A study on the run length properties of the side sensitive group runs double sampling (SSGRDS) control chart

Communications in Statistics - Simulation and Computation

Castagliola

et al. 2021

Adapted from the acceptance sampling field, the double sampling monitoring schemes implement a two-stage strategy to decide whether the process being monitored is in-control or out-of-control. That is, a master sample is split into two separate subgroup samples, with the first subgroup sample used in the first stage and, depending on which type of double sampling method is used, either only the second or the combined first and second, subgroup sample(s) are used in the second stage. This strategy has been proven to effectively decrease the sampling effort and, at the same time, to decrease the time to detect potential out-of-control situations. For these reasons, it has received some attention in the statistical process monitoring (SPM) literature and, in this review paper, all 87 existing publications on the basic double sampling monitoring schemes and other different schemes that are integrated with the basic double sampling schemes are reviewed. The double sampling schemes are categorized and summarized so that any research gaps in the SPM literature can easily be identified. Finally, concluding remarks and some directions for future research ideas are given.

Section: Group-runs Schemementioning

confidence: 99%

Double sampling monitoring schemes: a literature review and some future research ideas

Motsepa

Communications in Statistics - Simulation and Computation

Castagliola

et al. 2021

“…The sample of size

n_{1}

is used in stage 1, while in stage 2, the two samples are combined. Since then, many researchers have been developing the DS monitoring scheme (for some recent developments, see for example 3,7–12 ). Daudin 6 and Costa 13 reported that the DS

\overset{X}{true}

monitoring scheme performs better than the Shewhart

\overset{X}{true}

scheme; hence, these two articles and others suggest that for parametric schemes, the DS‐type schemes are superior to the basic Shewhart‐type schemes.…”

Section: Introductionmentioning

confidence: 99%

Distribution‐free double‐sampling precedence monitoring scheme to detect unknown shifts in the location parameter

Quality & Reliability Eng

Shongwe

Aslam

et al. 2021

Self Cite

In most applications, parametric monitoring schemes are used to monitor the majority of industrial and nonindustrial processes in order to improve the quality of the outputs or services. However, parametric monitoring schemes are known to underperform when the normality assumption is not met or when there is not enough information about the symmetry or asymmetry nature of the process underlying distribution. Hence, in this paper, a new nonparametric Phase II Shewhart‐type double‐sampling (DS) monitoring scheme based on the precedence statistic is proposed in order to efficiently monitor quality processes when the underlying process distribution departs from normality. The performance is investigated using the average run length (ARL), standard deviation of the run length (SDRL), expected ARL (EARL) and expected average number of observations to signal (EANOS), and the average sample sizes (ASS) metrics. The latter metrics are computed using Monte Carlo simulation and exact formulae. In general, it is shown that the new DS precedence scheme outperforms the existing basic Shewhart precedence scheme with and without supplementary runs rules in many situations. A real‐life illustrative example based on a filling process of milk bottles is provided to demonstrate the application and implementation of the new DS precedence monitoring scheme.

“…The majority of literature on DS schemes is based on the assumption of known IC process parameters (i.e. Case K), see for example: Costa (1994), Irianto and Shinozaki (1998), He, Grigoryan and Sigh (2002), Carot, Jabaloyes and Carot (2002), Khoo et al (2011), Lee, Torng and Liao (2012), Khoo et al (2013a), Costa and Machado (2015), Costa (2017), You (2017), Chong et al (2018), Khoo (2018, 2019), Malela-Majika and Rapoo (2019), Malela-Majika (2019), etc. Although there is a lots of research work based on Case K, in practice, the process parameters are generally unknown (i.e.…”

Section: Introductionmentioning

confidence: 99%

A side-sensitive double sampling X¯ monitoring scheme with estimated process parameters

Motsepa

Communications in Statistics - Simulation and Computation

Castagliola

et al. 2020

In statistical process monitoring (SPM), most of the monitoring schemes are designed assuming that the process parameters for the underlying distribution are known (i.e. Case K). In a variety of contexts, it has been shown that when the parameters used to design the control limits are unknown (i.e. Case U), this greatly affects the monitoring schemes properties. Hence, in this paper, we study the parameter estimation effect of the side-sensitive double sampling (SSDS) 𝑋 ̅ monitoring scheme for detecting changes in the process mean when distribution design parameters are estimated from an in-control retrospective sample. A thorough investigation is conducted using the unconditional run-length properties (i.e. average, standard deviation and percentiles), average sample size (ASS) and average number of observations to signal (ANOS) through exact integral formulas and simulations. In addition, the average extra quadratic loss (AEQL), average ratio of the average run-length (ARARL) and performance comparison index (PCI) are used to quantify the run-length of the SSDS scheme from an overall performance perspective. Comparisons with other established monitoring schemes when parameters are unknown indicate that the SSDS scheme has a better overall performance. An illustrative example is also given to facilitate the design and implementation of the new scheme. An additional section briefly discussing the synthetic version of the SSDS scheme is also provided.