{"id":586,"date":"2024-03-14T21:00:07","date_gmt":"2024-03-14T21:00:07","guid":{"rendered":"https:\/\/sites.rutgers.edu\/yasai\/?page_id=586"},"modified":"2024-03-14T21:22:42","modified_gmt":"2024-03-14T21:22:42","slug":"belts-example","status":"publish","type":"page","link":"https:\/\/sites.rutgers.edu\/yasai\/belts-example\/","title":{"rendered":"Part Replacement Problem"},"content":{"rendered":"

A Dynamic Simulation Model<\/h3>\n

Your factory’s production equipment contains a belt that must operate under extreme environmental conditions. The belts fail frequently, and the exact probability of failure depends on a belt’s age, as follows:<\/p>\n\n\n\n\n\n\n\n\n\n
Day of Use<\/u><\/strong><\/td>\nChance of Belt Failure<\/u><\/strong><\/td>\n<\/tr>\n
1<\/td>\n3%<\/td>\n<\/tr>\n
2<\/td>\n7%<\/td>\n<\/tr>\n
3<\/td>\n12%<\/td>\n<\/tr>\n
4<\/td>\n20%<\/td>\n<\/tr>\n
5<\/td>\n34%<\/td>\n<\/tr>\n
6 or more<\/p>\n<\/td>\n40%<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

If a belt fails while in use, it must be replaced on an emergency basis. This causes you to lose the remainder of the day’s production on the equipment, with a cost uniformly distributed between $1000 and $2000. In this case, you start the next day with a fresh belt.<\/p>\n

A working belt can also be replaced just before the start of any day’s production. This scheduled\u00a0 replacement is much cheaper than emergency replacement, costing only $450, and allows you to start that day with a fresh belt.<\/p>\n

The firm’s strategy is to replace each belt after n<\/em> days of use, or as soon as it fails, whichever comes first. What is the best choice of n<\/em> out of the possibilities 1, 2, 3, 4, 5, and 6?\u00a0 Simulate each policy for 100 days with a sample size of 1000.\u00a0 Assume that you start the 100-day period with a scheduled replacement.<\/p>\n

For the best policy, what is the average number of scheduled and emergency replacements in the 100-day period?<\/p>\n","protected":false},"excerpt":{"rendered":"

A Dynamic Simulation Model Your factory’s production equipment contains a belt that must operate under extreme environmental conditions. The belts fail frequently, and the exact probability of failure depends on … Read More<\/a><\/p>\n","protected":false},"author":3356,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"footnotes":""},"class_list":["post-586","page","type-page","status-publish","hentry"],"acf":[],"yoast_head":"\nPart Replacement Problem - YASAI Simulation<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/sites.rutgers.edu\/yasai\/belts-example\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Part Replacement Problem - YASAI Simulation\" \/>\n<meta property=\"og:description\" content=\"A Dynamic Simulation Model Your factory’s production equipment contains a belt that must operate under extreme environmental conditions. 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