On line process control for attributes in presence of misclassification errors: an economical approach with repeated classifications. (Spanish. English summary) Zbl 1161.62082
Summary: The procedure to control on-line processes for attributes proposed by G. Taguchi et al. [Quality engineering in production systems. NY: McGraw-Hill (1989)] consists of sampling a single item of m produced ones. If the examined item is non-conforming, the process is said to be out of control (the fraction of conforming items is reduced) and is stopped for adjustment. However, the inspection procedure is subject to misclassification errors. So a probabilistic model was developed considering the results of repetitive and independent classifications of the examined items. Employing properties of ergodic Markov chains, an expression of the expected cost function for the control system was obtained to be minimized by three parameters: sampling interval, number of repetitive classifications, and the minor number of conforming classifications (among the repetitive classifications) to declare an item as conforming. A numerical example illustrates the proposed model.
MSC:
| 62P30 | Applications of statistics in engineering and industry; control charts |
| 60J20 | Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) |
References:
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