In this paper, a new nonparametric CONTROL CHART based on two (EWMA) statistics is proposed for monitoring process deviation from the target value. The performance comparison of the proposed CHART with the existing nonparametric (EWMA) sign CONTROL CHART and a nonparametric CUSUM mean CONTROL CHART are made by using out-of-CONTROL AVERAGE run length. The simulation study showed the superiority of the suggested CHART over the four other parametric and nonparametric CHARTs. An empirical illustration is also provided for performance evaluation of the proposed CHART. By comparing the proposed CHART with the existing CHARTs, it is concluded that the proposed CHART is more sensitive in detecting a small shift in the process.

This study proposed a dual EXPONENTIALLYWEIGHTED MOVING AVERAGE ((EWMA)) statistics based nonparametric sign CONTROL CHART to monitor the process deviation from the targeted value. The performance of the proposed CHART is compared with the existing nonparametric version of the (EWMA) sign and Cumulative Sum (CUSUM) mean CONTROL CHARTs by using out-of-CONTROL AVERAGE run length for various shifts in the process. The simulation study showed the superiority of the suggested CHART over the existing counterparts. A real dataset is also considered for the application of the proposed CHART.

Purpose: This paper aims to study the effect of inertia on the performance of the (EWMA) CONTROL CHART for attribute characteristics and to investigate the effects of inertia properties on CONTROL CHARTs with attribute characteristics. Design/methodology/approach: By calculating the inertia criterion, the effectiveness of the CONTROL CHART can be measured in identifying changes and how one can reduce the inertial properties of the CONTROL CHARTs. MATLAB software has been used to conduct simulation studies. The effect of inertia on the performance of an EXPONENTIALLY WEIGHTED MOVING AVERAGE CONTROL CHART and modified EXPONENTIALLY WEIGHTED MOVING AVERAGE CONTROL CHART for observations caused by correlated processes based on Poisson distribution has been investigated. Findings: After calculating and analyzing the results, it was determined that the modified exponential MOVING AVERAGE CONTROL CHART performs better than the exponential MOVING AVERAGE CONTROL CHART based on the Poisson distribution in the worst-case signal resistance. Also, by decreasing the parameter λ, the inertia value of the CONTROL CHARTs increased. Research limitations/implications: Other CONTROL CHARTs that follow different distributions can be used, or the effect of inertia on the performance of CONTROL CHARTs in multivariable processes can be considered as a subject for further study. Practical implications: After analyzing the positive properties of inertia, it is possible to increase productivity in production processes. This research purposed new indicators to evaluate the performance of CONTROL CHARTs in terms of inertial properties. Social implications: In the field of manufacturing industries, it is possible to increase productivity by examining the appropriate characteristics of inertia. On the other hand, regarding the use of CONTROL CHARTs for monitoring chemical and petrochemical processes and evaluating the inertia index, it is possible to reduce the variability of the process in long term, which will have an impact on environmental issues. Originality/value: Measuring the inertia of the EXPONENTIALLY WEIGHTED MOVING AVERAGE CONTROL CHART when the observations are independent and follow the Poisson distribution, in addition to measuring the inertia of the EXPONENTIALLY WEIGHTED MOVING AVERAGE CONTROL CHART in the presence of correlated observations distinguishes this research from previous studies.

Several researchers have investigated the e ect of measurement errors on adaptive Shewhart CHARTs. However, the e ect of measurement errors on the performance of Variable Sample Size EXPONENTIALLY WEIGHTED MOVING AVERAGE (VSS (EWMA)) CONTROL CHARTs has not been evaluated yet. In this regard, the present study aims to investigate the performance of the VSS (EWMA) CHART in the presence of measurement errors using a linear covariate error model and Markov chain method. The results indicated that the presence of measurement errors could signi cantly a ect the performance of the VSS (EWMA) CHART. In addition, the e ect of taking multiple measurements for each item in a subgroup on the performance of the VSS (EWMA) CHART was evaluated. Moreover, the performance of the VSS (EWMA) CONTROL CHART was compared with those of several other CONTROL CHARTs in the presence of measurement errors. Finally, an illustrative example was presented to demonstrate the application of the VSS (EWMA) CONTROL CHART with measurement errors.

The cost parameters in economic-statistical models of CONTROL CHARTs are usually assumed to be deterministic in the literature. Considering uncertainty in the cost parameters of CONTROL CHARTs is very common in application. So, several researchers used scenario-based approach for robust economic-statistical design of CONTROL CHARTs. In this paper, we specifically concentrate on the Multivariate EXPONENTIALLY WEIGHTED MOVING AVERAGE (M(EWMA)) CONTROL CHART and consider interval uncertainty in the cost parameters of the M(EWMA) CONTROL CHART and develop a robust economic-statistical design of the M(EWMA) CONTROL CHART by using interval robust optimization technique. Meanwhile, the Lorenzen and Vance cost function is used, and to calculate the AVERAGE run length criterion, the Markov chain approach is applied. Then, genetic algorithm for obtaining optimal solution of the proposed robust model is used and effectiveness of this model is illustrated through a numerical example. Also, a comparison with certain situation of the cost parameters is performed. Finally, a sensitivity analysis is done to investigate the effect of changing the intervals of cost parameters of the Lorenzen and Vance model on the optimal solutions. Furthermore, a sensitivity analysis on the other certain cost parameters of the Lorenzen and Vance model is done.

CONTROL CHARTs are powerful tools of statistical process CONTROL (SPC) used for monitoring processes. CONTROL CHARTs are not only used to detect changes in process, but also enable the quality engineers to prepare the system for an appropriate response before production of the faulty products. The main objective of most researches on CONTROL CHARTs is developing a favorable and cost-effective design as well as most appropriate sampling methods. In most of the researches that have been done in this field, the CONTROL CHARTs are designed based on simple random sampling (SRS). However, there are many CHARTs in the literature of statistical process CONTROL that are not based on SRS and use alternative methods such as ranked set sampling (RSS) or generalized methods. The RSS method is an alternative to SRS when taking actual measurement of the quality characteristic is costly or production of the faulty products is expensive. In this paper, in order to improve the performance of mixed (EWMA)-CUSUM (MEC) and mixed CUSUM-(EWMA) (MCE) CONTROL CHARTs in estimating the population mean, ranked set sampling method rather than common simple random sampling method is used to design these mixed CONTROL CHARTs. The performances of the proposed MEC-RSS and MCE-RSS CONTROL CHARTs are evaluated through simulation studies using the AVERAGE run length (ARL) criterion. Moreover, the performances of the proposed CONTROL CHARTs are compared with those of CUSUM-SRS, CUSUM-RSS, (EWMA)-SRS, (EWMA)-RSS, MEC-SRS, and MCE-SRS CONTROL CHARTs. The results revealed that RSS method improves CONTROL CHARTs performance compared to SRS method because it provides an efficient estimation of the mean and variance of the population. In addition, using the ranked set sampling scheme makes the proposed mixed CONTROL CHARTs more sensitive to detecting the small and moderate shifts in the process mean than the other corresponding classical CONTROL CHARTs. Moreover, based on the same sampling methods, the performances of mixed CONTROL CHARTs are better than those of the single CUSUM and (EWMA) CONTROL CHARTs.

One of the most important quality characteristics in a production process is the product lifetime. The production of highly reliable products is a concern of manufacturers. Since it is time-consuming and costly to measure lifetime data, designing a CONTROL CHART seems difficult. To solve the problem, lifetime tests are employed. In the present study, one-sided and two-sided (EWMA) CONTROL CHARTs are designed under a type II censoring (failure censoring) life test. Product lifetime is a quality characteristic dealt with in this study. It is assumed to follow the Weibull distribution with a fixed shape parameter and a variable scale parameter. In order to design a CONTROL CHART, first, the CONTROL CHART limits are calculated for different parameters, and then the AVERAGE Run Length (ARL) in the out-of-CONTROL state is used to evaluate the performance of the proposed CONTROL CHART. Next, a comprehensive sensitivity analysis is performed for the different parameters involved. The computational results show that the one-sided CONTROL CHART has better performance to detect the shift of lifetime data than the two-sided CONTROL CHART. The AVERAGE run length curve of the two-sided CONTROL CHART is biased, while that of the one-sided CONTROL CHART is unbiased. A very effective parameter that increases the performance of a CONTROL CHART is found to be the number of failures in the failure censoring process. Finally, simulated and real examples are provided to show the performance of the proposed CONTROL CHART.

Banks as fund intermediaries in providing and allocating resources to the community, encounter market risk, liquidity risk and etc. In this study, the market risk, is taken into consideration in order to determine the optimal currency basket, one of the fundamental aspects of Foreign Currency Reserve Management in banks, which itself is also affected by fluctuating interest rates, exchange rates, stock prices and etc. The approach used in this paper is the value-at-risk criterion (VaR) the variance-covariance method, along with the EXPONENTIALLY WEIGHTED MOVING AVERAGE ((EWMA)) technic. Value at risk actually summarizes the types of risks in a single digit, and it releases the senior management from bunches of risk calculations. The purpose is to design a model which provide an optimal combination for holding 6 currency reserves such as U. S. dollar, Dirham, Yen, Lira, Won, and Euro in Bank Mellat using the reference rates data of the aforementioned currencies in 2018. At the end, the model was solved using LINGO and Excel software. The results show that the maximum share of the US dollar and the dirhams in the currency basket of Bank Mellat are 33% and 67%, respectively. Accordingly, if the share of that currencies mentioned above exceed the obtained digits in the currency basket, then the maximum expected losses on the currency portfolio increase over the time and at the level of desired level of confidence. Also, other currencies are so risky, therefore Mellat Bank, to hold these currencies must plan more based on its trading needs.

CONTROL CHARTs are one of the most effective tools used in quality CONTROL to monitor various quality characteristics in a process with the aim to improve quality of the product. Usually, in Shewhart CONTROL CHARTs, the normality assumption met for the data, but sometimes there is lack of information regarding the statistical distribution of the observations. For this reason, non-parametric CONTROL CHARTs are used in this situation. In this research, non-parametric sign CHARTs are introduced to deal with the lack of information regarding observations’ statistical distribution. Nonparametric Generalized WEIGHTED MOVING AVERAGE Sign CONTROL CHART (NS GWMA) designed using statistical design and AVERAGE run length (ARL) and its statistical performance was studied. But statistical design is not enough to ensure the performance of a CONTROL CHART, so in the next steps, economic design (ED) and economic-statistical design (ESD) were applied using cost model of Lorenzen and Vance, in order to optimize both statistical and economical characteristics of the CONTROL CHART. The results show that the non-parametric sign-generalized WEIGHTED MOVING AVERAGE sign CONTROL CHART performed well in detecting small shifts in the process and also had optimized cost and time to perform.