The Dansoman Fitness Centre is constantly trying new initiatives to keep its clients fit. Recent studies show that using several different cardio regimes for short periods of time is more effective than an extended period on one type of equipment. The Manager, Ms. Gloria Abba Sam has pulled together some of the existing cardio equipment and arranged them in line as follow: stationary bike, treadmill, stair stepper. Clients would select this part of the gym for cardio “circuit training,” spending 20 minutes at each piece of equipment for a total cardio workout time of 1 hour. i. If the reliability of the bike is 99%, the treadmill is 98%, and the stair stepper is 97%, what is the probability that a cardio circuit training by a client will be interrupted as a result of a faulty equipment? ii. Gloria has added a second cardio “line” for circuit training with the same type of equipment (i.e. stationary bike, treadmill, and stair stepper) as the first line. This equipment, however, is older with reliabilities of 90%, 88% and 85% for the bike, treadmill, and stair stepper respectively to be used as a backup for faulty equipment in the first line. What is the revised probability of a client completing a workout uninterrupted? iii. Within a cardio circuit workout session, customers usually experience three interruptions as a result of a faulty equipment. If this fault can be rectified in 15 minutes, determine the system’s average availability.
b. The Dansoman Fitness Centre is constantly trying new initiatives to keep its clients fit. Recent
studies show that using several different cardio regimes for short
periods of time is more effective than an extended period on one type of equipment. The
Manager, Ms. Gloria Abba Sam has pulled together some of the existing cardio equipment and
arranged them in line as follow: stationary bike, treadmill, stair stepper. Clients would select
this part of the gym for cardio “circuit training,” spending 20 minutes at each piece of
equipment for a total cardio workout time of 1 hour.
i. If the reliability of the bike is 99%, the treadmill is 98%, and the stair stepper is 97%, what
is the probability that a cardio circuit training by a client will be interrupted as a result of a
faulty equipment?
ii. Gloria has added a second cardio “line” for circuit training with the same type of equipment
(i.e. stationary bike, treadmill, and stair stepper) as the first line. This equipment, however,
is older with reliabilities of 90%, 88% and 85% for the bike, treadmill, and stair stepper
respectively to be used as a backup for faulty equipment in the first line. What is the revised
probability of a client completing a workout uninterrupted?
iii. Within a cardio circuit workout session, customers usually experience three interruptions
as a result of a faulty equipment. If this fault can be rectified in 15 minutes, determine the
system’s average availability.
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