International Journal of Reliability, Quality and Safety Engineering

A consecutive linear (circular) $k$-out-of-$r$-from-$n$: $F$ system consists of $n$ linear (circular) ordered components such that the system fails if and only if there exist a set of $r$ consecutive linear (circular) component that contains at least $k$ failed components. The optimal maintenance of the consecutive $k$-out-of-$r$-from-$n$: $F$ system to linear and circular states is investigated in this paper. First, an integrated strategy of corrective maintenance and preventive maintenance is introduced. Then, for first time, optimal maintenance has been applied to these systems, and optimum maintenance time has been achieved with this strategy. Also, real-world practical examples for this system have been presented.

This paper deals with the study of the reliability of multicomponent stress–strength model assuming that the strength components are independently and identically distributed as power transformed half-logistic (PHL) distribution. The strength components which are subject to a common stress are assumed to be independent with either Weibull distribution or PHL distribution. The maximum likelihood estimates of the multicomponent stress–strength reliability and its asymptotic confidence interval under the above said conditions are obtained. The Bayes estimates of the multicomponent stress–strength reliability are also obtained under squared error loss function and using gamma priors for the parameters. To evaluate the performance of the procedure, a simulation study is considered. For illustration purpose of the proposed model, two real life examples are given.

This paper studies the method to estimate the location parameter of a three-parameter Weibull life distribution in the situation of multiple censoring life data available, the effect of sample size and minimal outcome on life and reliability estimation, and the policy to choose favorable data from operation records. First of all, a method to estimate the location parameter of the Weibull distribution is presented in the scenario of product probabilistic life and reliability estimation. Relationships between the estimated life distribution parameter and the right-censored life data applied is demonstrated, a rule is proposed to choose the appropriate number of censoring life data by discarding some shorter operation time records. It is illustrated that an appropriate combination of sample size and the minimum observation value (right-censored life time) is reasonable for the balance between estimation confidence level and reliability value.

In this paper, we consider the estimation of the reliability in a stress–strength model by the maximum likelihood and Bayesian methods under generalized exponential distribution. We provide the estimation of the reliability with simple random sampling and ranked set sampling methods. Lindley’s algorithm is used to obtain the approximate Bayesian estimation of the reliability with gamma priors. The results are compared in terms of relative efficiency in different sample sizes through a simulation study with R-software. Finally, two real data examples are presented to estimate reliability.

This research proposesalpha ($\alpha )$-cut Exponentially Weighted Moving Average (EWMA) and Cumulative Sum (CUSUM) control charts with fuzzy response observations in a manufacturing process under the existence of mean shift utilizing the fuzzy logic. In this research, the replicate’s observation is a fuzzy number represented by a triangular membership function, with the lower, average, and upper observation values. The fuzzy numbers are then normalized and assigned as input to the fuzzy logic, while a common output measure (COM) value is the output. Finally, the original values of the COM values are employed in developing the EWMA and CUSUM control charts with different $\alpha$-cut values. Three real case studies are adopted to illustrate the proposed EWMA and CUSUM control charts; including piston inside diameter, cap’s angel, and tablet weight. Results showed that the proposed EWMA and CUSUM control charts efficiently monitor fuzzy observations and detect the shift in process means. Moreover, the amount mean shift and $\alpha$-cut values affect the decision on process condition. In conclusion, the proposed approach is found effective in monitoring quality characteristic of fuzzy observations under mean shift which can be applied in a wide range of business applications.

The use of semi-Markov process and regenerative point has been made for determining reliability measures of a computer system. The stochastic model is developed by considering the ideas of unit wise redundancy and failure of service facility. The treatment to the failed service facility is given in order to resume the jobs with full efficiency. The system is analyzed at different time points in the steady state. The profit of the system model has been obtained under the following two policies: In first policy, the profit is evaluated by taking cost per unit time for busy period of the service facility and cost per unit time treatment of the service facility. In second policy, the profit is evaluated by taking cost per unit hardware repair, per unit time software up-gradation and cost per unit time treatment of the service facility. The behavior of some reliability measures, such as MTSF, availability and profit function, has been shown graphically for arbitrary values of the parameters.

The multi-state consecutive linear (circular) $k$-out-of-$r$-from-$n:F$ system consists of $n$ linear (circular) ordered multi-state components. Both the system and its components can have $m$ different states: from complete failure (zero state) up to perfect functioning (($m-$1) state). In this paper we suggest, for the first time, exact reliability for these models. The system is at state below $j$ if and only if at least $k_j$ components out of any $r$ consecutive are in state below $j$ $(k_1\le k_2\le \cdots \le k_{m-1})$. Recent efforts in these branches have focused on simple situations or approximation bands for their reliability in two-state or multi-state models but closed form and exact amount not gained. In the continuation, there are the matlab programs of linear (circular) reliability system and $j$ state probability for $k_j$ in system. In the following, we applied comparative and numerical results and calculated the exact reliability of this strategic systems. Finally, we calculated the exact reliability for two real-world practical examples.

In this paper, we consider a generalized past entropy of order $\alpha$ and type $\beta$ and have characterized some distributions of random lifetimes in continuous and discrete situations. Further, we propose a weighted version of generalized past entropy for continuous and discrete cases and have proved the characterization results. Also, we study a generalized weighted residual entropy for the discrete case. At the end, the concept of generalized cumulative past entropy are also discussed.