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The purpose of this paper is to use Bayesian probability theory to analyze the software reliability model with multiple types of faults. The probability that all faults are detected and corrected after a series of independent software tests and correction cycles is presented. This in turn has a number of applications, such as how long to test a software, estimating the cost of testing, etc.

The use of Bayesian probabilistic models, when compared to traditional point forecast estimation models, provides tools for risk estimation and allows decision makers to combine historical data with subjective expert estimates. Probability evaluation is done both prior to and after observing the number of faults detected in each cycle. The conditions under which these two measures, the conditional and unconditional probabilities, are the same is also shown. Expressions are derived to evaluate the probability that, after a series of sequential independent reviews have been completed, no class of fault remains in the software system by assuming the prior distribution as Poisson and binomial.

From results in Sections 4 and 5 it can be observed that the conditional and unconditional probabilities are the same if the prior probability distribution is Poisson and binomial. In these cases the confidence that all faults are deleted is not a function of the number of faults observed during the successive reviews but it is a function of the number of reviews, the detection probabilities and the mean of the prior distribution. This is a remarkable result because it gives a circumstance in which the statistical confidence from a Bayesian analysis is actually independent of all observed data. From the result in Section 4 it can be seen that exponential formula could be used to evaluate the probability that no fault remains when a Poisson prior distribution is combined with a multinomial detection process in each review cycle.

The paper is part of research work for a PhD degree.

Although in principle prior information can significantly improve inference, incorporating incorrect prior information will bias the estimates of any inferential analysis. This fact deters many scientists from incorporating prior information into their inferential analyses. In the natural sciences, where experiments are more regularly conducted, and can be combined with other relevant information, prior information is often used in inferential analysis, despite it being sometimes nontrivial to specify what that information is and how to quantify that information. In the social sciences, however, prior information is often hard to come by and very hard to justify or validate. We review a number of ways to construct such information. This information emerges naturally, either from fundamental properties and characteristics of the systems studied or from logical reasoning about the problems being analyzed. Borrowing from concepts and philosophical reasoning used in the natural sciences, and within an info-metrics framework, we discuss three different, yet complimentary, approaches for constructing prior information, with an application to the social sciences.

Bayesian A/B inference (BABI) is a method that combines subjective prior information with data from A/B experiments to provide inference for lift – the difference in a measure of response in control and treatment, expressed as its ratio to the measure of response in control. The procedure is embedded in stable code that can be executed in a few seconds for an experiment, regardless of sample size, and caters to the objectives and technical background of the owners of experiments. BABI provides more powerful tests of the hypothesis of the impact of treatment on lift, and sharper conclusions about the value of lift, than do legacy conventional methods. In application to 21 large online experiments, the credible interval is 60% to 65% shorter than the conventional confidence interval in the median case, and by close to 100% in a significant proportion of cases; in rare cases, BABI credible intervals are longer than conventional confidence intervals and then by no more than about 10%.

As an important load-bearing component of cable-stayed bridge, the cable-stayed cable is an important load-bearing link for the bridge superstructure and the load transferred directly to the bridge tower. In order to better manage the risk of the cable system in the construction process, the purpose of this paper is to study a new method of dynamic risk analysis of the cable system of the suspended multi-tower cable-stayed bridge based on the Bayesian network.

First of all, this paper focuses on the whole process of the construction of the cable system, analyzes the construction characteristics of each process, identifies the safety risk factors in the construction process of the cable system, and determines the causal relationship between the risk factors. Secondly, the prior probability distribution of risk factors is determined by the expert investigation method, and the risk matrix method is used to evaluate the safety risk of cable failure quantitatively. The function expression of risk matrix is established by combining the probability of risk event occurrence and loss level. After that, the topology structure of Bayesian network is established, risk factors and probability parameters are incorporated into the network and then the Bayesian principle is applied to update the posterior probability of risk events according to the new information in the construction process. Finally, the construction reliability evaluation of PAIRA bridge main bridge cable system in Bangladesh is taken as an example to verify the effectiveness and accuracy of the new method.

The feasibility of using Bayesian network to dynamically assess the safety risk of PAIRA bridge in Bangladesh is verified by the construction reliability evaluation of the main bridge cable system. The research results show that the probability of the accident resulting from the insufficient safety of the cable components of the main bridge of PAIRA bridge is 0.02, which belongs to a very small range. According to the analysis of the risk grade matrix, the risk grade is Ⅱ, which belongs to the acceptable risk range. In addition, according to the reverse reasoning of the Bayesian model, when the serious failure of the cable system is certain to occur, the node with the greatest impact is B3 (cable break) and its probability of occurrence is 82%, that is, cable break is an important reason for the serious failure of the cable system. The factor that has the greatest influence on B3 node is C6 (cable quality), and its probability is 34%, that is, cable quality is not satisfied is the main reason for cable fracture. In the same way, it can be obtained that the D9 (steel wire fracture inside the cable) event of the next level is the biggest incentive of C6 event, its occurrence probability is 32% and E7 (steel strand strength is not up to standard) event is the biggest incentive of D9 event, its occurrence probability is 13%. At the same time, the sensitivity analysis also confirmed that B3, C6, D9 and E7 risk factors were the main causes of risk occurrence.

This paper proposes a Bayesian network-based construction reliability assessment method for cable-stayed bridge cable system. The core purpose of this method is to achieve comprehensive and accurate management and control of the risks in the construction process of the cable system, so as to improve the service life of the cable while strengthening the overall reliability of the structure. Compared with the existing evaluation methods, the proposed method has higher reliability and accuracy. This method can effectively assess the risk of the cable system in the construction process, and is innovative in the field of risk assessment of the cable system of cable-stayed bridge construction, enriching the scientific research achievements in this field, and providing strong support for the construction risk control of the cable system of cable-stayed bridge.

The traditional literature dealing with statistical decision problems usually assumes that previous information about an associated experiment may be expressed by means of conditional probabilistic information, and the actual experimental outcomes can be perceived with exactness by the statistician. We now consider statistical decision problems satisfying the first assumption above, so that the actual available information cannot be exactly perceived, but rather it may be assimilated with fuzzy information (as defined by Zadeh et al.).

In the last two decades there has been considerable progress made in the development of alternative estimation techniques to ordinary least squares (OLS) regression. The search for alternative estimators has no doubt been motivated by the observance of erratic OLS estimator behavior in cases where there are too few observations, multicollinearity problems, or simply “information‐poor” data sets. Imprecise and unreliable OLS coefficient estimates have been the result.

The purpose of this paper is to present a new efficient method for the tolerance–reliability analysis and quality control of complex nonlinear assemblies where explicit assembly functions are difficult or impossible to extract based on Bayesian modeling.

In the proposed method, first, tolerances are modelled as the random uncertain variables. Then, based on the assembly data, the explicit assembly function can be expressed by the Bayesian model in terms of manufacturing and assembly tolerances. According to the obtained assembly tolerance, reliability of the mechanical assembly to meet the assembly requirement can be estimated by a proper first-order reliability method.

The Bayesian modeling leads to an appropriate assembly function for the tolerance and reliability analysis of mechanical assemblies for assessment of the assembly quality, by evaluation of the assembly requirement(s) at the key characteristics in the assembly process. The efficiency of the proposed method by considering a case study has been illustrated and validated by comparison to Monte Carlo simulations.

The method is practically easy to be automated for use within CAD/CAM software for the assembly quality control in industrial applications.

Bayesian modeling for tolerance–reliability analysis of mechanical assemblies, which has not been previously considered in the literature, is a potentially interesting concept that can be extended to other corresponding fields of the tolerance design and the quality control.

Purpose – The purpose of this paper is to propose a risk‐based approach for spare parts demand forecast and spare parts inventory management for effective allocation of limited resources. Design/methodology/approach – To meet the availability target and to reduce downtime, process facilities usually maintain inventory of spare parts. The maintaining of non‐optimized spare parts inventory claims more idle investment. Even if it is optimized, lack of attention towards the critical equipment spares could threaten the availability of the plant. This paper deals with the various facets of spare parts inventory management, mainly risk‐based spare parts criticality ranking, forecasting, and effective risk reduction through strategic procurement policy to ensure spare parts availability. A risk‐based approach is presented that helps managing spare parts requirement effectively considering the criticality of the components. It also helps ensuring the adequacy of spare parts inventory on the basis of equipment criticality and dormant failure without compromising the overall availability of the plant. Findings – The paper proposes a risk‐based approach that used conjugate distribution technique with the capability to incorporate historical failure rate as well as expert judgment to estimate the future spare demand through posterior demand distribution. The approach continuously updates the prior distribution with most recent observation to give posterior demand distribution. Hence the approach is unique in its kind. Practical implications – Appropriate spare parts unavailability could have great impact on process operation and result in costly downtime of the plant. Following proposed approach the availability target can be achieved in process industry having limited maintenance resources, by forecasting spare parts demand precisely and maintaining inventory in good condition. Originality/value – Adopting the approach proposed in the paper, risk level can be minimized and plant availability can be maximized within the financial constraint. The resources are allocated to the most critical components and thereby increased availability, and reduce risk.