International Journal of Reliability, Quality and Safety Engineering

In this paper, we developed a method for constructing confidence intervals for the parameters of lifetime distributions based on progressively type II censored data. The method produces closed form expressions for the bounds of the confidence intervals for several special cases of parameters and lifetime distributions. Closed form approximations are derived for the intervals for the parameters of the location or scale families of distributions. The method is illustrated with several examples and analyses of real data sets are included to illustrate the application of the method.

In this work, a methodology that uses the dynamic Bayesian networks (DBNs) in combination with an idea algebra is developed for assessing the dynamic reliability of engineering systems. A network representation of the system topology is first introduced in the form of “idea” objects representing components and their functional interfaces, thus integrating the functional and material descriptions of the system. Various time-dependent functionalities can thus be mapped to segments or loops of the resulting network, which are then translated automatically into the form of a DBN, thereby avoiding the need to manually generate the dynamic fault tree (DFT) logic that would normally serve as a starting point. The methodology is demonstrated in a case study, where reliability analysis of an automobile system is performed. The idea algebra is automatically deployed in Mathematica and evaluated in the GeNIe platform. Weibull distribution was used for the generation of the dynamic values for the reliability analysis of the system within a certain period.

This paper is the stochastic analysis of a complex repairable system comprising of subsystems in a series arrangement under the $k$-out-of-$n$: $G$ type configuration. Both of the subsystems are in series arrangement and having auto transfer switches when some unit fails. Subsystem 1 is supposed to work under the $k$-out-of-$n$: $G$, scheme, and subsystem 2 which has four indistinguishable units in parallel arrangement with an auto switch functioning under the 1-out-of-4: $G$ scheme. A catastrophic failure is characterized as causing damage to the entire system. Units’ failure, switch failures, and catastrophic failure rates are constant, but repair rates are treated as variables with two types of distributions: general distribution and copula distribution. The model is analyzed using a supplementary variables approach, with probabilistic measures such as availability, reliability, MTSF, and profit functions derived.

This paper considers the estimation of the stress-strength parameter $R=P(X>Y)$ under progressive type-II censored samples, where $X$ is the strength and $Y$ is the stress follow extended Chen distribution. It is assumed that $X$ and $Y$ are independent. Two cases are studied. The uniformly minimum variance unbiased estimator is derived when a common scale parameter and a common shape parameter are known. In both the cases, the maximum likelihood estimates are computed using numerical iteration technique. Sufficient conditions are derived under which the MLEs of $R$ exist and unique. The Bayes estimates with respect to the squared error loss function are evaluated using Lindley’s and MCMC methods. Interval estimates are also constructed using asymptotic and bootstrap techniques. A simulation study is carried out to compare the proposed methods. Finally, data analysis has been performed on two real-life data sets for the purpose of illustration.

A new research area namely, precision business management, is quietly blooming through network theory. In precision business management, several new management tools can be developed to precisely adjust the behavior of the entities in the company to satisfy the management requirement. This paper deals with the situation when specific business process pattern should be recognized, and the related entities in the process have to be identified. It is referred to a kind of covering problem in network reliability. Minimal path set can be considered as a set of flow combinations. However, in some cases, a subset of the flow combination may be required for applications. Therefore, techniques for dealing such cases are needed. This paper proposes a heuristic approach to solve the covering problem in network reliability. Some numerical examples are presented for explanation. The results show that the cases are interesting in the discussion.

The ability to accurately determine the temporal safe region in time-variant reliability analysis is seminal for reliability-based design. When stochastic excitations are present and discrete-time approaches are invoked, the errors can be large when one uses only one past safe event (and one new failure event) at each time-step. Furthermore, when all previous safe events are accumulated and used, the calculations can be time consuming and the accuracy not ensured. In this paper, a minimal, or a so-called extreme limit-state, surface is obtained to identify the system temporal safe region in an economical manner. To do this, the limit-state surface motion for each failure mode is recorded as a parametric polar plot that provides both magnitude and relative angle of the vectors from the origin to the most-likely failure points (MLFPs) in standard normal space. The angle differences provide correlation and the magnitude differences provide importance. At the component-level, a few logical policies that compare correlation and the magnitude ensure that the safe region is sufficiently recognized. At the system-level, the temporal average of correlations and the magnitudes at the component-level, along with series or parallel system designations, foretells which failure modes are needed to form the system extreme limit-state surface. The impact of the work includes an immediate recognition of the important failure modes and reduced computation for methods such as multi-normal integration. Case studies of both series-system reliability and parallel-system reliability are presented using structural beams excited by stochastic loads and plagued with degrading material properties and dimensions. The accuracy of the extreme LSS is demonstrated cogently. The use of the polar plots as a design tool becomes evident.

In this paper, the stress–strength reliability of two multicomponent parallel systems with heterogeneous exponentiated half logistic-$F$ components under the same and the different baseline distribution functions are compared. The comparisons are carried out concerning the usual stochastic order and reversed hazard rate order with majorized shape parameters of the distributions. Also, the maximum likelihood estimator (MLE) and uniformly minimum variance unbiased estimator (UMVUE) of the stress–strength reliability of the aforementioned multicomponent parallel system are obtained and then compared via Monte Carlo simulations.