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Concordia University *
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INDU 6311
Subject
Statistics
Date
Apr 3, 2024
Type
docx
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27
Uploaded by MagistrateFinch4209
Contents
Mazhar
........................................................................................................................................................
1
Destiny/Susmita
..........................................................................................................................................
2
Destiny/Susmita
..........................................................................................................................................
3
Destiny/Susmita
..........................................................................................................................................
4
Team on Saturday (8PM)
.............................................................................................................................
5
Matt
.............................................................................................................................................................
5
Saad
.............................................................................................................................................................
6
Dhruvin
........................................................................................................................................................
7
Team on Saturday (8PM)
.............................................................................................................................
8
Model 1 = 1ST Alternative
Model 2 = 2ND Alternative
Model 3 = 3RD Alternative
NEXT MEETING SAT 8PM – 835H
Output Analysis of Model 1
Mazhar
1.
State and explain the run parameters by answering the following.
a)
State how many replications you ran: We ran all the three alternative with 122
number of replication.
b)
Provide an explanation of how you calculated the above number of replications: Initial Number of Replications = n
0
= 20
Confidence Interval = CI = 95%
Alpha = ∝
= 0.05
Based on Method 3 n
=
n
0
β
0
β
For Alternative 1:
Key Performance Indicator
Average
Current Half Width (
β
o
)
Current Error (%)
Desired Half Width (
β
)
No of Replications
(n)
Final No of
Replication
Wait time to see doctor without priority
20.4785
0.98
0.04785506
8
1.023925
19
32
Wait time to see nurse
2.5655
0.03
0.01169362
7
0.128275
2
Doctor wait time priority
1
15.7622
0.41
0.02601159
7
0.78811
6
Doctor wait time priority
2
17.2173
0.62
0.03601029
2
0.860865
11
Doctor wait time priority
3
24.1691
1.52
0.06289021
9
1.208455
32
Total time in system priority 1
35.2427
0.96
0.02723968
4
1.762135
6
Total time in system priority 2
36.5906
1.07
0.02924248
3
1.82953
7
Total time in system priority 3
43.5569
1.75
0.04017733
1
2.177845
13
Last Time When Patient Leaves System
628.34
10.65
0.01694942
2
31.417
3
Total Time in System for Patient
39.7211
1.14
0.02870011
2
1.986055
7
For Alternative 2: Key Performance Indicator
Average
Current Half Width (
β
o
)
Current Error (%)
Desired Half Width (
β
)
No of Replications
(n)
Final No of
Replication
Wait time to see doctor without priority
52.4926
5.11
0.097347055
2.62463
76
Wait time to see appointment doctor without priority
47.8589
3.92
0.08190744
2.392945
54
Wait time to see nurse
2.811
0.06
0.021344717
0.14055
4
Doctor wait time priority
1
19.574
0.75
0.038316134
0.9787
12
Doctor wait time priority
2 26.0451
1.21
0.046457875
1.302255
18
Doctor wait time priority
80.4677
9.39
0.116692785
4.023385
109
3 122
Doctor wait time priority
1 appointment patient
48.0727
5.93
0.123354835
2.403635
122
Doctor wait time priority
2 appointment patient
48.5123
4.16
0.085751449
2.425615
59
Doctor wait time priority
3 appointment patient
47.3924
3.8
0.080181632
2.36962
52
Total time in system priority 1 48.3294
2.5
0.051728348
2.41647
22
Total time in system priority 2 52.5132
1.52
0.028945103
2.62566
7
Total time in system priority 3 89.2476
6.53
0.073167234
4.46238
43
Last Time When Patient Leaves System
742.95
24.87
0.033474662
37.1475
9
Total Time in System for Patient
57.1716
3.56
0.062268679
2.85858
32
Total Time in System for Appointment Patient
66.9744
4.18
0.062411907
3.34872
32
For Alternative 3 : Key Performance Indicator
Average
Current Half Width (
β
o
)
Current Error (%)
Desired Half Width (
β
)
No of Replications
(n)
Final No of Replication
Wait time to see doctor without priority
55.4494
5
0.090172301
2.77247
66
88
Wait time to see appointment doctor without priority
17.9753
0.3
0.016689568
0.898765
3
Wait time to see nurse
2.8036
0.03
0.010700528
0.14018
1
Doctor wait time priority 1
21.4001
0.98
0.045794179
1.070005
17
Doctor wait time priority 2 28.7041
2.04
0.071069987
1.435205
41
Doctor wait time priority 3 82.7143
8.67
0.104818635
4.135715
88
Doctor wait time priority 1 appointment
patient
17.958
0.78
0.043434681
0.8979
16
Doctor wait time priority 2 appointment
patient
17.8941
0.4
0.022353737
0.894705
4
Doctor wait time priority 3 appointment
patient
18.0324
0.37
0.020518622
0.90162
4
Total time in system priority 1 39.3832
1.11
0.028184607
1.96916
7
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Total time in system priority 2 45.0381
1.66
0.036857683
2.251905
11
Total time in system priority 3 81.2205
5.91
0.072764881
4.061025
43
Last Time When Patient Leaves System
695.34
18.3
0.02631806
34.767
6
Total Time in System for Patient
59.3934
3.5
0.058929107
2.96967
28
Total Time in System for Appointment Patient
37.3242
0.67
0.01795082
1.86621
3
So we maximum form all the three alternatives which is 122.
c)
Insert a screenshot of your run parameters (should match your model!):
2.
Present a table of 95% confidence intervals for all major performance
metrics in table format, corresponding to the setting above. (Note I am not
listing all performance metrics, you can add all the ones you used in your
analysis.)
Destiny/Susmita
Alternative 1:
Performance Metric
Average 95% Confidence Interval Wait time to see Nurse
3.06
[3.0279, 3.0921]
Wait time to see Doctor
Priority 1 Patient
18.3
[18.113, 18.487]
Priority 2 Patient
22.2
[21.895, 22.505]
Priority 3 Patient
66.2
[63.36, 69.04]
Total time in the system
Priority 1 Patient
38
[37.653, 38.347]
Priority 2 Patient
41.8
[41.411, 42.189]
Priority 3 Patient
85.7
[ 82.78, 88.62]
Average Nurse Queue Time (Waiting Time)
0.617
[0.588, 0.646]
Last Time when patient leaves the system
707
Average Doctor Queue Time (Waiting Time)
30.1
[28.58, 31.62]
Average Doctor Queue Time without
Priority (Waiting Time)
43.9
[42.38, 45.52]
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Destiny/Susmita
Alternative 2:
Performance Metric
Average 95% Confidence Interval Wait time to see Nurse
2.8
[ 2.7791, 2.8209]
Wait time to see Doctor
Priority 1 Patient
20.3
[19.981, 20.619]
Priority 2 Patient
26.6
[26.045, 27.155]
Priority 3 Patient
82.6
[78.76, 86.44]
Wait time to see Appointment Doctor
Priority 1 Patient
48.8
[46.23, 51.37]
Priority 2 Patient
48.7
[46.43, 50.97]
Priority 3 Patient
48.8
[46.46, 51.14]
Total time in the system
Priority 1 Patient
48.9
[47.86, 49.94]
Priority 2 Patient
53.1
[52.286, 53.914]
Priority 3 Patient
91.5
[88.78, 94.22]
Latest time a patient leaves the clinic
Day 1
342
[ 337.11, 346.89]
Day 2
338
[333, 343]
Day 3
336
[331.14, 340.86]
Day 4
339
[334.5, 343.5]
Day 5
339
[334.28, 343.72]
Day 6
337
[332.41, 341.59]
Day 7
338
[333.47, 342.53]
Average Nurse Queue Time (Waiting Time)
0.384
[0.3645, 0.4035]
Average Doctor Queue Time (Waiting Time)
40.5
[38.44, 42.56]
Average Doctor Queue Time without Priority (Waiting Time)
54
[51.93, 56.07]
Average Appointment Doctor Queue time without priority
48.8
[46.56, 51.04]
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Destiny/Susmita
Alternative 3:
Performance Metric
Average 95% Confidence Interval Wait time to see Nurse
2.81
[2.7887, 2.8313]
Wait time to see Doctor
Priority 1 Patient
21.3
[20.946, 21.654]
Priority 2 Patient
28.1
[27.37, 28.83]
Priority 3 Patient
75.1
[71.65, 78.55]
Wait time to see Appointment Doctor
Priority 1 Patient
17.5
[17.229, 17.771]
Priority 2 Patient
17.7
[17.525, 17.875]
Priority 3 Patient
17.8
[17.64, 17.96]
Total time in the system
Priority 1 Patient
39.5
[39.084, 39.916]
Priority 2 Patient
44.3
[43.704, 44.896]
Priority 3 76.6
[74.09, 79.11]
Patient
Latest time a patient leaves the clinic
Day 1
331
[ 326.94, 335.06]
Day 2
327
[322.13, 331.87]
Day 3
323
[319.19, 326.81]
Day 4
326
[321.68, 330.32]
Day 5
328
[323.73, 332.27]
Day 6
323
[318.64, 327.36]
Day 7
324
[318.98, 329.02]
Average Nurse Queue Time (Waiting Time)
0.409
[0.3894, 0.4286]
Average Doctor Queue Time (Waiting Time)
27.1
[25.7, 28.5]
Average Doctor Queue Time without Priority (Waiting Time)
51.2
[49.22, 53.18]
Average Appointment Doctor Queue time without priority
17.8
[17.664, 17.936]
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Team on Saturday (8PM)
3.
Describe any missing information about your alternatives below. Add as
many alternative labels as needed. For each alternative, specify the changes
you have made in the model. Please add a reference to the file name
corresponding to each alternative (.doe file).
Alternative 1: Current state (as in part 1) “1ST Alternative.Doe” seeks to model exactly what is stated in the question. In order to achieve 7 distinct days of 9 working hours, the “Logic Section” of “1ST
Alternative.Doe” utilizes two create modules to control the “entities per arrival” variable
which is “PatientsPerArrival”.
Here are how the two logical entities control the working day time frames:
The “Patients Arrive at Clinic” create module creates patients according to an EXPO (7)
distribution. However, the entities per arrival alternates between 1 and 0 to control when
the office is open and closed, respectively. The “PatientsPerArrival” variable is initially
set to 1 by default in the variable table. At 540 Minutes, a logical entity is created via the
“Create Stop Arrival Logic Entity” create module. This entity allows for the
“PatientsPerArrival” variable to be set to 0, halting patient arrivals. Any entities still in
the system will be processed. At 1440 minutes, the “Create start Arrival Logic Entity”
module will create a logical entity to set the “PatientsPerArrival” variable back to 1 to
allow patients to start coming to the hospital again. Every 1440 minutes, the “Create Stop
Arrival Logic Entity” and “Create start Arrival Logic Entity” will flip the
“PatientsPerArrival” variable between 0 and 1 respectively to control the operating hours.
The model runs for 7 total days of 24 hours however, so this will trigger the end of the
work week and replication. Pending Explanation: Record KPIs, how the output is calculated.
Alternative 2: Appointment-based system for one doctor with a walk-in system for
the other two doctors 1.
A logic is created to decrement slots every 15 minutes as a function of time. In
total, there are 245 slots (7*(540/15) -7 = 245) slots from 8 AM to 4:45 PM.
2.
Another logic is created for patients who calls for an appointment. Which are first
checked to see if any slots are available in 7 consecutive days using decision module. So,
if slots are available then the appointment patients are delayed 30 minutes which is time
to reach hospital otherwise rejected.
3.
After that there is increment in variable "number of appointment patients”. At
same time, the status of “Appointment patient reserved” changes to 1 which indicates
there are patients who got appointment. This logical entity is then disposed.
4.
The “Appointment Patients Arrivals” module creates arrival of actual
appointment patients one by one after a period of 15 minutes. The arrival of appointment
patients is controlled by “Appointment Patients Reserved * PatientsPerArrival” in create
module entities per arrival. So, if appointment patient called at 08:03 then its first delayed
30 minutes after that entities per arrival turns 1 from zero at 08:33. As “Appointment
Patients Arrivals” creates entities after every 15 minutes so the earliest it can entity for
appointment patient is at 08:45 AM after 08:03 AM which is first patient arrival time.
5.
After that there is decrement in variable "number of appointment patients” and
decision to check if any appointment patients are left. If there are no appointment patients
left then entities per arrival changes to 0.
6.
Appointment patients can only come if clinic is open and there are patients who
got appointment. If clinic is close and “number of appointment patients” > 0 then rest of
patients will start coming from next day 8 AM. The last time when appointment patient
can come is 04:45 PM as arrivals stops at 04:59 PM. 7.
The process is separated based on patient type using decision module.
Alternative 3: Description: Explain your alternative 3. Implementation: Please
provide an explanation of your implementation. Please include the file name of the
file that contains your implementation
Explanation
: In our alternate model 3, we have continued the modelling process by
taking inspiration from the alternate 2. But, we have made some significant changes in
the model that results in reduced average time for patients in the system. The changes
made include:
1.
Assigning priority to a patient type i.e. “Walk-in” and “Appointment patients”
using “Priority” attribute upon arrival. 2.
As per alternate 2, this model also gives the priority to a patient based on the pain
with “lowest attribute value”.
3.
Compared to the alternative 2, alternate 3 creates a combined priority by taking a
product of the priority given based on patient type and the pain level of the patients by an
attribute called Mixed Priority. (Mixed Priority = Patient Type Priority * Pain Type
Priority).
4.
In alternative 3, all the doctors are combined as a single resource with capacity 3
and catering the patients based on their attribute value of “Mixed priority”.
4.
Results of comparison of alternatives (Add all the relevant metrics you
have considered.)
Matt
a)
Alternative 1 vs Alternative 2
N=122
set expo to 5 for all files compared
Metric
Confidence
Interval
for
Difference
of
Means
Significant
Difference?
Explain.
Conclusion (e.g., is one
better than the other
or
there
is
no
statistical difference?)
Waiting time until
nurse
[0.2273, 0.3047]
We have the same
conclusion for all
metrics. There is a
significant
difference for each
metric since "0" is
not contained in
their
respective
Confidence
Intervals.
This
implies that we can
reject
the
hypothesis of zero
At a 95% confidence
level, we can conclude
that Alternative 1 has
longer wait times for
seeing the nurse. For
this
metric,
Alternative 2 is better.
Waiting
time until
doctor
Priority 1
[-2.382, -1.638]
At a 95% confidence
level, we can conclude
that Alternative 2 has
longer wait times for
seeing a doctor as a
priority 1 patient. For
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difference for each
metric at the 5%
significance level.
In other words,
Alternative 1 and 2
are different for
these metrics.
this
metric,
Alternative 1 is better.
Priority 2
[-5.004, -3.756]
At a 95% confidence
level, we can conclude
that Alternative 2 has
longer wait times for
seeing a doctor as a
priority 2 patient. For
this
metric,
Alternative 1 is better.
Priority 3
[-20.93, -12.07]
At a 95% confidence
level, we can conclude
that Alternative 2 has
longer wait times for
seeing a doctor as a
priority 3 patient. For
this
metric,
Alternative 1 is better.
Total system time
[-10.59, -6.35]
At a 95% confidence
level, we can conclude
that Alternative 2
takes longer to process
patients. For this
metric, Alternative 1 is
better.
Total system
time
with
priority
Priority
1
[-11.95, -9.85]
At a 95% confidence
level, we can conclude
that Alternative 2
takes longer to process
patients with priority
1. For this metric,
Alternative 1 is better.
Priority
2
[-12.176, -10.424]
At a 95% confidence
level, we can conclude
that Alternative 2
takes longer to process
patients with priority
2. For this metric,
Alternative 1 is better.
Priority
3
[-9.57, -1.99]
At a 95% confidence
level, we can conclude
that Alternative 2
takes longer to process
patients with priority
3. For this metric,
Alternative 1 is better.
Latest time a patient
leaves the clinic
[-55.6, -31.8]
At a 95% confidence
level, we can conclude
that Alternative 2 has
a greater maximum
time that a patient will
be in the system (on
average). For this
metric, Alternative 1 is
better.
Metric
Estimated
Mean
Difference
Half Width
Waiting time until nurse
0.266
0.0387
Waiting
time until
doctor
Priority 1
-2.01
0.372
Priority 2
-4.38
0.624
Priority 3
-16.5
4.43
Total system time
-8.47
2.12
Total
system time
with priority
Priority 1
-10.9
1.05
Priority 2
-11.3
0.876
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Priority 3
-5.78
3.79
Latest time a patient leaves the
clinic
-43.7
11.9
Saad
b)
Alternative 1 vs Alternative 3
Metric
Confidence
Interval
for
Difference
of
Means
Significant
Difference?
Explain.
Conclusion (e.g., is one
better than the other
or
there
is
no
statistical difference?)
Waiting time until
nurse
[0.209, 0.287]
We have the same
conclusion for all
metrics. For some
metrics there is a
small
differernce
such
as
the
"waiting time to
see a nurse"
while
for others we have a
significant
differences
since
"0" is not contained
in their respective
Confidence
Intervals.
This
implies that we can
reject
the
At a 95% confidence
level, we can conclude
that Alternative 1 has
longer wait times for
seeing the nurse. For
this metric, Alternative
3 is better.
Waiting
time until
doctor
Priority 1
[-3.42, -2.63]
At a 95% confidence
level, we can conclude
that Alternative 3 has
longer wait times for
seeing a doctor as a
priority 1 patient. For
this metric, Alternative
1 is better.
Priority 2
[-6.7, -5.11]
At a 95% confidence
level, we can conclude
hypothesis of zero
difference for each
metric at the 5%
significance level.
In other words,
Alternative 1 and 3
are different for
these metrics.
that Alternative 3 has
longer wait times for
seeing a doctor as a
priority 2 patient. For
this metric, Alternative
1 is better.
Priority 3
[-13.6, -4.31]
At a 95% confidence
level, we can conclude
that Alternative 3 has
longer wait times for
seeing a doctor as a
priority 3 patient. For
this metric, Alternative
1 is better.
Total system time
[1.1, 5.6]
At a 95% confidence
level, we can conclude
that Alternative 1 takes
longer
to
process
patients. For this metric,
Alternative 3 is better.
Total system
time
with
priority
Priority
1
[-2.05, -0.974]
At a 95% confidence
level, we can conclude
that Alternative 3 takes
longer
to
process
patients with priority 1.
For
this
metric,
Alternative 1 is better
Priority
2
[-3.25, -1.8]
At a 95% confidence
level, we can conclude
that Alternative 3 takes
longer
to
process
patients with priority 2.
For
this
metric,
Alternative 1 is better.
Priority
3
[5.12, 13.2]
At a 95% confidence
level, we can conclude
that Alternative 1 takes
longer
to
process
patients with priority 3.
For
this
metric,
Alternative 3 is better.
Latest time a patient
leaves the clinic
[7, 26.8]
At a 95% confidence
level, we can conclude
that Alternative 1 has a
greater maximum time
that a patient will be in
the system (on average).
For
this
metric,
Alternative 3 is better.
Metric
Estimated
Mean
Difference
Half Width
Waiting time until nurse
0.248
0.0393
Waiting
time until
doctor
Priority 1
-3.02
0.395
Priority 2
-5.9
0.794
Priority 3
-8.96
4.65
Total system time
3.33
2.23
Total
system time
with priority
Priority 1
-1.51
0.538
Priority 2
-2.52
0.722
Priority 3
9.14
4.03
Latest time a patient leaves the
clinic
16.9
9.9
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Dhruvin
c)
Alternative 2 vs Alternative 3
Metric
Confidence Interval for
Difference of Means
Significant Difference?
Explain.
Conclusion (e.g., is
one better than the
other or there is no
statistical
difference?)
Waiting time until
nurse
[-0.0504, 0.0136]
FAIL TO REJECT H0
=>
MEANS
ARE
EQUAL AT 0.05
LEVEL
At a 95% confidence
level,
we
can
conclude
that
Alternative 2 has
similar wait times for
seeing the nurse with
an error of [-
0.0504,0.0136]. For
this
metric,
Alternative 2 and 3
are similar.
Waiting
time
until
doctor
Priority
1
[-1.483, -0.537]
We have the same conclusion for the selected metrics except waiting time until patients
sees the nurse. There is a significant difference for each metric since "0" is not contained in their respective Confidence At a 95% confidence
level,
we
can
conclude
that
Alternative 3 has
longer wait times for
seeing a doctor as a
priority 1 patient. For
this
metric,
Alternative
2
is
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Intervals. This implies that we can reject the hypothesis of zero difference for the rest of the metrics at the 5% significance level. In other
words, Alternative 2 and 3
are different for each metric except the first one.
better.
Priority
2
[-2.467, -0.573]
At a 95% confidence
level,
we
can
conclude
that
Alternative 3 has
longer wait times for
seeing a doctor as a
priority 2 patient. For
this
metric,
Alternative
2
is
better.
Priority
3
[2.2, 12.84]
At a 95% confidence
level,
we
can
conclude
that
Alternative 2 has
longer wait times for
seeing a doctor as a
priority 3 patient. For
this
metric,
Alternative
3
is
better.
Total system time
[9.69, 13.9]
At a 95% confidence
level,
we
can
conclude
that
Alternative 2 takes
longer to process
patients. For this
metric, Alternative 3
is better.
Total
system
time
with
priority
Priority
1
[8.35, 10.51]
At a 95% confidence
level,
we
can
conclude
that
Alternative 2 takes
longer to process
patients with priority
1. For this metric,
Alternative
3
is
better.
Priority
2
[7.817, 9.743]
At a 95% confidence
level,
we
can
conclude
that
Alternative 2 takes
longer to process
patients with priority
2. For this metric,
Alternative
3
is
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better.
Priority
3
[11.24, 18.56]
At a 95% confidence
level,
we
can
conclude
that
Alternative 2 takes
longer to process
patients with priority
3. For this metric,
Alternative
3
is
better.
Latest time a
patient leaves the
clinic
[49.2, 72.1]
At a 95% confidence
level,
we
can
conclude
that
Alternative 2 has a
greater
maximum
time that a patient
will be in the system
(on average). For this
metric, Alternative 3
is better.
Metric
Estimated
Mean
Difference
Half Width
Waiting time until nurse
-0.0184
0.032
Waiting
time until
doctor
Priority 1
-1.01
0.473
Priority 2
-1.52
0.947
Priority 3
7.52
5.32
Total system time
11.8
2.11
Total
system time
with priority
Priority 1
9.43
1.08
Priority 2
8.78
0.963
Priority 3
14.9
3.66
Latest time a patient leaves the
clinic
60.6
11.4
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\\filer-users\S_S17690\My Documents\ARENA LAB\Project+Assignment\
PROJECT\Final Folder\Final Folder\A1 VS A3\Total time in system by
priority 1 type Patient.dat
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(Include as many tables as needed. Alternative formats accepted as long as
you make it clear where there is a significant difference between alternatives
and where there is not, and clearly state the conclusion that is being made.)
Team on Saturday (8PM)
5.
What recommendations would you like to make to MTL Clinic? Please
justify your suggestions based on the above analysis.
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