The reliability of a non-repairable component always decreases with time, but for repairable systems the term “reliability growth” refers to the process of gradual product improvement through the elimination of design deficiencies. In repairable systems, reliability growth is observable through an increase in the interarrival times of failures. Reliability growth is applicable to all levels of design decomposition from complete systems down to components. The maximum achieveable reliability is locked in by design, so reliability growth above the design reliability is only possible through design changes. It may be possible to achieve some reliability growth through other improvements (such as optimizing the maintenance program) though these improvements will only help the system to achieve its design reliability.

The model developed is realistic, easy to use, and gives a better prediction of reliability of a software. In summary, all of three tests using different versions of Apache failure data sets suggest that our proposed model well fits the real data and presents better performance than the benchmarks in error occurrence prediction. Besides, both the testing effort and the error interdependency effects play an important role in the parameter estimation. Section 4 gives the approach to check the validity of the proposed model. Section 6 presents the machine learning technique used to select appropriate weights of the proposed model.
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An all-stage truncated multiple change point model for software reliability assessment

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Rejected, or Superseded. Haul Truck 1 was purchased for a shipping firm as a used vehicle with
11,028 miles. The truck now runs varied routes depending on the number
of shipments to which it is assigned.
IRGT simply piggybacks reliability failure reporting, in an
informal fashion, on all engineering tests. When a potential reliability
problem is observed, reliability engineering is notified and

Model development

appropriated design action is taken. IRGT will usually be implemented at
the same time as the basic reliability tasks. In addition to IRGT,
reliability growth may take place during early prototype testing, during
dedicated system testing, during production testing, and from feedback

• The software fails as a function of operating time as opposed to calendar time.
• The
  technical number of the piece of equipment for which the recommendation
  is being made.
• If the data is event-based, certain labels will also look different depending on whether or not the data contains dates.
• Specifically, for an NHPP-based SRGM, it is assumed that follows a Poisson distribution with a mean value function .
• You
  can set this value to True
  to indicate that this recommendation is complete.
• Sometimes, you may want to
  perform a Reliability Growth Analysis on a variable that does not measure a specific
  event (e.g., an amount).

from any manufacturing or quality testing or inspections. The formal
dedicated testing or RGDT will typically take place after the basic
reliability tasks have been completed. The management strategy

may be driven by budget and schedule but it is defined by the actual

actions of management in correcting reliability problems.
We use the mean value function (MVF) to denote the expected cumulative number of detected failures in the time period . That is,where means the expectation operator and is called failure intensity function which indicates the instantaneous fault-detection rate at time . Specifically, for an NHPP-based SRGM, it is assumed that follows a Poisson distribution with a mean value function . That is, the model can be mathematically characterized aswhere is the Poisson probability mass function (pmf) with mean [29, 30]. Generally, one can obtain different NHPP models by taking different mean value functions.

Figures 1 and 2 demonstrate two plots that present reliability growth results over time. Figure 1 presents the expected number of failures and Figure 2 presents the instantaneous MTBF. As stated above, it is essential to consider fault interdependency when modeling software reliability growth processes. Specifically, in this work we propose three generations of interdependent errors. reliability growth model That is, the detection of the second-generation errors relies on the first generation, and the detection of the third-generation errors depends on the second generation. Moreover, the second-generation errors are detectable only if the first-generation errors have been removed, and the third-generation errors are detectable only if the second-generation errors have been removed.
Another stream adopts the multiattribute utility theory (MAUT) to decide the release time. For instance, Singh et al. [27] built an SRGM based on the Yamada two-stage model and focused on two different attributes to investigate the release time. Pachauri et al. [28] studied an SRGM incorporating a generalized modified Weibull testing-effort function in an imperfect debugging environment and the optimal release policy is examined using both genetic algorithm (GA) and MAUT. (iii) For Apache 2.0.39, the estimated results are presented in Table 4, with , , , , and for our proposed model. The ratios of three generations of errors become about 53%, 38%, and 9%, respectively. Then, the ratio for errors is approximately 59%, the ratio for errors is around 28%, and the leftover are errors.

In the development process, a variety of tests need to be conducted to ensure the reliability of the software system. In this work, we propose a framework for software reliability modeling that simultaneously captures effects of testing effort and interdependence between error generations. In order to evaluate our proposed model, we compare its performance with other existing models by doing experiments with actual software failure data, that is, three versions of Apache. The numerical analysis from all three Apache versions demonstrates that the proposed model fits the real-world data very well and exhibits a high level of prediction capability. The objective of the study is to offer a more accurate software reliability growth model that can be a reference to decision-making for software developers and testing personnel. By using the proposed model, the optimal timing at which software is released to the market can be obtained that is subject to the software reliability threshold and the testing cost.
Yeu-Shiang Huang is currently a professor in the Department of Industrial and Information Management at National Cheng Kung University, Taiwan. And Ph.D. degrees in Industrial Engineering from the University of Wisconsin–Madison, U.S.A. His research interests include operations management, supply chain management, reliability engineering, and decision analysis. A (basic) straight-line fitting with certain plane points is more persuasive and has more empirical power than the fact that the points may be approximated by a higher-order curve (not simple).
For example, the bar chart in Figure 5 displays the actual (current) failure rate with the predicted failure rate for all the B modes in the analysis. In these charts, the red bar (left) represents the actual failure rate and the green bar (right) represents the failure rate after the fixes have been implemented. From the chart in Figure 5, you can see how each failure mode is contributing to the failure rate of the system. In addition, you can also see how the failure rate for each failure mode is decreasing after the implementation of the fix.