Few studies have investigated the integration of triple components including statistical process monitoring (SPM), maintenance policy (MP), and economic production quantity (EPQ). Of those, no research is found to monitor autocorrelated data. Moreover, although delayed monitoring (DM) policy was proposed for an integrated model of SPM and MP, it has not been extended by considering EPQ. We propose an integrated model of triple components subject to some constraints, in which the following features are considered: (1) DM policy that postpones the monitoring action until a determinable time to avoid the possible unnecessary costs, and (2) autocorrelation that, if ignored, can lead to a significant influence on the statistical performance of traditional control charts. ARMA control chart is used to monitor the autocorrelated data. Due to the complexity of the model, a particle swarm optimization algorithm is applied to obtain optimal solution(s). An industrial example, some comparisons and sensitivity analysis are provided for more investigations.

Box‐Jenkins methodology is one of the most famous modeling approaches to describe the underlying stochastic structure and forecasting future values of various phenomena. In this methodology, the models are of type ARIMA, that is, autoregressive integrated moving average. Some advantages of those include robustness, easiness to use, and wide applicability in various disciplines ranging from engineering to economics. Inflation has been a highly discussed issue in economics. This research focuses on modeling and forecasting the yearly inflation rate of Iran from 1960 to 2019 using ARIMA. According to various measures, different ARIMA models are investigated to confirm their effectiveness. It is here showed that non‐seasonal ARIMA (1,0,0) is the most appropriate model for this application.

Organizations that achieved higher capabilities to meet expectations by successfully implementing quality improvement plans can make adjustments to process monitoring without any losses for customers. This approach may reduce costs due to desensitization in monitoring. In this regard, the acceptance control chart (ACC) under the assumptions of independence and normality has already been introduced. However, in practice, particular correlation patterns can be extracted among samples that violate the assumption of independence. Autocorrelation reduces the performance of traditional control charts. In the present study, three types of ACC are extended for monitoring the mean of the most widely used autocorrelated processes. The performance of the proposed charts is evaluated using statistical measures. It is found that the residual-based exponentially weighted moving average ACC (R-EWMA-ACC) has the best performance. Also, two numerical examples illustrate its application. Moreover, optimizing the economic-statistical model indicates that the R-EWMA-ACC spends less than the ARMA control chart.

We aim to extend the Markov System Dynamic method (MSD) to evaluate the reliability of repairable systems in two-state weather (2SW) models. Increasing the number of components in real practices has limited the use of the Markov method, because of increasing the number of equations and the complexity of the problem. There is no such restriction in the MSD method. Thus, it can be applied to complex systems. Theoretically, we indicate that the 2SW model is a type of linear dynamical system. Therefore, we can use MSD to solve it. Through an example, the validity of the proposed method is confirmed in comparison to the Markov method for the 2SW model. Since the MSD method does not use equations, it can be a preferred alternative for calculating the reliability of 2SW models. Accordingly, we apply the MSD method for assessing the reliability of a four-component system.