{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T09:57:22Z","timestamp":1773655042487,"version":"3.50.1"},"reference-count":29,"publisher":"Allerton Press","issue":"3","license":[{"start":{"date-parts":[[2019,5,1]],"date-time":"2019-05-01T00:00:00Z","timestamp":1556668800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2019,5,1]],"date-time":"2019-05-01T00:00:00Z","timestamp":1556668800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Aut. Control Comp. Sci."],"published-print":{"date-parts":[[2019,5]]},"DOI":"10.3103\/s0146411619030088","type":"journal-article","created":{"date-parts":[[2019,7,23]],"date-time":"2019-07-23T06:04:29Z","timestamp":1563861869000},"page":"223-235","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["A New Technique of Intelligent Constructing Unbiased Prediction Limits on Future Order Statistics Coming from an Inverse Gaussian Distribution under Parametric Uncertainty"],"prefix":"10.3103","volume":"53","author":[{"given":"N. A.","family":"Nechval","sequence":"first","affiliation":[]},{"given":"G.","family":"Berzins","sequence":"additional","affiliation":[]},{"given":"K. N.","family":"Nechval","sequence":"additional","affiliation":[]},{"given":"J.","family":"Krasts","sequence":"additional","affiliation":[]}],"member":"1627","published-online":{"date-parts":[[2019,7,23]]},"reference":[{"key":"7123_CR1","doi-asserted-by":"publisher","first-page":"2719","DOI":"10.1080\/03610928608829278","volume":"15","author":"J.K. Patel","year":"1986","unstructured":"Patel, J.K., Tolerance limits: A review, Commun. Stat.: Theory Methodol., 1986, vol. 15, pp. 2719\u20132762.","journal-title":"Commun. Stat.: Theory Methodol."},{"key":"7123_CR2","doi-asserted-by":"publisher","first-page":"317","DOI":"10.1080\/00401706.1978.10489677","volume":"20","author":"J.R. Dunsmore","year":"1978","unstructured":"Dunsmore, J.R., Some approximations for tolerance factors for the two parameter exponential distribution, Technometrics, 1978, vol. 20, pp. 317\u2013318.","journal-title":"Technometrics"},{"key":"7123_CR3","first-page":"333","volume":"18","author":"W.C. Guenther","year":"1976","unstructured":"Guenther, W.C., Patil, S.A., and Uppuluri, V.R.R., One-sided \u03b2-content tolerance factors for the two parameter exponential distribution, Technometrics, 1976, vol. 18, pp. 333\u2013340.","journal-title":"Technometrics"},{"key":"7123_CR4","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1080\/00401706.1978.10489615","volume":"20","author":"M. Engelhardt","year":"1978","unstructured":"Engelhardt, M. and Bain, L.J., Tolerance limits and confidence limits on reliability for the two-parameter exponential distribution, Technometrics, 1978, vol. 20, pp. 37\u201339.","journal-title":"Technometrics"},{"key":"7123_CR5","doi-asserted-by":"publisher","first-page":"309","DOI":"10.1002\/nav.3800190208","volume":"19","author":"W.C. Guenther","year":"1972","unstructured":"Guenther, W.C., Tolerance intervals for univariate distributions, Nav. Res. Logist. Q., 1972, vol. 19, pp. 309\u2013333.","journal-title":"Nav. Res. Logist. Q."},{"key":"7123_CR6","doi-asserted-by":"publisher","DOI":"10.1002\/9780470316771","volume-title":"Statistical Intervals: A Guide for Practitioners","author":"G.J. Hahn","year":"1991","unstructured":"Hahn, G.J. and Meeker, W.Q., Statistical Intervals: A Guide for Practitioners, New York: John Wiley & Sons, 1991."},{"key":"7123_CR7","doi-asserted-by":"publisher","first-page":"133","DOI":"10.1016\/S0360-8352(99)00039-X","volume":"37","author":"K.N. Nechval","year":"1999","unstructured":"Nechval, K.N. and Nechval, N.A., Constructing lower simultaneous prediction limits on observations in future samples from the past data, Comput. Ind. Eng., 1999, vol. 37, pp. 133\u2013136.","journal-title":"Comput. Ind. Eng."},{"key":"7123_CR8","unstructured":"Nechval, N.A. and Vasermanis, E.K., Improved Decisions in Statistics, Riga: Izglitibas soli, 2004."},{"key":"7123_CR9","doi-asserted-by":"publisher","first-page":"1","DOI":"10.11648\/j.ajtas.s.2016050201.11","volume":"5","author":"N.A. Nechval","year":"2016","unstructured":"Nechval, N.A. and Nechval, K.N., Tolerance limits on order statistics in future samples coming from the two-parameter exponential distribution, Am. J. Theor. Appl. Stat., 2016, vol. 5, pp. 1\u20136.","journal-title":"Am. J. Theor. Appl. Stat."},{"key":"7123_CR10","doi-asserted-by":"publisher","first-page":"423","DOI":"10.3103\/S0146411616060055","volume":"50","author":"N.A. Nechval","year":"2016","unstructured":"Nechval, N.A., Nechval, K.N., Prisyazhnyuk, S.P., and Strelchonok, V.F., Tolerance limits on order statistics in future samples coming from the Pareto distribution, Autom. Control Comput. Sci., 2016, vol. 50, pp. 423\u2013431.","journal-title":"Autom. Control Comput. Sci."},{"key":"7123_CR11","doi-asserted-by":"publisher","first-page":"47","DOI":"10.14738\/aivp.42.2014","volume":"4","author":"N.A. Nechval","year":"2016","unstructured":"Nechval, N.A., Nechval, K.N., and Strelchonok, V.F., A new approach to constructing tolerance limits on order statistics in future samples coming from a normal distribution, Adv. Image Video Process., 2016, vol. 4, pp. 47\u201361.","journal-title":"Adv. Image Video Process."},{"key":"7123_CR12","doi-asserted-by":"publisher","first-page":"331","DOI":"10.3103\/S0146411617050054","volume":"51","author":"N.A. Nechval","year":"2017","unstructured":"Nechval, N.A., Berzins, G., Balina, S., Steinbuka, I., and Nechval, K.N., Constructing unbiased prediction limits on future outcomes under parametric uncertainty of underlying models via pivotal quantity averaging approach, Autom. Control Comput. Sci., 2017, vol. 51, pp. 331\u2013346.","journal-title":"Autom. Control Comput. Sci."},{"key":"7123_CR13","series-title":"A new technique for constructing exact tolerance limits on future outcomes under parametric uncertainty","volume-title":"Advanced Mathematical Techniques in Engineering Sciences","author":"N.A. Nechval","year":"2018","unstructured":"Nechval, N.A., Nechval, K.N., and Berzins, G., A new technique for constructing exact tolerance limits on future outcomes under parametric uncertainty, in Advanced Mathematical Techniques in Engineering Sciences, Ram, M. and Davim, J.P., Eds., London: Taylor & Francis Group, 2018, pp. 203\u2013226."},{"key":"7123_CR14","doi-asserted-by":"publisher","first-page":"476","DOI":"10.3103\/S0146411618060081","volume":"52","author":"N.A. Nechval","year":"2018","unstructured":"Nechval, N.A., Nechval, K.N., and Berzins, G., A new technique for intelligent constructing exact \u03b3-content tolerance limits with expected (1 \u2013 \u03b1) confidence on future outcomes in the Weibull case using complete or type II censored data, Autom. Control Comput. Sci., 2018, vol. 52, pp. 476\u2013488.","journal-title":"Autom. Control Comput. Sci."},{"key":"7123_CR15","doi-asserted-by":"publisher","first-page":"439","DOI":"10.1109\/TR.1982.5221421","volume":"R-31","author":"G.K. Bhattacharyya","year":"1980","unstructured":"Bhattacharyya, G.K. and Fries, A., Fatigue failure models\u2014Birnbaum-Saunders vs. inverse Gaussian, IEEE Trans. Reliab., 1980, vol. R-31, pp. 439\u2212440.","journal-title":"IEEE Trans. Reliab."},{"key":"7123_CR16","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1016\/0951-8320(89)90060-4","volume":"25","author":"G.J. Goh","year":"1989","unstructured":"Goh, G.J., Tang, L.C., and Lim, S.C., Reliability modelling of stochastic wear-out failure, Reliab. Eng. Syst. Saf., 1989, vol. 25, pp. 303\u2013314.","journal-title":"Reliab. Eng. Syst. Saf."},{"key":"7123_CR17","doi-asserted-by":"publisher","first-page":"1323","DOI":"10.1016\/0026-2714(96)00051-0","volume":"36","author":"R.K. Jain","year":"1996","unstructured":"Jain, R.K. and Jain, S., Inverse Gaussian distribution and its application to reliability, Microelectron. Reliab., 1996, vol. 36, pp. 1323\u20131335.","journal-title":"Microelectron. Reliab."},{"key":"7123_CR18","volume-title":"The Inverse Gaussian Distribution: Theory, Methodology, and Applications","author":"R.S. Chhikara","year":"1989","unstructured":"Chhikara, R.S. and Folks, J.L., The Inverse Gaussian Distribution: Theory, Methodology, and Applications, New York: Marcel Dekker, Inc., 1989."},{"key":"7123_CR19","volume-title":"The Inverse Gaussian Distribution: A Case Study in Exponential Families","author":"V. Seshadri","year":"1993","unstructured":"Seshadri, V., The Inverse Gaussian Distribution: A Case Study in Exponential Families, New York: Oxford University Press, 1993."},{"key":"7123_CR20","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-1456-4","volume-title":"The Inverse Gaussian Distribution: Statistical Theory and Applications","author":"V. Seshadri","year":"1999","unstructured":"Seshadri, V., The Inverse Gaussian Distribution: Statistical Theory and Applications, New York: Springer, 1999."},{"key":"7123_CR21","doi-asserted-by":"publisher","first-page":"211","DOI":"10.1016\/S0378-3758(01)00099-4","volume":"102","author":"G.S. Mudholkar","year":"2002","unstructured":"Mudholkar, G.S. and Tian, L., An entropy characterization of the inverse Gaussian distribution and related goodness-of-fit tests, J. Stat. Plann. Inference, 2002, vol. 102, pp. 211\u2013221.","journal-title":"J. Stat. Plann. Inference"},{"key":"7123_CR22","doi-asserted-by":"publisher","first-page":"1514","DOI":"10.1080\/01621459.1968.10480942","volume":"63","author":"J. Shuster","year":"1968","unstructured":"Shuster, J., On the inverse Gaussian distribution function, J. Am. Stat. Assoc., 1968, vol. 63, pp. 1514\u20131516.","journal-title":"J. Am. Stat. Assoc."},{"key":"7123_CR23","first-page":"145","volume":"7","author":"K.Sh. Zigangirov","year":"1962","unstructured":"Zigangirov, K.Sh., Expression for the Wald distribution in terms of normal distribution, Radio Eng. Electron. Phys., 1962, vol. 7, pp. 145\u2013148.","journal-title":"Radio Eng. Electron. Phys."},{"key":"7123_CR24","doi-asserted-by":"publisher","first-page":"250","DOI":"10.1080\/01621459.1974.10480165","volume":"69","author":"R.S. Chhikara","year":"1974","unstructured":"Chhikara, R.S. and Folks, J.L., Estimation of the inverse Gaussian distribution function, J. Am. Stat. Assoc., 1974, vol. 69, pp. 250\u2013254.","journal-title":"J. Am. Stat. Assoc."},{"key":"7123_CR25","doi-asserted-by":"publisher","first-page":"461","DOI":"10.1080\/00401706.1977.10489586","volume":"19","author":"R.S. Chhikara","year":"1977","unstructured":"Chhikara, R.S. and Folks, J.L., The inverse Gaussian distribution as a lifetime model, Technometrics, 1977, vol.\u00a019, pp. 461\u2013468.","journal-title":"Technometrics"},{"key":"7123_CR26","doi-asserted-by":"publisher","first-page":"273","DOI":"10.6028\/jres.057.033","volume":"47","author":"J. Lieblein","year":"1956","unstructured":"Lieblein, J. and Zelen, M., Statistical investigation of the fatigue life of deep-groove ball bearing, J. Res. Natl. Bur. Stand., 1956, vol. 47, pp. 273\u2013316.","journal-title":"J. Res. Natl. Bur. Stand."},{"key":"7123_CR27","doi-asserted-by":"publisher","first-page":"327","DOI":"10.1016\/0167-9473(92)00072-Y","volume":"17","author":"R.W. Mee","year":"1994","unstructured":"Mee, R.W. and Kushary, D., Prediction limits for the Weibull distribution utilizing simulation, Comput. Stat. Data Anal., 1994, vol. 17, pp. 327\u2013336.","journal-title":"Comput. Stat. Data Anal."},{"key":"7123_CR28","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1080\/00401706.1982.10487738","volume":"24","author":"M. Engelhardt","year":"1982","unstructured":"Engelhardt, M. and Bain, L.J., On prediction limits for samples from a Weibull or extreme-value distribution, Technometrics, 1982, vol. 24, pp. 147\u2013150.","journal-title":"Technometrics"},{"key":"7123_CR29","doi-asserted-by":"publisher","first-page":"857","DOI":"10.1080\/00401706.1973.10489118","volume":"15","author":"J.F. Lawless","year":"1973","unstructured":"Lawless, J.F., On the estimation of safe life when the underlying life distribution is Weibull, Technometrics, 1973, vol. 15, pp. 857\u2013865.","journal-title":"Technometrics"}],"container-title":["Automatic Control and Computer Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.3103\/S0146411619030088.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.3103\/S0146411619030088","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.3103\/S0146411619030088.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,15]],"date-time":"2026-03-15T21:59:16Z","timestamp":1773611956000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.3103\/S0146411619030088"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,5]]},"references-count":29,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2019,5]]}},"alternative-id":["7123"],"URL":"https:\/\/doi.org\/10.3103\/s0146411619030088","relation":{},"ISSN":["0146-4116","1558-108X"],"issn-type":[{"value":"0146-4116","type":"print"},{"value":"1558-108X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,5]]},"assertion":[{"value":"11 March 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"28 March 2019","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 March 2019","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 July 2019","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"There is no conflict of interest.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"CONFLICT OF INTEREST"}}]}}