Double sampling plan is an examination with a certain parameter, so it cannot decide about manufactured products whose portion parameter ( ) is not certain. The main goal of this survey is to introduce double variable plan when  is indefinite to examine manufacturing products when concerned characteristics are normally distributed. Plan parameters are achieved by an optimization manner. Sum of ...

control chart is the most well-known chart to monitor the number of nonconformities per inspection unit where each sample consists of constant size. generally, the design of a control chart requires determination of sample size, sampling interval, and control limits width. optimally selecting these parameters depends on several process parameters, which have been considered from statistical and...

Designs of the double sampling (DS) X chart are traditionally based on the average run length (ARL) criterion. However, the shape of the run length distribution changes with the process mean shifts, ranging from highly skewed when the process is in-control to almost symmetric when the mean shift is large. Therefore, we show that the ARL is a complicated performance measure and that the median r...

The continuous development of SPC is driven by challenges arising from practical applications across diverse industries. Among others, adaptive charts are becoming more and more popular due to their capability in tackling these challenges by learning unknown shifts and tracking time-varying patterns. This chapter reviews recent development of adaptive charts and classifies them into two categor...

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 ...