based cohesion metrics provide a higher level quantifica- The third research question(RQ3)of this study investigates tion of software quality than the most commonly used code whether slice-based cohesion metrics predict post-release and process metrics.Consequently,it is reasonable to expect TABLE 5 The Most Commonly Used Code and Process Metrics(i.e.the Baseline Metrics in This Study) Category Characteristic Metric Description Product Size SLOC Source lines of code in a function (excluding blank lines and comment lines) Structural FANIN Number of calling functions plus global variables read complexity FANOUT Number of calling functions plus global variables set NPATH Number of possible paths,not counting abnormal exits or gotos Cyclomatic Cyclomatic complexity CyclomaticModified Modified cyclomatic complexity CyclomaticStrict Strict cyclomatic complexity Essential Essential complexity Knots Measure of overlapping jumps Nesting Maximum nesting level of control constructs MaxEssentialKnots Maximum Knots after structured programming constructs have been removed MinEssentialKnots Minimum Knots after structured programming constructs have been removed Software n1 Total number of distinct operators of a function science n2 Total number of distinct operands of a function Total number of operators of a function N2 Total number of operands of a function Process Code churn Added Added source lines of code,normalized by function size Deleted Deleted source lines of code,normalized by function size Modified Modified source lines of code,normalized by function sizeexcellent quantitative measure of function cohesion [5], [13]. In particular, for each of the investigated slice-based cohe￾sion metrics, a large value indicates a high cohesion. From this reasoning, we set up the following null hypothesis H20 and alternative hypothesis H2A for RQ2: H20. There is no significant correlation between slice-based cohe￾sion metrics and post-release fault-proneness. H2A. There is a significant correlation between slice-based cohe￾sion metrics and post-release fault-proneness. The third research question (RQ3) of this study investigates whether slice-based cohesion metrics predict post-release fault-prone functions more accurately than the most com￾monly used code and process metrics do. From Table 5, we can see that the most commonly used code and process met￾rics are based on either simple syntactic information or con￾trol flow structure information among statements in a function. In contrast, slice-based cohesion metrics make use of the semantic dependence information among the state￾ments in a function. In other words, they are based on pro￾gram behaviors as captured by program slices. In this sense, slice-based cohesion metrics provide a higher level quantifica￾tion of software quality than the most commonly used code and process metrics. Consequently, it is reasonable to expect TABLE 4 Example Metrics Computations at the Data-Token Level Type Metric Computation Value End slice Coverage ¼ 1/3 (21/34 þ 18/34 þ 32/34) ¼ 0.696 MaxCoverage ¼ 32/34 ¼ 0.941 MinCoverage ¼ 18/34 ¼ 0.529 Overlap ¼ 1/3 (12/21 þ 12/18 þ 12/32) ¼ 0.538 Tightness ¼ 12/34 ¼ 0.353 SFC ¼ 12/34 ¼ 0.353 WFC ¼ 27/34 ¼ 0.794 A ¼ (21 þ 18 þ 32)/(3 34) ¼ 0.696 SBFC ¼ (12 3 2 þ 15 2 1)/(34 3 2) ¼ 0.500 NHD ¼ 12/(3 34 33) (21 13 þ 18 16 þ 32 2) ¼ 0.629 Metric slice Coverage ¼ 1/3 (25/34 þ 30/34 þ 32/34) ¼ 0.853 MaxCoverage ¼ 32/34 ¼ 0.941 MinCoverage ¼ 25/34 ¼ 0.735 Overlap ¼ 1/3 (24/25 þ 24/30 þ 24/32) ¼ 0.837 Tightness ¼ 24/34 ¼ 0.706 SFC ¼ 24/34 ¼ 0.706 WFC ¼ 31/34 ¼ 0.912 A ¼ (25 þ 30 þ 32)/(3 34) ¼ 0.853 SBFC ¼ (24 3 2 þ 7 2 1)/(34 3 2) ¼ 0.775 NHD ¼ 12/(3 34 33) (25 9 þ 30 4 þ 32 2) ¼ 0.757 TABLE 5 The Most Commonly Used Code and Process Metrics (i.e. the Baseline Metrics in This Study) Category Characteristic Metric Description Product Size SLOC Source lines of code in a function (excluding blank lines and comment lines) Structural complexity FANIN Number of calling functions plus global variables read FANOUT Number of calling functions plus global variables set NPATH Number of possible paths, not counting abnormal exits or gotos Cyclomatic Cyclomatic complexity CyclomaticModified Modified cyclomatic complexity CyclomaticStrict Strict cyclomatic complexity Essential Essential complexity Knots Measure of overlapping jumps Nesting Maximum nesting level of control constructs MaxEssentialKnots Maximum Knots after structured programming constructs have been removed MinEssentialKnots Minimum Knots after structured programming constructs have been removed Software science n1 Total number of distinct operators of a function n2 Total number of distinct operands of a function N1 Total number of operators of a function N2 Total number of operands of a function Process Code churn Added Added source lines of code, normalized by function size Deleted Deleted source lines of code, normalized by function size Modified Modified source lines of code, normalized by function size YANG ET AL.: ARE SLICE-BASED COHESION METRICS ACTUALLY USEFUL IN EFFORT-AWARE POST-RELEASE FAULT-PRONENESS... 337