Designing of X-bar control charts based on process capability index using repetitive sampling

Abstract

A control chart, being an important tool of statistical process control, has been used for process monitoring and detection of any out-of-control process situation. In this paper, the Shewhart [Formula: see text] chart, also known as the traditional control chart, in combination with the process capability index [Formula: see text] proposed by Subramani and Balamurali, is presented under the repetitive sampling scheme. The optimal design parameters of the proposed control chart are calculated. The performance of the proposed control chart is evaluated through the average run lengths (ARLs). Numerical tables have been constructed for the purpose of comparing the in-control ARL and the out-of-control ARL with the single sampling scheme. The findings of the study show that the newly suggested sampling scheme is better than the existing single sampling scheme in detection of mean shift of the process.

Dispersion chart for some popular distributions under repetitive sampling

“…The sensitive statistics of the above mentioned equation with are plotted on a chart with center line and control limits and The proposed control chart is defined in a way to study only the upward shifts (increase in the process dispersion as decrease in the process dispersion is an indication of the process improvement) and therefore we required only the and . The statistic for the chart defines the area between central line and the being in-control process (Ahmad et al, 2014b).…”

A control chart for monitoring the lognormal process variation using repetitive sampling

“…It was originally proposed by Sherman to give a more precise acceptance sampling plan, and Balamurali and Jun have explained that RS‐based functional production procedures are more efficient than sequential and double sampling schemes. The efficient application of RS in acceptance sampling plans has inspired the researchers to apply this concept in the construction of the control charts, as can be seen in previous studies . All such literature was based on symmetrical normal distribution behavior, whereas real‐life practices do not follow this symmetrical attitude.…”

The design of a new repetitive sampling control chart based on process capability index

“…Ahmad et al (2014) proposed X-bar control chart based on process capability index using repetitive sampling. More detail can be seen in (Ahmad et al 2014;Aslam et al 2012;Aslam et al 2013a;Aslam et al 2013b;Aslam et al 2013c;Aslam et al 2014a;Aslam et al 2014b;Balamurali and Jun, 2006;Balamurali et al 2005;Liu and Wu, 2013;Sherman, 1965, Teh et al 2011Zhang et al 2011) So far, few attempts have been made to introduce repetitive sampling schemes in the area of quality control. Therefore, the main objective of this paper is to develop a control chart for quick detection of the out-of-control process based on PCI C pk under the repetitive sampling scheme, which will be called a repetitive C pk control chart.…”