An adaptive multivariate EWMA mean chart with variable sample sizes and/or variable sampling intervals

Abstract

New adaptive multivariate EWMA (AME) charts based on the variable sample size (VSS), variable sampling interval (VSI) and variable sample size and sampling interval (VSSI) techniques are proposed to reduce the time of the existing AME chart in detecting a mean shift in the multivariate normal process. A Monte Carlo simulation is conducted to compare the time to signal characteristics of the new VSS/VSI/VSSI AME and existing fixed sampling rate (FSR) AME and VSSI multivariate EWMA (ME) charts. It is found that the VSS/VSI/VSSI AME charts generally surpass the existing FSR AME and the non‐adaptive VSSI ME charts in detecting small and moderate shifts in the mean of a multivariate normal process, in terms of the expected weighted time‐to‐signal and expected relative average time‐to‐signal performance measures. An example is given to show the implementation of the existing and proposed charts.

Directionally sensitive adaptive MEWMA charts with fixed and variable sampling rates

“…The EWTS is defined as the expected value of the weighted ATSs based on the probability distribution of the mean shift 𝛿, while the ERATS is a measure of the closeness of the performance of a chart to the optimal ATS for each 𝛿. 16 The values of the warning limit (𝑤) and decision interval (ℎ) of the 1AME-VSSI and 1ME-VSSI charts for the ZS case, as well as the values of ℎ of these two charts for the SS case, considered in Tables 2 and 3, and Figures 1 and 2, are all obtained from Table 1 for 𝑝 ∈ {2, 3, 5, … , 10}, where it is obvious that 𝑤 and ℎ increase as 𝑝 increases. In Tables 2 and 3, the out-of-control ATS (ATS 1 ), EWTS and ERATS values of the 1AME-FSR charts are given in the first row of each value of 𝑝.…”

“…It is thus a common approach in the statistical process control literature to consider simulated dataset when demonstrating the implementation of the Phase-II control chart that employs the VSS, VSI, and VSSI features. On the lines of Montgomery 2 and Haq and Khoo, 16 two datasets (each dataset comprises forty samples) of different samples sizes, say (𝑛 0 , 𝑛 1 , 𝑛 2 ), are generated from a multivariate normal distribution with the following choices of the parameters: first dataset considers 𝝁 1 = (𝛿∕ √ 𝑛 0 , 0) ′ and 𝚺 = 𝑰, where 𝛿 = 0.5 with 𝑛 0 = 5, whilst the second dataset considers 𝝁 1 = (𝛿∕ √ 𝑛 0 , 0, 0, 0, 0) ′ and 𝚺 = 𝑰, where 𝛿 = 1.0 with 𝑛 0 = 5. For a multivariate chart with the FSR feature, both the sample size (𝑛 0 = 5) and the sampling interval time (𝑡 0 = 1.0) remain constant over time.…”

Comprehensive Scientometric Analysis and Longitudinal SDG Mapping of Quality and Reliability Engineering International Journal

“…Based on APY, the most recent topic from the cluster is "adaptive multivariate EWMA", with an APY score of 2020.2. Zhang et al [57] and Testik et al [58] feature as the top-cited articles on CUSUM and multivariate EWMA with 91 and 48 citations, respectively, while Haq and Khoo [59] article is the most recent on adaptive multivariate EWMA.…”

Proposed variable sampling interval maximum EWMA and distance EWMA charts with unknown process parameters

“…Numerous works on EWMA charts have been made over the years. The more recent ones were conducted by Abubakar et al (2021), Alevizakos et al (2021), Talib et al (2022), Hu et al (2022), Chatterjee et al (2022a, 2022b), Saha et al (2022), Haq, Iqbal, and Khoo (2022), Haq and Khoo (2019), Haq and Khoo (2022a, 2022b), to name some.…”

“…Saccucci et al (1992) developed the VSI EWMA chart for the process mean, and they demonstrated that the developed chart outperforms the VSI CUSUM chart in detecting small shifts, as well as the VSI SH and non-adaptive EWMA charts in detecting all sizes of shifts. Recent studies on control charts with the VSI approach include those by Haq et al (2021), Tran et al (2021), Nguyen et al (2021), Umar et al (2021), Haq, Sadia, and Khoo (2022) and Haq and Khoo (2022a).…”