Handbook of Reliability Engineering

Chapter 27: The Application of Capture-Recapture Methods in Reliability Studies

Paul S.F.Yip, Yan Wang and Anne Chao

27.1 Introduction

Suppose there are an unknown number v of faults in a computer program. A fault is some defect in the code which (under at least one set of conditions) will produce an incorrect output, i.e. a failure. The program is executed for a total time ? under a range of conditions to simulate the operating environment. Failures occur on N ? occasions at times 0< t 1 2 < < < ?. The time until the detection of fault i is a positive random variable with hazard function ? i (t) ( i= 1, 2, , v). The first column of Table 27.1 gives a set of failure data for an information system (seconds CPU time). The data can be found in Moek [1]. The main purpose of this study is to estimate the total number of remaining faults in the system.

Table 27.1: Real and simulated failure times of Moek s data [1]

Fault#

First

Subsequent simulated failure times

1

880

64 653

329 685

520 016

2

4310

305 937

428 364

432 134

576 243

3

7170

563 910

4

18 930

186 946

195 476

473 206

5

23 680

259 496

469 180

6

23 920

126 072

252 204

371 939

7

26 220

251 385

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