Bayesian Decision Making of an Imperfect Debugging Software Reliability Growth Model with Consideration of Debuggers’ Learning and Negligence Factors
Abstract
:1. Introduction
2. Imperfect Debugging Software Reliability Growth Model with Consideration of Debuggers’ Learning and Negligence Factors
2.1. Basic Model Development
2.2. Parameter Estimation and Models Validation
3. Bayesian Analysis for SRGM and Optimal Decision of Software Release
3.1. Bayesian Analysis under Insufficient Historical Data
3.2. Cost Models for Optimal Decision of Software Release
4. Application and Numerical Analysis
5. Conclusions and Future Works
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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: the autonomous errors-detected factor |
: the learning factor |
: the negligent factor |
: the joint prior distribution for ,, |
: the likelihood function regarding NHPP with the collected dataset |
: the posterior distribution for ,, |
: the initial number of all potential errors in the software system |
: the function of the total errors at time in the software system |
: the mean value function, which represents the accumulated number of software errors detected during the time interval (0,) |
: the intensity function that denotes the number of the errors detected at time |
: the function of the error detection rate |
Dataset | Reference | Source |
---|---|---|
(1) | Zhang & Pham (2006) [46] | Failure data of telecommunication system |
(2) | Wang et al. (2016) [47] | Medium-scale software project |
(3) | Peng et al. (2014) [16] | Testing data for the Room Air Development Center |
(4) | Singpurwalla & Willson (1999) [48] | Failure data of NTDS system |
Imperfect Debugging SRGMs | |
---|---|
Pham et al. (1999) [3] | . |
Kapur et al. (2008) [9] | . |
Wang et al. (2015) [17] | . |
Proposed model | . |
Alternative 1 | Alternative 2 | Alternative 3 |
---|---|---|
Low-Intensity Testing Resource | Medium-Intensity Testing Resource | High-Intensity Testing Resource |
= 1.9 | ||
Time T | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 2 | 3 | 1 | 2 | 3 | 1 | 2 | 3 | 1 | 2 | 3 | |
4 | 1223 | 1575 | 1592 | $667,547 | $540,660 | $570,689 | $417,191 | $212,092 | $202,653 | 0.556 | 0.650 | 0.698 |
4.2 | 1260 | 1608 | 1622 | $655,754 | $533,214 | $565,149 | $394,921 | $193,977 | $186,180 | 0.574 | 0.681 | 0.730 |
4.4 | 1296 | 1637 | 1649 | $645,163 | $527,293 | $560,886 | $373,985 | $177,704 | $171,304 | 0.591 | 0.710 | 0.760 |
4.6 | 1329 | 1663 | 1673 | $635,707 | $522,756 | $557,778 | $354,302 | $163,094 | $157,865 | 0.609 | 0.737 | 0.787 |
4.8 | 1360 | 1687 | 1695 | $627,323 | $519,473 | $555,717 | $335,798 | $149,983 | $145,719 | 0.627 | 0.763 | 0.812 |
5 | 1390 | 1709 | 1716 | $619,948 | $517,324 | $554,605 | $318,399 | $138,221 | $134,737 | 0.645 | 0.787 | 0.835 |
5.2 | 1418 | 1729 | 1734 | $613,527 | $516,201 | $554,354 | $302,037 | $127,670 | $124,801 | 0.663 | 0.809 | 0.855 |
5.4 | 1445 | 1746 | 1751 | $608,000 | $516,007 | $554,885 | $286,643 | $118,205 | $115,807 | 0.681 | 0.829 | 0.873 |
5.6 | 1470 | 1762 | 1766 | $603,316 | $516,652 | $556,128 | $272,156 | $109,714 | $107,659 | 0.698 | 0.847 | 0.889 |
5.8 | 1494 | 1777 | 1780 | $599,428 | $518,059 | $558,021 | $258,518 | $102,094 | $100,275 | 0.715 | 0.864 | 0.903 |
6 | 1516 | 1790 | 1793 | $596,289 | $520,155 | $560,507 | $245,675 | $95,255 | $93,578 | 0.732 | 0.879 | 0.916 |
6.2 | 1537 | 1802 | 1805 | $593,857 | $522,876 | $563,535 | $233,574 | $89,114 | $87,499 | 0.748 | 0.893 | 0.927 |
6.4 | 1558 | 1812 | 1815 | $592,090 | $526,167 | $567,061 | $222,167 | $83,597 | $81,978 | 0.763 | 0.905 | 0.937 |
6.6 | 1577 | 1822 | 1825 | $590,953 | $529,975 | $571,044 | $211,410 | $78,638 | $76,961 | 0.778 | 0.916 | 0.945 |
6.8 | 1595 | 1830 | 1834 | $590,409 | $534,257 | $575,448 | $201,260 | $74,180 | $72,397 | 0.792 | 0.926 | 0.953 |
7 | 1612 | 1838 | 1842 | $590,427 | $538,970 | $580,240 | $191,680 | $70,168 | $68,243 | 0.806 | 0.935 | 0.959 |
7.2 | 1628 | 1845 | 1850 | $590,976 | $544,081 | $585,393 | $182,631 | $66,556 | $64,460 | 0.819 | 0.943 | 0.965 |
7.4 | 1644 | 1852 | 1856 | $592,028 | $549,555 | $590,880 | $174,081 | $63,303 | $61,011 | 0.831 | 0.949 | 0.969 |
7.6 | 1658 | 1858 | 1863 | $593,558 | $555,366 | $596,678 | $165,999 | $60,370 | $57,866 | 0.843 | 0.955 | 0.974 |
7.8 | 1672 | 1863 | 1868 | $595,540 | $561,487 | $602,766 | $158,353 | $57,725 | $54,995 | 0.854 | 0.961 | 0.977 |
8 | 1685 | 1868 | 1874 | $597,952 | $567,896 | $609,125 | $151,119 | $55,337 | $52,373 | 0.864 | 0.966 | 0.980 |
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Tian, Q.; Yeh, C.-W.; Fang, C.-C. Bayesian Decision Making of an Imperfect Debugging Software Reliability Growth Model with Consideration of Debuggers’ Learning and Negligence Factors. Mathematics 2022, 10, 1689. https://doi.org/10.3390/math10101689
Tian Q, Yeh C-W, Fang C-C. Bayesian Decision Making of an Imperfect Debugging Software Reliability Growth Model with Consideration of Debuggers’ Learning and Negligence Factors. Mathematics. 2022; 10(10):1689. https://doi.org/10.3390/math10101689
Chicago/Turabian StyleTian, Qing, Chun-Wu Yeh, and Chih-Chiang Fang. 2022. "Bayesian Decision Making of an Imperfect Debugging Software Reliability Growth Model with Consideration of Debuggers’ Learning and Negligence Factors" Mathematics 10, no. 10: 1689. https://doi.org/10.3390/math10101689
APA StyleTian, Q., Yeh, C. -W., & Fang, C. -C. (2022). Bayesian Decision Making of an Imperfect Debugging Software Reliability Growth Model with Consideration of Debuggers’ Learning and Negligence Factors. Mathematics, 10(10), 1689. https://doi.org/10.3390/math10101689