Is There Such a Thing as Software Reliability?
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1 Is There Such a Thing as Software Reliability? Dick Hamlet Department of Computer Science Portland State University Portland, OR hamlet@cs.pdx.edu
2 The probability R(N) that sth. will operate according to specification N times in a row Defining Reliability
3 Defining Reliability The probability R(N) that sth. will operate according to specification N times in a row The specification is essential defines failure Large enough N always means R(N) = 0 How to measure (estimate) R? Confidence in measurements?
4 1 Start with a new (one-slice) toaster i Life Testing Toasters 2 Toast 1, 2,..., N i pieces of bread until toaster i fails 3 Repeat 1 2 for i = 1,2,...,m
5 1 Start with a new (one-slice) toaster i Life Testing Toasters 2 Toast 1, 2,..., N i pieces of bread until toaster i fails 3 Repeat 1 2 for i = 1,2,...,m 4 Reliability estimate ˆR(j) is the fraction of m for which N i j
6 1 Start with a new (one-slice) toaster i Life Testing Toasters 2 Toast 1, 2,..., N i pieces of bread until toaster i fails 3 Repeat 1 2 for i = 1,2,...,m 4 Reliability estimate ˆR(j) is the fraction of m for which N i j If out of 100, one toaster fails first at 379 slices and one lasts longest to 420 slices, then ˆR(1) = ˆR(2) =... = ˆR(378) = 1.0 ˆR(379) = 0.99,..., ˆR(419) = 0.01 ˆR(420) = ˆR(421) =... = 0
7 1 Start with a new (one-slice) toaster i Life Testing Toasters 2 Toast 1, 2,..., N i pieces of bread until toaster i fails 3 Repeat 1 2 for i = 1,2,...,m 4 Reliability estimate ˆR(j) is the fraction of m for which N i j 5 An estimate of the mean runs to failure (MRTF) is the average N of N i
8 1 Start with a new (one-slice) toaster i Life Testing Toasters 2 Toast 1, 2,..., N i pieces of bread until toaster i fails 3 Repeat 1 2 for i = 1,2,...,m 4 Reliability estimate ˆR(j) is the fraction of m for which N i j 5 An estimate of the mean runs to failure (MRTF) is the average N of N i 6 Calculate standard error σ of the N i 7 Confidence that the actual MRTF is within the interval [ N 2σ, N + 2σ] is roughly 95%
9 Assumptions Required for Life Testing (Toasters) 1 Toaster behavior is continuous 2 Toasters have no systematic cause of failure 3 Each toasting run is independent of the others (Bernuilli trials) 4 Test circumstances duplicate actual toasting Then the measured MRTF and confidence are accurate predictions
10 Assumptions Required for Life Testing (Toasters) 1 Toaster behavior is continuous 2 Toasters have no systematic cause of failure 3 Each toasting run is independent of the others (Bernuilli trials) 4 Test circumstances duplicate actual toasting Then the measured MRTF and confidence are accurate predictions Interaction between 2 and 4 : Gap in screen guarding the heating element ( 2 false) Tests use sliced bread but usage is for fat bagels ( 4 false) Bagel protrudes through the gap and burns out heating element long before the predicted MRTF
11 Five years of breakfast is about 3000 slices Can t Wait for Failure? Time for each toaster to fail is about N, the MRTF 3,000 slices can be toasted in about 5 days (@2 min each overheating violates assumption 4!) But suppose the MRTF is actually 30,000?!
12 Five years of breakfast is about 3000 slices Can t Wait for Failure? Time for each toaster to fail is about N, the MRTF 3,000 slices can be toasted in about 5 days (@2 min each overheating violates assumption 4!) But suppose the MRTF is actually 30,000?! What can be predicted from runs that do not fail? Confidence C that the failure probability is below f max based on T runs: C = 1 (1 f max ) T For toasters, 95% confidence in a MRTF of better than 3000 requires T 9000 For T = 3000: confidence 95% 75% 63% 50% MRTF
13 Objections to Software Reliability Software need never fail: R(N) = 1.0 for all N
14 Objections to Software Reliability Software need never fail: R(N) = 1.0 for all N OK, predict a large enough MRTF from no failures
15 Objections to Software Reliability Software need never fail: R(N) = 1.0 for all N Software failure isn t probablistic each run is deterministic
16 Objections to Software Reliability Software need never fail: R(N) = 1.0 for all N Software failure isn t probablistic each run is deterministic The minefield analogy
17 Objections to Software Reliability Software need never fail: R(N) = 1.0 for all N Software failure isn t probablistic each run is deterministic The minefield analogy
18 Objections to Software Reliability Software need never fail: R(N) = 1.0 for all N Software failure isn t probablistic each run is deterministic The minefield analogy
19 Objections to Software Reliability Software need never fail: R(N) = 1.0 for all N Software failure isn t probablistic each run is deterministic The minefield analogy
20 Objections to Software Reliability Software need never fail: R(N) = 1.0 for all N Software failure isn t probablistic each run is deterministic The minefield analogy 12 rocks thrown with no explosion 70% confidence that 10 steps are safe Mindfield field mines path rocks thrown explosions steps on the path Software input space failure inputs usage profile tests executed failures runs
21 Objections to Software Reliability Software need never fail: R(N) = 1.0 for all N Software failure isn t probablistic each run is deterministic Assumptions of life testing are false
22 Objections to Software Reliability Software need never fail: R(N) = 1.0 for all N Software failure isn t probablistic each run is deterministic Assumptions of life testing are false Software dis 1 Toaster behavior is c ontinuous Software bugs are 2 Toasters have no systematic cause s of failure Hard to make software runs 3 Each toasting run is independent of the others (Bernuilli trials) Hard to make software 4 Test circu mstances duplicate actual toasting usage
23 Conclusions HELP WANTED SOFTWARE RESEARCHER The successful applicant will have degrees in mathematical probability and in software engineering plus a minimum of five years experience in software test. This position requires creativity and the ability to reject accepted ideas about reliability and reinvent the subject. Salary commeasurate with results. Theory is lacking Experiments needed How important is continuity? Is MRTF well defined for software? Study minefield simulations?
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