Exercise 1-
Suppose that 7.3, 6.1, 3.8 ,8.4, 6.9 ,7.1, 5.3, 8.2, 4.9, and 5.8 are 10 observations from a distribution (not highly skewed) with unknown mean µ,. Compute x‾ (10) , S2 (10), and an approximate 95 percent confidence interval for µ . For above data, test the null hypothesis
H0: µ = 6 at level α = 0.05.
Exercise 2-
Parts arrive at a single workstation system according to an exponential interarrival distribution with mean 21.5 seconds; the first arrival is at time 0. Upon arrival, the parts are initially processed. The processing-time distribution is TRIA (16, 19, 22) seconds. There are several easily identifiable visual characteristics that determine whether a part has a potential quality problem. These parts, about 10% (determined after the initial processing), are sent to a station where they undergo a thorough inspection. The remaining parts are considered good and are sent out of the system. The inspection-time distribution is 95 plus a WEIB(48.5, 4.04) random variable, in seconds. About 14% of these parts fail the inspection and are sent to scrap. The parts that pass the inspection are classified as good and are sent out of the system (so these parts didn't need the thorough inspection, but you know what they say about hindsight). Run the simulation for10,000 seconds to observe the number of good parts that exit the system, the number of scrapped parts, and the number of parts that received the thorough inspection. Animate your model. Put a text box in your model with the output performance measures requested, and make just one replication.
Exercise 3-
An acute-care facility treats non-emergency patients (cuts, colds, etc.). Patients arrive according to an exponential interarrival-time distribution with a mean of 11 (all times are in minutes). Upon arrival they check in at a registration desk staffed by a single nurse. Registration times follow a triangular distribution with parameters 6, 10, and 19. After completing registration, they wait for an available examination room; there are three identical rooms. Data show that patients can be divided into two groups with regard to different examination times. The first group (55% of patients) has service times that follow a triangular distribution with parameters 14, 22, and 39. The second group (45%) has triangular service times with parameters 24, 36, and 59. Upon completion, patients are sent home. The facility is open 16 hours each day. Make 200 independent replications of 1 day each and observe the average total time patients spend in the system. Put a text box in your Arena file with the numerical results requested.