Improved Nonparametric Control Chart Based on Ranked Set Sampling with Application of Chemical Data Modelling

Abstract

The statistical performance of parametric control charts is questionable when the underlying process does not follow any specified probability distribution. Nonparametric control charts are the best substitute for this situation. On the other hand, the ranked set sampling technique is preferred over the simple random sampling technique because it reduces the variability of process parameters and improves the control chart’s performance. This study aims to offer a nonparametric double homogeneously weighted moving average control chart under Wilcoxon signed-rank test considering the ranked set sampling technique (regarded as NPDHWMA RSS ), to further enhance the process location monitoring. The proposed chart’s run-length performance is compared with competing control charts, such as DEWMA- X ¯ , NPDEWMA-SR, NPRDEWMA-SR, DHWMA, and NPHWMA RSS control charts. The comparison revealed that the proposed NPDHWMA RSS control chart outperformed the other competing control charts, particularly for small to moderate shifts in process location. Finally, a real-life application is also offered for quality practitioners to show the strength of the proposed control chart.

Ranked-Set Sampling Based Distribution Free Control Chart with Application in CSTR Process

“…Also, Anwar et al [15] suggested auxiliary information-based (AIB) MEC and MCE control charts for monitoring the process location parameter. For other CUSUM and EWMA based studies, the readers are referred to the work of Adegoke et al [16], Sanusi et al [17], Haq [18], Zaman et al [19], Aslam et al [20], Adeoti et al [21], Anwar et al [15], Abbasi et al [22], Rasheed et al [23], Rasheed et al [24], Anwar et al [25], Liu et al [26], and Rasheed et al [27].…”

Triple Homogeneously Weighted Moving Average Charts for Monitoring Process Dispersion

“…Similarly, Riaz et al [21] proposed the THWMA (triple HWMA) chart for the process mean, which uniformly outperformed the HWMA and DHWMA charts. Other HWMA-based studies for mean process monitoring are ofered by Rasheed et al [22], Rasheed et al [23], and Zhang et al [24]. After that, Knoth et al [25] highlighted a few concerns about the HWMA chart when compared to the EWMA chart in the case of the steady-state comparison scenario.…”

A review of ranked set sampling and modified methods in designing control charts

“…The RSS methods are recommended in the SPM literature as these sampling approaches decrease the variability and improve the efficiency of the associated control charts 53,54 . For example, hazardous waste sites with different levels of contamination can be visually classified based on the color of the soil, while actual statistics of toxic chemicals and quantifying their ecological impacts are prohibitively expensive 55 . The other applications of RSS methods in SPM area are discussed in the papers such as Muttlak and Al‐Sabah, 56 Al‐Omari and Haq, 57 Haq et al., 58 Haq et al., 59 Riaz et al., 60 Mehmood et al., 61 Ali et al., 62 Nawaz and Han, 63 Malela‐Majika et al., 64 Mehmood et al 65 …”

“…53,54 For example, hazardous waste sites with different levels of contamination can be visually classified based on the color of the soil, while actual statistics of toxic chemicals and quantifying their ecological impacts are prohibitively expensive. 55 The other applications of RSS methods in SPM area are discussed in the papers such as Muttlak and Al-Sabah, 56 Al-Omari and Haq, 57 Haq et al, 58 Haq et al, 59 Riaz et al, 60 Mehmood et al, 61 Ali et al, 62 Nawaz and Han, 63 Malela-Majika et al, 64 Mehmood et al 65 The use of the RSS method in the construction of control charts is a relatively new topic. The RSS scheme in SPM was first used by Salazar and Sinha 66 for constructing the Shewhart control chart.…”