標題: On the sampling distributions of the estimated process loss indices with asymmetric tolerances
作者: Chang, Y. C.
Pearn, W. L.
Wu, Chien-Wei
工業工程與管理學系
Department of Industrial Engineering and Management
關鍵字: asymmetric tolerances;decision-making rule;process capability indices;process loss indices;sampling distributions.
公開日期: 2007
摘要: Pearn et al. (2006a) proposed a new generalization of expected loss index L-e '' to handle processes with both symmetric and asymmetric tolerances. Putting the loss in relative terms, a user needs only to specify the target and the distance from the target at which the product would have zero worth to quantify the performance of a process. The expected loss index L-e '' may be expressed as L-e '' = L-ot '' + L-pe '' which provides an uncontaminated separation between information concerning the process accuracy and the process precision. In order to apply the theory of testing statistical hypothesis to test whether a process is capable or not under normality assumption, in this paper we first derive explicit form for the cumulative distribution function and the probability density function of the natural estimator of the three indices L-ot '', L-pe '', and L-e ''. We have proved that the sampling distributions of (L) over cap (pe)'' and (L) over cap (ot)'' may And the distribution of (L) over cap (e)'' can be described in terms of a mixture of the chi-square distribution and the normal distribution. Then, we develop a decision-making rule based on the estimated index (L) over cap (e)''. Finally, an example of testing L-e '' is also presented for illustrative purpose.
URI: http://hdl.handle.net/11536/11287
http://dx.doi.org/10.1080/03610910701569168
ISSN: 0361-0918
DOI: 10.1080/03610910701569168
期刊: COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION
Volume: 36
Issue: 6
起始頁: 1153
結束頁: 1170
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