TOPIC: MARKOV CHAINS An electronic device manufacturer orders 2-meter-long conductors from a supplier, who claims that the wire in its conductors has the specified mechanical strength desired by its engineers. that the wire of its conductors has the specified mechanical strength desired by the company's engineers for use in experimental models. for use in experimental models. Each shipment is rated by the technicians who use it as "satisfactory" (nothing is reported to the supplier), as "substandard" (the supplier is notified in writing that the consignment does not meet the standards), or as "substandard" (the supplier is notified in writing that the consignment does not meet the standards). (the supplier is notified in writing that the shipment does not meet specifications), or as "unacceptable" (the shipment is returned, and in accordance with the the supplier replaces it with another one that has been 100% verified). The classification thus depends on the degree to which the material shipped does or does not meet the supplier's claims for strength. Engineers have observed that if a given shipment is rated as satisfactory, the next shipment will be satisfactory 4/5 of the time. also satisfactory 4/5 of the time, substandard 3/20 of the time, and unacceptable 1/20 of the time. If a If a shipment is classified as substandard, the next shipment is satisfactory 19/20 of the time, substandard 1/20 of the time, and never unacceptable 1/20 of the time. What proportion of shipments are satisfactory, substandard and unacceptable, in the long run?
TOPIC: MARKOV CHAINS
An electronic device manufacturer orders 2-meter-long conductors from a supplier, who claims that the wire in its conductors has the specified
that the wire of its conductors has the specified mechanical strength desired by the company's engineers for use in experimental models.
for use in experimental models. Each shipment is rated by the technicians who use it as
"satisfactory" (nothing is reported to the supplier), as "substandard" (the supplier is notified in writing that the consignment does not meet the standards), or as "substandard" (the supplier is notified in writing that the consignment does not meet the standards).
(the supplier is notified in writing that the shipment does not meet specifications), or as "unacceptable" (the shipment is returned, and in accordance with the
the supplier replaces it with another one that has been 100% verified). The classification thus depends on the
degree to which the material shipped does or does not meet the supplier's claims for strength.
Engineers have observed that if a given shipment is rated as satisfactory, the next shipment will be satisfactory 4/5 of the time.
also satisfactory 4/5 of the time, substandard 3/20 of the time, and unacceptable 1/20 of the time. If a
If a shipment is classified as substandard, the next shipment is satisfactory 19/20 of the time, substandard 1/20 of the time, and never unacceptable 1/20 of the time.
What proportion of shipments are satisfactory, substandard and unacceptable, in the long run?
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