In order to meet the requirements of 6σ management and to overcome the deficiencies of the theory for using the pre-control chart to evaluate and monitor quality stability, the purpose of this paper is to probe into the quality stability evaluation and monitoring guidelines of small batch production process based on the pre-control chart under the conditions of the distribution center and specifications center non-coincidence (0<ɛ≤1.5σ), the process capability index C p ≥2 and the virtual alarm probability α=0.27 percent.
First, the range of the quality stability evaluation sampling number in initial production process is determined by using probability and statistics methods, the sample size for the quality stability evaluation is adjusted and determined in initial production process according to the error judgment probability theory, and the guideline for quality stability evaluation has been proposed in initial production process based on the theory of small probability events. Second, the alternative guidelines for quality stability monitoring and control in formal production process are proposed by using combination theory, the alternative guidelines are initially selected based on the theory of small probability events, a comparative analysis of the guidelines is made according to the average run lengths values, and the monitoring and control guidelines for quality stability are determined in formal production process.
The results obtained from research indicate that when the virtual alarm probability α=0.27 percent, the shifts ɛ in the range 0<ɛ≤1.5σ and the process capability index C p ≥2, the quality stability evaluation sample size of the initial production process is 11, whose scondition is that the number of the samples falling into the yellow zone is 1 at maximum. The quality stability evaluation sample size of the formal production process is 5, and when the number of the samples falling into the yellow zone is ≤1, the process is stable, while when two of the five samples falling into the yellow, then one more sample needs to be added, and only if this sample falls into the green zone, the process is stable.
Research results can overcome the unsatisfactory 6σ management assumptions and requirements and the oversize virtual alarm probability α of the past pre-control charts, as well as the shortage only adaptable to the pre-control chart when the shifts ɛ=0. And at the same time, the difficult problem hard to adopt the conventional control charts to carry out process control because of a fewer sample sizes is solved.
The authors are grateful to the authors of references, and this research is funded by the National Social Science Fund (08XJY014), Shaanxi provincial project of special foundation of key disciplines (No. 107-00X901) and Shaanxi provincial key project of soft science (2012KRZ20). This study was supported by the NNSFC under Grants 70872091.
Qing Liu, S., Su, Q. and Li, P. (2014), "Research on the quality stability evaluation and monitoring based on the pre-control chart", International Journal of Quality & Reliability Management, Vol. 31 No. 9, pp. 966-982. https://doi.org/10.1108/IJQRM-02-2013-0032Download as .RIS
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