Shewhart type simultaneous univariate control chart based on ranked set sampling scheme

The article introduces a novel Bayesian AEWMA Control Chart that integrates different loss functions (LFs) like the square error loss function and Linex loss function under an informative prior for posterior and posterior predictive distributions, implemented across diverse ranked set sampling (RSS) designs. The main objective is to detect small to moderate shifts in the process mean, with the average run length and standard deviation of run length serving as performance measures. The study employs a hard bake process in semiconductor production to demonstrate the effectiveness of the proposed chart, comparing it with existing control charts through Monte Carlo simulations. The results underscore the superiority of the proposed approach, particularly under RSS designs compared to simple random sampling (SRS), in identifying out-of-control signals. Overall, this study contributes a comprehensive method integrating various LFs and RSS schemes, offering a more precise and efficient approach for detecting shifts in the process mean. Real-world applications highlight the heightened sensitivity of the suggested chart in identifying out-of-control signals compared to existing Bayesian charts using SRS.

In this article, we propose a generalized ranked set sampling (RSS) scheme, namely, varied L-RSS (VLRSS), for estimating the population mean. The VLRSS scheme encompasses several existing RSS schemes and helps in selecting more representative samples from the target population. It is shown that for a symmetric population, the mean estimator under VLRSS scheme is unbiased, and with reasonable assumptions, it is considerably better than the mean estimators based on RSS and LRSS schemes. Moreover, we also study the effect of imperfect ranking on the performance of VLRSS-based mean estimator. It turns out that, under an imperfect VLRSS scheme, the proposed estimator outperforms its counterparts. The proposed scheme is also illustrated with a case study using a real data set.

ABSTRACTRecently, a hybrid ranked set sampling (HRSS) scheme has been proposed in the literature. The HRSS scheme encompasses several existing ranked set sampling (RSS) schemes, and it is a cost-effective alternative to the classical RSS and double RSS schemes. In this paper, we propose an improved estimator for estimating the cumulative distribution function (CDF) using HRSS. It is shown, both theoretically and numerically, that the CDF estimator under HRSS scheme is unbiased and its variance is always less than the variance of the CDF estimator with simple random sampling (SRS). An unbiased estimator of the variance of CDF estimator using HRSS is also derived. Using Monte Carlo simulations, we also study the performances of the proposed and existing CDF estimators under both perfect and imperfect rankings. It turns out that the proposed CDF estimator is by far a superior alternative to the existing CDF estimators with SRS, RSS and L-RSS schemes. For a practical application, a real data set is considered on the bilirubin level of babies in neonatal intensive care.

To detect sustainable changes in the production processes, memory-type control charts are frequently utilized. This study is conducted to assess the performance of the Bayesian adaptive exponentially weighted moving average (AEWMA) control chart using ranked set sampling schemes following two different loss functions in the presence of a measurement error for posterior and posterior predictive distributions using conjugate priors. This study is based on the covariate model and multiple measurement methods in the presence of a measurement error (ME). The performance of the proposed Bayesian-AEWMA control chart with ME has been evaluated through the average run length and the standard deviation of the run length. Finally, a real-life application in semiconductor manufacturing was conducted to evaluate the effectiveness of the proposed Bayesian-AEWMA control chart with a measurement error based on different ranked set sampling schemes. The results demonstrate that the proposed control chart, in the presence of a measurement error, performed well in detecting out-of-control signals compared to the existing control chart. However, the median ranked set sampling scheme (MRSS) proved to be better than the other two schemes in the presence of a measurement error.

Control charts are widely used to identify changes in a production process. Nonparametric or distribution-free charts can be useful when there is a lack of underlying process distribution. A nonparametric exponentially weighted moving average (EWMA) control chart based on sign test using ranked set sampling (RSS) is proposed to monitor the possible small shifts in the process mean. The performance of the proposed chart is evaluated in terms of average run length, median run length, and standard deviation of the run length distribution. It has been observed that the proposed version of the EWMA sign chart, using RSS shows better detection ability than that version of the EWMA sign chart and the parametric EWMA control chart using simple random sampling scheme. An application with real data-set is also provided to explain the proposal for practical considerations.

Stress-strength models are considered of great significance due to their applicability in varied fields. We address the estimation of the system reliability of a multicomponent stress-strength model, say Rs,k, of an s out of k system when the pair stress and strengths are drawn from a generalized inverted exponential distribution. The system is deemed as working if at least s out of k strengths be more than its stress. We obtain the reliability estimators when the data of strength and stress distributions are collected from three sampling schemes, specifically; simple random sampling, ranked set sampling, and median ranked set sampling. We obtain four estimators of Rs,k out from median ranked set sampling. The behavior of different estimates is examined via a simulation study based on mean squared errors and efficiencies. The simulation studies point out that the reliability estimates of Rs,k, from the ranked set sampling scheme are preferred than other estimates picked from the simple random sample and median ranked set sampling in a majority of the situations. The theoretical studies are explained with the aid of real data analysis.

Exponentially Weighted Moving Average (EWMA) control charts yield insights into data in a way more comprehensible to the practitioners and researchers because of its capability in discovering small to moderate process mean shifts. EWMA control chart is incorporated with conforming run length (CRL) chart, named synthetic EWMA chart, to enhance the performance of the chart in detecting the out-of-control signal. Synthetic EWMA chart based on ranked set sampling (RSS) for monitoring process mean has been proposed as it advanced the detection of chart over a series of mean shifts. With the situation that normality assumption is scarcely attain in practice, we proposed synthetic EWMA median chart based on RSS. Rather than select average run length (ARL) as sole performance evaluating tool, the median and percentiles of run-length distribution are used to examine the performance of the proposed chart as it provides more information on the entire run-length distribution. Near-optimal parameters of the proposed chart will be acquired by setting the incontrol ARL at a designated value. The run length performances of the proposed chart are then compared with the existing charts such as EWMA median chart based on RSS.

This paper presents some novel entropy estimators of a continuous random variable using simple random sampling (SRS), ranked set sampling (RSS), and double RSS (DRSS) schemes. The theoretical results of the proposed entropy estimators are derived. The proposed entropy estimators are compared in terms of the bias and the root mean squared errors, theoretically and numerically, with the Vasicek O. [A test for normality based on sample entropy, J. R. Stat. Soc. B 38:54–59, 1976.] entropy estimators using SRS, RSS, and DRSS schemes. It turns out that the new novel entropy estimators are substantially better than the existing Vasicek’s entropy estimators.

The neoteric ranked set sampling (NRSS) scheme is an effective design compared to the usually ranked set sampling (RSS) scheme. Herein, we regard reliability estimation of the stress-strength (SS) model using the maximum likelihood procedure via NRSS and RSS designs. Assume that stress Y and strength X are exponentiated exponential random variables with the same scale parameter. Various sample strategies are used to evaluate the reliability estimator. We acquire an estimate of R when the samples of stress and strength random variables are chosen from the same sampling methods, such as RSS or NRSS. Furthermore, we derive R estimator when X and Y are chosen from RSS and NRSS, respectively, and vice versa. A simulation investigation is formed to assay and compare the accuracy of estimates for all proposed schemes. We conclude based on study outcomes that the reliability estimates of the stress-strength model via NRSS are more efficient than the others via RSS. Analysis of real data is displayed to investigate the usefulness of the proposed estimators.

Controlling over-adjusted process means and variances using VSI cause selecting control charts

This study is focused on ranked set sampling theory which is constructive and cost efficient. Estimation for population mean for different sample sizes based on new ranked set sampling (NRSS) scheme is explored. A simulation study has been conducted and a comparison has been made with simple random sampling (SRS), ranked set sampling (RSS), extreme ranked set sampling (ERSS) and quartile ranked set sampling (QRSS) for normal and non – normal distributions.

This paper explores the effect of measurement errors on a joint monitoring control chart by using three different techniques (i) covariate method (ii) multiple measurements (iii) linear increasing variance. The joint monitoring control chart in the presence of measurement errors are discussed by using an exponentially weighted moving average statistic in the generalized likelihood ratio (GLR) test statistic under ranked set sampling and pair ranked set sampling (PRSS) procedures. For this purpose, different out-of-control scenarios including mean shifts, variance shifts, and simultaneous shifts are discussed under the considered sampling schemes. The performance of the joint monitoring control chart is evaluated in terms of average run length (ARL) and the standard deviation of run length (SDRL) by conducting an extensive simulation study. The results show that PRSS procedure can reduce the adverse effect of measurement errors on the detection ability of joint monitoring control chart. An example is provided with real data set for the implementation of the joint monitoring control chart in the presence of measurement errors.

Runs rules are used to increase the sensitivity of the Shewhart control chart in detecting small and moderate process mean shifts. Most of the charts incorporating runs rules are designed based on the average run length (ARL). It is known that the shape of the run length distribution changes according to the magnitude of the shift in the process mean, ranging from highly skewed when the process is in-control to approximately symmetric when the shift is large. Since the shape of the run length distribution changes with the magnitude of the shift in the mean, the median run length (MRL) provides a more meaningful explanation about the in-control and out-of-control performances of a control chart. In this article, we propose the design of the revised m-of-k runs rule based on MRL. In addition, the standard deviation of the run length (SDRL) of the revised m-of-k rule will also be studied. The revised m-of-k runs rule, suggested by Antzoulakos and Rakitzis (2008), was originally designed based on ARL. The Markov chain technique is employed to obtain the MRLs. Compared with the standard chart, the MRL results show that the revised rules give better performances for small and moderate mean shifts, while maintaining the same sensitivity towards large mean shifts. The MRL results are in accordance with the results obtained by Antzoulakos and Rakitzis (2008), where the rules are designed based on ARL.

The implementation of Statistical Quality Control (SQC) has been tracked in various areas, such as agriculture, environment, industry, and health services. The employment of SQC methodologies is frequently employed for monitoring and identification of process irregularities across various fields. This research proposes and implements a novel SQC methodology in agricultural areas. A control chart is one of the SQC tools that facilitates real-time monitoring of multiple activities, including agricultural yield, industrial yield, and hospital outcomes. Advanced control charts with symmetrical data are being subjected to the new SQC method, which is suitable for this purpose. This research aims to develop a novel hybrid exponentially weighted moving average control chart for detecting the coefficient of variation (CV) using a repetitive sampling method called the HEWMARS-CV control chart. It is an effective tool for monitoring the mean and variance of a process simultaneously. The HEWMARS-CV control chart used the repetitive sampling scheme to generate two pairs of control limits to enhance the performance of the control chart. The proposed control chart is compared with the classical HEWMA and Shewhart control charts regarding the average run length (ARL) when the data has a normal distribution. The Monte Carlo simulation method is utilized to approximate the ARL values of the proposed control charts to determine their performance. The proposed control chart detects small shifts in CV values more effectively than the existing control chart. An illustrative application related to monitor the wheat yield at Rothamsted Experimental Station in Great Britain is also incorporated to demonstrate the efficiency of the proposed control chart. The efficiency of the proposed HEWMARS-CV control chart on the real data shows that the proposed control chart can detect a shift in the CV of the process, and it is superior to the existing control chart in terms of the average run length.

Three statistical control chart methods were investigated to determine the one with the highest detection probability and the best average run length (ARL). The three control charts include the Shewhart control chart of count data, cumulative sum (CUSUM) analysis of count data (Poisson CUSUM), and CUSUM analysis of time-interval (time difference between two consecutive radiation pulses) data (time-interval CUSUM). The time-interval CUSUM (CUSUMti) control chart was compared with the Poisson CUSUM (CUSUMcnt) and the Shewhart control charts with experimental and simulated data. The experimental data were acquired with a DGF-4C (XIA, Inc.) system in list mode. Simulated data were obtained by using Monte Carlo techniques to obtain a random sampling of a Poisson process. All statistical algorithms were developed using R (R Development Core Team). Detection probabilities and ARLs for the three methods were compared. The time-interval CUSUM control chart resulted in a similar detection probability as that of the Poisson CUSUM control chart but had the shortest ARL at relatively higher radiation levels; e.g., about 40% shorter than the Poisson CUSUM at 10.0 counts per second (cps) (five times above the background count rate). Both CUSUM control charts resulted in a higher detection probability than that of the Shewhart control chart; e.g., 100% greater than the Shewhart control method at 4.0 cps (two times above the background count rate). In addition, when time-interval information was used, the CUSUM control chart coupled with a modified runs rule (mrCUSUMti) showed the ability to further reduce the time needed to respond to changes in radiation levels and keep the false positive rate at a required level.