{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,1]],"date-time":"2025-11-01T14:49:40Z","timestamp":1762008580995,"version":"build-2065373602"},"reference-count":4,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[1959,7,1]],"date-time":"1959-07-01T00:00:00Z","timestamp":-331516800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[1959,7,1]]},"abstract":"<jats:title>Summary<\/jats:title>\n               <jats:p>The problem is that of maximizing the average efficiency of a machine which (i) stops when its total running time has reached a fixed value a, (ii) has accidental stops, and (iii) is patrolled for servicing (i.e. re-starting if necessary) at a fixed interval p which may be less than a, efficiency being defined as the ratio of the running time to the total time under consideration. The probability distribution of the number of patrols required to exhaust the total running time of the machine is derived in the case where the accidental stops have uniform probability, and is found to be expressible in terms of Laguerre polynomials. The properties of the distribution are illustrated by an example. its asymptotic normality as a increases is established. The properties of the average efficiency are discussed.<\/jats:p>","DOI":"10.1111\/j.2517-6161.1959.tb00345.x","type":"journal-article","created":{"date-parts":[[2018,12,7]],"date-time":"2018-12-07T06:53:37Z","timestamp":1544165617000},"page":"381-395","source":"Crossref","is-referenced-by-count":2,"title":["The Efficiency of Automatic Winding Machines with Constant Patrolling Time"],"prefix":"10.1093","volume":"21","author":[{"given":"A. J.","family":"Howie","sequence":"first","affiliation":[{"name":"Royal College of Science and Technology , Glasgow"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"L. R.","family":"Shenton","sequence":"additional","affiliation":[{"name":"Manchester College of Science and Technology"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2018,12,5]]},"reference":[{"volume-title":"Higher Transcendental Functions","year":"1953","author":"Bateman","key":"2024090921032959900_cit1"},{"key":"2024090921032959900_cit2","doi-asserted-by":"crossref","first-page":"166","DOI":"10.1111\/j.2517-6161.1957.tb00253.x","article-title":"The efficiency of N machines uni-directionally patrolled by one operative when walking time and repair times are constants","volume":"19","author":"Mack","year":"1957","journal-title":"J. R. Statist. Soc. B"},{"key":"2024090921032959900_cit3","first-page":"64","article-title":"Distributions associated with random walk and recurrent events","volume":"19","author":"Skellam","year":"1957","journal-title":"J. R. Statist. Soc. B"},{"volume-title":"Th\u00e9orie des Fonctions.","year":"1942","author":"Valiron","key":"2024090921032959900_cit4"}],"container-title":["Journal of the Royal Statistical Society Series B: Statistical Methodology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1111%2Fj.2517-6161.1959.tb00345.x","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/21\/2\/381\/49099135\/jrsssb_21_2_381.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/21\/2\/381\/49099135\/jrsssb_21_2_381.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,9]],"date-time":"2024-09-09T22:00:16Z","timestamp":1725919216000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jrsssb\/article\/21\/2\/381\/7028008"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1959,7,1]]},"references-count":4,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2018,12,5]]},"published-print":{"date-parts":[[1959,7,1]]}},"URL":"https:\/\/doi.org\/10.1111\/j.2517-6161.1959.tb00345.x","relation":{},"ISSN":["1369-7412","1467-9868"],"issn-type":[{"type":"print","value":"1369-7412"},{"type":"electronic","value":"1467-9868"}],"subject":[],"published-other":{"date-parts":[[1959,7]]},"published":{"date-parts":[[1959,7,1]]}}}