The two most significant sources of uncertainty are randomness and incomplete information. In real systems, we wish to monitor processes in the presence of these two kinds of uncertainty. This paper aims to construct a fuzzy STATISTICAL CONTROL CHART that can explain existing fuzziness in data while considering the essential variability between observations. The proposed CONTROL CHART avoids defuzzification methods such as fuzzy mean, fuzzy mode, fuzzy midrange, and fuzzy median. The out-of-CONTROL states are determined based on a fuzzy in-CONTROL region and a simple and precise graded exclusion measure that determines the degree to which fuzzy subgroups are excluded from the fuzzy in-CONTROL region. The proposed CHART is illustrated with a numerical example.

Acceptance CONTROL CHARTs (ACC), as an effective tool for monitoring highly capable processes, establish CONTROL limits based on specification limits when the fluctuation of the process mean is permitted or inevitable. For designing these CHARTs by minimizing economic costs subject to STATISTICAL constraints, an economic-STATISTICAL model is developed in this paper. However, the parameters of some processes are in practice uncertain. Such uncertainty could be an obstacle to getting the best design. Therefore, the parameters are investigated by a robust optimization approach. For this reason, a solution procedure utilizing a genetic algorithm (GA) is presented. The algorithm procedure is illustrated based on numerical studies. Additionally, sensitivity analysis and some comparisons are carried out for more investigations. The results indicate better performance of the proposed approach in designing ACC and more reliable solutions for practitioners.

We introduce a method for the STATISTICAL design of a depth-based CONTROL CHART, using the percentile-based approach. The proposed CONTROL CHART is affine invariant and is asymptotically distribution-free. Generally, the performance of a CONTROL CHART is evaluated with the average run length metric. The average run length metric has a geometric distribution skewed to the right with a large standard deviation and may not be a proper measure for evaluating the CONTROL CHART. Therefore, we use the STATISTICAL design method of CONTROL CHARTs with the PL approach, which is an improvement and development on classical STATISTICAL design. By employing constraints on average run length, the length of in-CONTROL and out-of-CONTROL performances are guaranteed with predetermined probabilities and we can ensure that the in-CONTROL run length exceeds the desired value and the out-of-CONTROL run length is less than the desired value. Simulation studies show that the proposed CONTROL CHART is more efficient than the average run length approach.

Cumulative Count of Conforming (CCC) CHARTs are utilized for monitoring the quality characteristics in high-quality processes. Executive cost of CONTROL CHARTs is a motivation for researchers to design them with the lowest cost. Usually, in most researches, only one objective named cost function is minimized subject to STATISTICAL constraints, which is not effective method for economic-STATISTICAL design of CONTROL CHARTs. In this paper, a multi-objective model for the economic-STATISTICAL design of the CCC CONTROL CHART is developed. Then, multi-objective evolutionary algorithm (NSGA-II) for obtaining the Pareto optimal solution of the model is proposed. A numerical example is applied to illustrate the effectiveness of the proposed model. This model leads to lower cost and smaller probability of Type I and Type II errors, compared with economic model. In addition, a sensitivity analysis is done to investigate the effect of input parameters on the best solutions of the proposed model.

Traditionally, the STATISTICAL quality CONTROL techniques utilize either an attributes or variables product quality measure. Recently, some methods such as three-level CONTROL CHART have been developed for monitoring multi attribute processes. CONTROL CHART usually has three design parameters: the sample size (n), the sampling interval (h) and the CONTROL limit coefficient (k). The design parameters of the CONTROL CHART are generally specified according to STATISTICAL or/and economic criteria. The variable sampling interval (VSI) CONTROL scheme has been shown to provide an increase to the detecting efficiency of the CONTROL CHART with fixed sampling rate (FRS). In this paper a method is proposed to conduct the economic-STATISTICAL design for variable sampling interval of the three-level CONTROL CHARTs. We use the cost model developed by Costa and Rahim and optimize this model by genetic algorithm approach. We compare the expected cost per unit time of the VSI and FRS 3-level CONTROL CHARTs. Results indicate that the proposed CHART has improved performance.

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.

In recent years, the development of CONTROL CHARTs has attracted the attention of researchers in healthcare systems. The purpose of this paper is to design a riskadjusted cumulative sum (CUSUM) CONTROL CHART to monitor the survival time of patients after performing a surgical operation. In this CONTROL CHART, risk adjustment is conducted to consider the impact of each patient's preoperative risks on survival times. It should be noted that the Parsonnet score has been calculated and recorded for each patient before undergoing a surgical operation. Moreover, a class of survival analysis regression models called accelerated failure time models has been employed for risk-adjustment. However, the implementation of the RACUSUM CONTROL CHART requires determining the design parameters such as the lower CONTROL limit and coe, cient for optimal design of CUSUM CONTROL CHART. These parameters should be selected in an optimal way putting the desired STATISTICAL and economic considerations into service. To this end, a multi-objective model, including three objectives of cost, the in-CONTROL ARL and the inverse of out-of-CONTROL ARL, has been proposed and the model is solved with the help of a multistage algorithm based on the data envelopment analysis (DEA) method. Then, to show the performance of the proposed procedure, a real case study has been considered in the cardiac surgery center in Iran. Doing so, a special kind of operation called coronary artery bypass grafting (CABG) surgery was selected, and the information associated with 100 patients was collected over time. Finally, a comparison has been made between the multi-objective design model and a pure economic design model. The results clearly reveal that with a relatively small increase in the cost function, the multi-objective design of the RACUSUM CHART has better STATISTICAL performance. Therefore, it is advisable to implement the proposed multi-objective model to design the riskadjusted CUSUM CONTROL CHART in healthcare systems.

The familiar multivariate process monitoring and CONTROL procedure is the Hotelling’s T2 CONTROL CHART, a direct analog of the univariate shewhart x¯ CHART. But, its efficiency for detecting small to moderate shifts in the process mean is poor.  To improve the power of CHART, this paper studies the STATISTICAL design of the T2 CHART with variable ratio sampling scheme. It is assumed that the length of time the process remains in CONTROL has exponential distribution. The CHART is modeled using Markov chains and is optimized using genetic algorithm optimization method. The results show that the T2 CHART with variable ratio sampling scheme is quicker than the classical one in detecting almost all shifts in the process mean.

The usual procedure when employing a T2 CONTROL CHART for multivariate process monitoring is to take samples of fixed size n0 every h0 hours from the process. Recent studies have shown that using variable parameters (VP) schemes results in CHARTs with more STATISTICAL power when detecting small to moderate shifts in the process mean vector. In this paper, the VPT2 CONTROL CHART for monitoring the process mean vector is economically designed. The cost model proposed by Lorenzen and Vance is used here and is minimized through a genetic algorithm (GA) approach.

The Hotelling's T2 CONTROL CHART, is the most widely used multivariate procedure for two or more related quality characteristics, but it’s power lacks the desired performance in detecting small to moderate shifts. Recently, the variable sampling intervals and CONTROL Limits (VSICL) CONTROL scheme has been proved to have a very good performance on detecting small to moderate shifts when it is compared to the fixed ratio sampling (FRS) T2 CONTROL CHART. Moreover, it is shown that the VSICL scheme is more economical than the classical one. This article studies the economic consequences of a new CONTROL scheme named variable sample sizes, sampling intervals and CONTROL limits (VSSICL) in that the sample size n, sampling interval h and CONTROL limit k vary between minimum and maximum values. We apply the cost model proposed by Costa and Rahim (2001). This model considers the cost of false alarms, the cost of finding and repairing an assignable cause, the cost of producing out of CONTROL items and the cost of sampling and testing. Furthermore, we assume that the length of time that the process remains in CONTROL is exponentially distributed which allows us to apply the Markov chain approach for developing the cost model. We apply genetic algorithm to determine the optimal values of model parameters by minimizing the cost function. Finally, the both VSICL and VSSICL T2 CONTROL CHARTs are compared with respect to the expected cost per unit time.