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 ...

It is a ubiquitous problem to estimate the means of bounded random variables. Specially, the problem of estimating the probability of an event can be formulated as the estimation of the mean of a Bernoulli variable. Moreover, in many applications, one needs to estimate a quantity μ which can be bounded in [0, 1] after proper operations of scaling and translation. A typical approach is to design...

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 ...

The idea of variable sampling interval and warning limits (VSIWL) is proposed for X charts. Expressions for the performance measures for the charts with VSIWL are developed. The methods presented are general and can be applied to other Shewhart control charts. The performances of VSIWL X charts are compared numerically with that of VSI X charts with and without runs rules for switching between ...