Nonparametric control chart based on signed-rank statistic is used for detecting changes in mean (median). Although the Sign-Rank (SR) chart is more efficient under heavy-tailed distributions (double exponential and Cauchy) but the performance of this chart is very inappropriate in light-tailed distributions (uniform and normal). In this paper, signed-rank chart is developed with variable sampling interval. The performance of signed-rank chart with variable sampling interval (VSI-SR) is compared to signed-rank chart with fixed sampling interval (FSI-SR) and `X chart. The numerical results demonstrated the VSI-SR chart is better from the FSI-SR chart. Also the VSI-SR chart is more efficient from `X chart in heavy-tailed distributions and some of changes under normal light-tailed distribution.

The control charts are graphical tools and proven techniques to improve the performance of a process. Usually, the processes are not naturally controlled, so the use of control charts will help to reduce the variability and increase the stability of the process. In the traditional approach, control charts with fix sample size and constant sampling intervals were used to identify the changes in the process. While, control charts can be examined from different statistical and economical directions using different sampling schemes for achieving a better result. In past studies, it has been shown that np control charts show better results in detecting shifts by using variable sampling schemes but it is also important to consider how the cost of using variable sampling schemes will be, since the cost of a process depends on the parameters of the control chart. In this paper, the economic-statistical design of np control chart with variable sample size and sampling interval (VSSI) is formulated and then we compare and analyze the resulted obtained with other schemes. Results show significant improvement in terms of economic and statistical performance.

The effect of measurement errors on adaptive and non-adaptive control charts has been occasionally considered by researchers throughout the years. However, that effect on the variable sample size and sampling interval (VSSI) X control charts has not so far been investigated. In this paper, we evaluate the effect of measurement errors on the VSSI X control charts. After a model development, the effect of measurement errors and multiple measurements on the performance of VSSI scheme are evaluated in terms of the out-of-control average time to signal (ATS) criterion, which is obtained using a Markov Chain approach. At last, a real case is presented to show the application of the proposed scheme.

The CCC-r chart is developed based on cumulative count of a conforming (CCC) control chart that considers the cumulative number of items inspected until observing r nonconforming ones. Typically, the samples obtained from the process are analyzed through 100% inspection to exploit the CCC-r chart. However, considering the inspection cost and time would limit its implementation. In this paper, we investigate the performance of CCC-r chart with variable sampling interval (CCC-rVSI chart). The efficiency of CCC-rVSI chart is compared with fixed sampling interval (FSI) scheme of CCC-r chart (CCC-rFSI chart) and CCCVSI chart. The comparison results show that CCC-rVSI chart is more efficient than the CCCVSI chart in reducing the average time to signal (ATS) and also CCC-rVSI chart performs better than CCC-rFSI chart. In addition, some sensitivity analyses are performed to illustrate the effect of the input parameters on the performance of CCC-rVSI chart.

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 familiar multivariate process monitoring and control procedure is the Hotelling’s T2 control chart, a direct analog of the univariate shewhart  chart. But, its efficiency for detecting small to moderate shifts in the process mean is poor. To improve the power of chart, this paper presents the variable sampling intervals (VSI) 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 present study aims to develop a new variable repetitive group sampling plan using the Exponentially Weighted Moving Average (EWMA) statistic based on the yield index for the submitted lot. The optimal parameters of the proposed plan were determined under three scenarios based on the Average Sample Number (ASN). ASN should be minimized to decrease the inspection time and cost using the optimization problem for the required quality levels and sundry combinations of producer's and consumer's risks. A comparison study was conducted to determine the e ciency of the proposed plan. Furthermore, the proposed plan was presented with an example elaborating its applicability in the industry. The proposed plan was compared with the single sampling plan and repetitive group sampling plan based on the yield index. The upshots were tabulated for di erent quality levels. The obtained results demonstrated that with respect to performance, the proposed sampling plan was more lucrative than the existing sampling plans in terms of ASN.

In this paper, an approximate tolerance interval is presented for the discrete size-biased Poisson-Lindley distribution. This approximate tolerance interval, is constructed based on large sample Wald confidence interval for the parameter of the size-biased Poisson-Lindley distribution. Then, coverage probabilities and expected widths of the proposed tolerance interval is considered. The results show that the coverage probabilities have a better performance for the small values of the parameter and are close to the nominal confidence level, and are conservative for the large values of the parameter. Finally, an applicable example is provided for illustrating approximate tolerance interval.

In this study, a novel variable impedance control for a lower-limb rehabilitation robotic system using voltage control strategy is presented. The majority of existing control approaches are based on control torque strategy, which require the knowledge of robot dynamics as well as dynamic of patients. This requires the controller to overcome complex problems such as uncertainties and nonlinearities involved in the dynamic of the system, robot and patients. On the other hand, how impedance parameters must be selected is a serious question in control system design for rehabilitation robots. To resolve these problems this paper, presents a variable impedance control based on the voltage control strategy. In contrast to the usual current-based (torque mode) the use of motor dynamics lees to a computationally faster and more realistic voltage-base controller. The most important advantage of the proposed control strategy is that the nonlinear dynamic of rehabilitation robot is handled as an external load, hence the control law is free from robot dynamic and the impedance controller is computationally simpler, faster and more robust with negligible tracking error. Moreover, variable impedance parameters based on interval Type-2 Fuzzy Logic (IT2Fl) is proposed to evaluate impedance parameters. The proposed control is verified by a stability analysis. To illustrate the effectiveness of the control approach, a 1-DOF lower-limb rehabilitation robot is designed. Voltage-based impedance control are simulated through a therapeutic exercise consist of Isometric and Isotonic exercises. Simulation results show that the proposed voltage-based variable impedance control is superior to voltage-based impedance control in therapeutic exercises.

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.