Statistical process control, a recognized technique for improving quality and productivity, has been widely employed throughout various industries. The conventional Shewhart control charts are applicable only when the collected sample data are real-valued data. For the purpose of controlling uncertain information when interval-valued data inevitably appear in the manufacturing or service proces...

In this paper, we propose a nonparametric CUSUM control chart for detecting a range of shifts in the location parameters based on previous research. This control chart is dynamically adaptive, ranks method-based nonparametric and self-starting; it can monitor various sizes of shifts in difference distributions simultaneously; and it can be used to monitor processes at the start-up stages. This ...

An extensive simulation study was conducted to optimize the number, r, of population members to be encountered from each random starting point in variable area transect (VAT) sampling. The quality of estimation provided by the original calculation formula presented by K. R. Parker in 1979 was compared to another formula that was a Morisita analog intended to reduce bias when sampling aggregated...

In statistical process control (SPC), the ratio of two normal random variables (RZ) is a valuable indicator to be taken as charting statistic. this work, we propose triple exponentially weighted moving average (TEWMA) chart for monitoring RZ. Additionally, variable sampling interval (VSI) strategy has been adopted different charts by researchers. With application strategy, VSI-TEWMA-RZ then dev...

In the context of economic design, a two-stage model is proposed that utilizes continuously variable sampling intervals. Specifically, each successive sampling interval is determined by the extremity of the latest sample. Modeling the situation as a Markov chain, the hourly cost is developed for any arbitrary set of design parameters. This proposed approach is found to be more economically desi...

Justification for the original sample size calculation is made in the trial protocol. In this additional file, we provide details of the assumptions and calculations in estimating the likely width of the 95% confidence interval (CI) for the estimators, the risk difference and the log odds ratio, for the primary practitioner outcome, x-ray referral. Table 1 contains the likely widths of the 95% ...