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Simultaneously guaranteeing the in‐control and out‐of‐control performances of the S 2 control chart with estimated variance
Author(s) -
Aparisi Francisco,
Mosquera Jaime,
Epprecht Eugenio K.
Publication year - 2018
Publication title -
quality and reliability engineering international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 62
eISSN - 1099-1638
pISSN - 0748-8017
DOI - 10.1002/qre.2311
Subject(s) - control chart , control limits , context (archaeology) , limit (mathematics) , variance (accounting) , control (management) , chart , computer science , statistical process control , mathematical optimization , reliability engineering , statistics , process (computing) , mathematics , engineering , artificial intelligence , economics , paleontology , mathematical analysis , accounting , biology , operating system
Recent studies on the effects of parameter estimation on control charts have focused on their conditional in‐control (IC) performance and recommended either the minimum number of Phase I samples ( m ) or adjustments to the control limit factor ( L ) that guarantee a desired IC performance with a high probability. In most cases, the numbers of samples required are prohibitively large in practice, and the adjustments for smaller numbers of samples entail as a counterpart a deterioration of the chart's out‐of‐control (OOC) performance. This presents the user with a hard decision, in which he or she will have difficulty in finding the best compromise between the objectives of good (or acceptable) IC performance, OOC performance, and a practicable number of Phase I samples. Therefore, in the context of the S 2 chart, we propose a new approach that takes both the desired IC and OOC performances (that should be within specified tolerances with a specified high joint probability) as constraints for the optimization of the pair ( L , m ). This is the first work that simultaneously treats the choice of m and the control limit adjustment in the framework of an optimization problem. With our model, the user can automatically obtain the most feasible (minimum m ) solution that satisfies his/her requirements on both the IC and OOC performances.