Design of variance control charts with estimated parameters: A head to head comparison between two perspectives

Exact tolerance interval with specified tail probabilities and a control chart for the sample variance

“…In addition, in Table 10, we calculate the charting constants under the same conditions (guaranteeing an $$ICARL$$ of at least 370 with probability $$\gamma \; = {\rm{\;}}\{ {0.9,0.95,0.99} \}$$) according to Guo and Wang [26] (also Sarmiento et al. [27]). From Tables 9 and 10, it is seen that the proposed charting constants are shifted to the right compared to the charting constants by Guo and Wang [26], which agrees with the finding made while comparing the corresponding TIs, that is, the TI by Sarmiento et al.…”

“…Guo and Wang [26] proposed an EPC based equal-tailed two-sided control chart for 𝑆 2 . Sarmiento et al [27] provided more in-depth discussion about the control charts for 𝑆 2 .…”

“…The computer program for the method in Section 2 can be used to obtain 𝑐 1 and 𝑐 2 for different values of 𝐼𝐶𝐴𝑅𝐿 0 (for varying values of 𝛼), 𝛿, and 𝛾. In addition, in Table 10, we calculate the charting constants under the same conditions (guaranteeing an 𝐼𝐶𝐴𝑅𝐿 of at least 370 with probability 𝛾 = {0.9, 0.95, 0.99}) according to Guo and Wang [26] (also Sarmiento et al [27]). From Tables 9 and 10, it is seen that the proposed charting constants are shifted to the right compared to the charting constants by Guo and Wang [26], which agrees with the finding made while comparing the corresponding TIs, that is, the TI by Sarmiento et al [8].…”

Optimal Design of 𝒕𝒓 -chart under Two Perspectives with Estimated Parameter

“…Some existing studies have suggested to design the control chart so that the desired IC performance can be achieved with the available amount of data (Diko et al, 2019;Epprecht et al, 2015;Faraz et al, 2018;Hu & Castagliola, 2017;Mosquera et al, 2019). There exist two perspectives in literature to design a control chart with specified IC performance; unconditional and conditional (Jardim et al, 2020, Kumar et al (2021, Kumar (2022), Sarmiento et al, 2020,). Under the unconditional perspective, the chart is design so that average of IC CARL (𝐶𝐴𝑅𝐿 𝑖𝑛 ) is equal to a desired nominal 𝐴𝑅𝐿 0 , i.e.…”