Question

Q1d08A.) Edward Shack is conducting a simulation of a serial production line for Lowliner Foods in St John’s, NL. The line processes fresh fish into frozen fish fingers. The line operates on three shift basis, 7.5 hours per shift, with a half-hour between shifts. Machines are idled between the shifts.

a.) Mr. Shack is very interested in determining the effect of unscheduled downtime of the flash freezing unit on shift output. Eddie has implemented a data collection procedure that will track the status of the machine over a fourteen day period. Ten instances of downtime are recorded during this data collection period. The time between failures is given below:

Down time Instance	MTBF (Days)
1	2.33
2	1.58
3	4.65
4	9.18
5	2.61
6	1.24
7	0.36
8	2.41
9	0.45
10	1.37

Hypothesize a distribution for this dataset and identify the best fit parameters(s) for your hypothesized distribution. In your answer described why you feel this selected distribution is appropriate.

b.) After an extensive data collection process, Eddie has determined that the mean time to repair (MTTR) for the flash freezer follows a lognormal distribution. Mr. Shack’s hypothesis is based on a data sample of 30 instances with a sample mean of 1.2 hours and a sample deviation of 0.35 hours. Assume that the simulation package that Mr. Shack uses produces the following random numbers: 0.23, 0.54, 0.81, 0.03, 0.91, and 0.42. Determine the simulated length of time to repair the flash freezer in Mr. Shack’s model for the first two instances of downtime.

c.) After reviewing the random number stream from his simulation model, Mr. Shack is concerned about the suitability of the random number generator in his simulation environment. He decides to test his own linear congruential generator with parameters Xo = 15, m = 64, c = 23, and a = 5. Generate the next two random numbers in this series and comment on the suitability of Eddie’s generator. Indicate whether you think Eddie’s generator is a good replacement for the simulation environment and briefly comment on two tests that Eddie could use to determine the suitability of an LCG.

NOTE: This is Industrial Engineering - Statistics for Simulation Modelling & Analysis subject...

Answer 1

(a)

Code : Import the data into R and store into a data frame dat

library(fitdistrplus)

fitdistr(dat$`MTBF (Days)`,"normal")

mean sd   

2.6180000 2.4828967

ks.test(dat$`MTBF (Days)`,rnorm(10, 2.6180000, 2.4828967))

Two-sample Kolmogorov-Smirnov test

data: dat$`MTBF (Days)` and rnorm(10, 2.618, 2.4828967)

D = 0.5, p-value = 0.1678

alternative hypothesis: two-sided

Interpretation -

Since,the p value is > 0.05, hence the Kolmogorv-Smirnov Test for the test of normality is accepted. Hence,the above variable MTBF has a normal distribution with Mean = 2.6180000 and Standard Deviation = 2.4828967.