{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,8]],"date-time":"2023-10-08T12:13:34Z","timestamp":1696767214485},"reference-count":23,"publisher":"Wiley","issue":"8","license":[{"start":{"date-parts":[[2017,4,17]],"date-time":"2017-04-17T00:00:00Z","timestamp":1492387200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Quality & Reliability Eng"],"published-print":{"date-parts":[[2017,12]]},"abstract":"Although the recently proposed Weibull process capability indices (PCIs) actually measure the times that the standard deviation (\u03c3<\/jats:italic>x<\/jats:italic><\/jats:sub>) is within the tolerance specifications, because they not accurately estimate neither the log\u2010mean (\u03bc<\/jats:italic>x<\/jats:italic><\/jats:sub>) nor the \u03c3<\/jats:italic>x<\/jats:italic><\/jats:sub> values, then the actual PCIs are biased. This actually because \u03bc<\/jats:italic>x<\/jats:italic><\/jats:sub> and \u03c3<\/jats:italic>x<\/jats:italic><\/jats:sub> are both estimated without considering the effect that the sample size (n<\/jats:italic>) has over their values. Hence, \u03bc<\/jats:italic>x<\/jats:italic><\/jats:sub> is subestimated and \u03c3<\/jats:italic>x<\/jats:italic><\/jats:sub> is overestimated. As a response to this issue, in this paper, \u03bc<\/jats:italic>x<\/jats:italic><\/jats:sub> and \u03c3<\/jats:italic>x<\/jats:italic><\/jats:sub> are estimated in function of n<\/jats:italic>. In particular, the PCIs' efficiency is based on the following facts: (1) the derived n<\/jats:italic> value is unique and it completely determines \u03b7<\/jats:italic>, (2) the \u03bc<\/jats:italic>x<\/jats:italic><\/jats:sub> value completely determines the \u03b7<\/jats:italic> value, and (3) the \u03c3<\/jats:italic>x<\/jats:italic><\/jats:sub> value completely determines the \u03b2<\/jats:italic> value. Thus, now, since \u03bc<\/jats:italic>x<\/jats:italic><\/jats:sub> and \u03c3<\/jats:italic>x<\/jats:italic><\/jats:sub> are in function of n<\/jats:italic> and they completely determine \u03b2<\/jats:italic> and \u03b7<\/jats:italic>, then the proposed PCIs are unbiased, and they completely represent the analyzed process also. Finally, a step by step numerical application is given.<\/jats:p>","DOI":"10.1002\/qre.2155","type":"journal-article","created":{"date-parts":[[2017,4,18]],"date-time":"2017-04-18T02:22:38Z","timestamp":1492482158000},"page":"1915-1920","source":"Crossref","is-referenced-by-count":4,"title":["Unbiased Weibull capabilities indices using multiple linear regression"],"prefix":"10.1002","volume":"33","author":[{"given":"Manuel R.","family":"Pi\u00f1a\u2010Monarrez","sequence":"first","affiliation":[{"name":"Manufacturing and Industrial Engineering Department of the Engineering and Technological Institute Universidad Aut\u00f3noma de Ciudad Ju\u00e1rez Cd. Ju\u00e1rez Chih Mexico"}]},{"given":"Manuel","family":"Baro\u2010Tijerina","sequence":"additional","affiliation":[{"name":"Doctoral Student of the Technological Doctoral Program at the Engineering and Technological Institute Universidad Aut\u00f3noma de Ciudad Ju\u00e1rez Cd. Ju\u00e1rez, Chih Mexico"}]},{"given":"Jes\u00fas F.","family":"Ortiz\u2010Ya\u00f1ez","sequence":"additional","affiliation":[{"name":"Validation Laboratory Department Ted de M\u00e9xico S.A de C.V. Cd. 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