On developing sensitive nonparametric mixed control charts with application to manufacturing industry

Abstract

Control charts are designed under the normality assumption of the quality characteristic of the process. However, the normality assumption rarely holds in practice. In non-normal conditions, parametric charts tend to display more false alarm rates and invalid out-of-control comparisons. The exponentially weighted moving average chart is a frequently used memory-type control chart for monitoring the process target that only performs effectively under the smoothing parameter's small choices. This study proposes a nonparametric mixed exponentially weighted moving average-progressive mean chart based on sign statistic (NPMEP SN ) under simple and ranked set sampling schemes to address this said drawback. Normal and non-normal distributions are included in this study to observe the proposed chart's in-control behavior and out-of-control efficacy. The prominent feature of the proposed schemes is that it works efficiently in detecting small and persistent shifts in the process location corresponding to the given values of the smoothing parameter. The proposed scheme is also tested under the ranked set sampling scheme to enhance the NPMEP SN chart's performance (hereafter named "NPMEP RSN "). The performance of the proposed charts is investigated through simulations using run-length profiles. The proposed schemes were seen to outperform other alternatives, specifically under the ranked set sampling scheme. A real data-set related to the diameter of a piston ring is included as a demonstration of the proposal.

The impracticality of homogeneously weighted moving average and progressive mean control chart approaches

“…Abbas et al 40 suggested the monitoring of a sign statistic using a PM scheme, while Abbas et al 41 repeated the analysis with double PM (DPM) approach (see below). Ali et al 42 combined the EWMA scheme with a PM approach using the sign statistic.…”

Multivariate cumulative sum control chart for compositional data with known and estimated process parameters

“…Since then, several modern control charts have been proposed for different data structures. (See for instance, 1–3 )…”

“…Since then, several modern control charts have been proposed for different data structures. (See for instance, [1][2][3] A control chart aims to detect assignable causes of the shifts so that they can be detected and removed before many nonconforming units have been produced. However, during the process, the main goal is to detect the shift as soon as possible, no matter if the size of the shift is large or small, and to find out the main cause of the shifts.…”

Design and analysis of exponentially weighted moving average control charts for monitoring the variability of log‐normal processes with estimated parameters

“…proposed the mixed progressive‐EWMA charts for efficient monitoring of the process mean. For further detail about the EWMA control chart, the interested readers can be seen the work of Macgregor and Harris, 26 Jones, 27 Castagliola, 28 Shu and Jiang, 29 Ali et al., 30,31 Abbas et al., 32 and Hussain et al 33 …”

“…Recently, Abbas et al 24 designed a mixed EWMA-progressive mean and Riaz et al 25 proposed the mixed progressive-EWMA charts for efficient monitoring of the process mean. For further detail about the EWMA control chart, the interested readers can be seen the work of Macgregor and Harris, 26 Jones, 27 Castagliola, 28 Shu and Jiang, 29 Ali et al, 30,31 Abbas et al, 32 and Hussain et al 33 Monitoring the dispersion has its importance in many applications such as industrial, manufacturing, and so on. Process dispersion is generally monitored by using sample standard deviation and is based on the assumption that the understudy quality characteristic follows the normal distribution.…”