Faculty of Industrial Engineering and Management Technion – Israel Institute of Technology

Faculty of Industrial Engineering and Management

Technion – Israel Institute of Technology

David Sinreich and Yariv Marmor

Can We Make Simulation More Accessible To Emergency

Department Decision Makers

Emergency Multidisciplinary Research UnitSMBD - Jewish General Hospital, August 29, 2005

The Healthcare Industry and Numbers

• The annual Canadian expenditure on healthcare in 2001 was estimated at $64.2 billion (~$2100 per person).

• According to 2005 issue of healthcare in Canada (CIHI) the healthcare expenditure in 2004 grow to about $100 billion (~$3200 per person) and accounted for 10% of the GDP.

• Hospitals represented 30% of the total healthcare expenditure in 2004.


• The annual U.S. expenditure on healthcare in 2003 was estimated at $1.5 trillion (~$5000 per person) and is expected to reach $2.8 trillion by the year 2011.

• Healthcare accounted for 13.2% of the GDP in 2000 and may reach 17% of the GDP by 2011.

• Hospitals represented 31.7% of the total healthcare expenditure in 2001. This expenditure is expected to decrease to 27% by 2012.

• According to the American College of Emergency Physicians (June 2003), the cost of Emergency Department (ED) operations amounted to 5% of the total US healthcare expenditure.


• The ICBS reports that the annual healthcare spending in Israel in 2003 reached $10.1 billion (~$1700 per person), which accounts for 8.8% of the GDP.

• This level of expenditure is similar to other OECD countries such as Germany 10.9%, France 9.7%, Sweden 9.2% and Australia 9.1% (number reflect expenditure in 2002)

• Hospitals accounted for 26.1% of the national expenditure on healthcare in 2001.


• The ICBS reports that the annual healthcare spending in Israel in 2003 reached $10.1 billion (~$1700 per person), which accounts for 8.8% of the GDP.

• This level of expenditure is similar to other OECD countries such as Germany 10.9%, France 9.7%, Sweden 9.2% and Australia 9.1% (number reflect expenditure in 2002)

• Hospitals accounted for 26.1% of the national expenditure on healthcare in 2001.

These numbers are a clear indication that increasing the efficiency and productivity of

hospital and ED operations is critical to the success of the entire

healthcare system

• The ED serves as the hospital’s “gate keeper“ and is the most difficult department to manage.

• The ED has to handle efficiently and effectively a random arrival stream of patients.

• The ED has to be highly versatile and flexible.

• The ED is required to have the ability to react quickly to fast unfolding events.

The Emergency Department

The Emergency Department

• There are 2.5 million patient visits each year at the 25 EDs in Israel. This translates to about 270 patient visits on average per day.

• On average there 30 - 40 beds in these EDs.

• Based on these number, there are around 7 - 8 patient turnarounds a day, this translates to an average length of stay of 3 - 3.5 hours.

• In reality there are 4 - 6 times more patient arrivals during pick hours (between 11 – 13 and 19 – 22) compared to other hours of the day.

• Hospital management is reluctant to accept change, particularly if it comes from a 'black-box' type of tool.

• Management often does not realize the benefits of using simulation-based analysis tools.

• Management is well aware of the time and cost that have to be invested in building detailed simulation models.

• Management believes that spending money on operational issues only diverts funds from patient care.

• Lack of experts with experience in modeling large, complex systems.

Simulation of Healthcare and ED Systems

Fixed Processes

The Model's Basic Building Blocks

Generic Activities

Generic Processes

High abstraction level

Flexible enough to model any system and scenario

Difficult to use requires knowledge and experience

Medium abstraction level

Flexible enough to model any system which uses a similar process

Simple and intuitive to use after a brief and short introduction

Low abstraction level

Can only model and analyze the system it was designed for

Simple and easy to use after a quick explanation

Modeling Options

It is essential to build up the models’ credibility:

• Hospital management should be directly involved in the development of simulation projects.

• The development of simulation projects should be done in-house by hospital personal.

Increasing Acceptance of Simulation in Healthcare


As a result the tool has to be:

• General, and flexible

• Include default values for most of the system parameters.

• Include a decision support system

• Simple to use

Essential Basic Condition

For the tool to be general and flexible

The process patients go through when visiting an ED has to be determined mainly by the patient type (Internal, Orthopedic, Surgical etc.) rather than by the hospital in which it is performed.

• Funded by the Israel National Institute for Health Policy (NIHP).

• 5 out of the 25 – 27 general hospitals operating in Israel participated in the study.

• Hospitals 1 and 3 are large (over 700 beds). Hospital 5 is medium (400 - 700 beds). Hospital 2 and 4 are small (less than 400 beds).

• Hospital 5 is a regional hospital and the rest are inner-city hospitals.

• Hospitals 1 and 3 are level 1 trauma centers and the rest are level 2 centers.

The Field Study

The Field Study

• Teams of supervised students equipped with standardized code lists of the different process elements conducted time and motion studies in the selected hospitals.

• Data was also gathered from each hospital’s information system.

• Additional data was gathered trough interviews with the hospital top management, ED chief physician and ED head nurse.

• Through observations, gathered data and interviews, 19 individual process charts each representing a typical patient types were identified.

Processes and Patient Types

HospitalPatient Type

1Fast-Track, Internal, Surgical, Orthopedic

2Internal, Surgical, Orthopedic

3Walk-In Internal, Walk-In Orthopedic, Walk-In Surgical, Internal, Trauma

4Internal Acute, Internal/Surgical Minor, Orthopedic

5Fast-Track, Internal, Surgical, Orthopedic

Resource 1

Activity

70%30%

Resource

Resource 1

Resource 1

Activity

Activity

Activity

Decision

Process Chart

PhysicianNurseImagingLabElse

60estimated max time

initialexamination

decision point for alternative processes

10%probability of events

06vital signs

07

E.C.G05

decision

awaitingdischarge

40

treatment 41

50

consultation

instructionsbefore discharge

discharge /hospitalization

els

e

triage04

43

54

reception03

observation

46

every 15minutes

followup47

bloodwork

1312

100%

imaging /consultation /treatment

17

14

decision

20

ultrasound

2928

21

Xray

2725,26

CT

3130

22

15

39

37

45

followup48

every 15minutes

49

11

handlingpatient&famil

y08

09

38imaging

36

3534

32,33 treatment18

56

hospitalization/discharge

awaiting fortransitvehical

55

52

53

10

treatment 19

16

discharge

51

else

treatment

42

44

reference point

labs labs

consultation

labs

consultation

imaging

decision

proportion of patients 01 process requires bed 02

23

24

The Similarity Measure - Activities

jiijij

ijij

bbeea

eij

i j

bij bji

e12=2 , a12=0.33b12=2 , b21=2

C

D

B

A

E

1 2

B

A

D

AA

BB

D

D

E

C

1 ,1 ,2k

c12 = 0+2+0+0+0+0+0+0+0 = 2

d12 = 0+0+2+2+0+1+0+1+0 = 6

lkikl

i

klfh

k l

jkl

ikl

ij hhc },{min

k l

jkl

ikl

ij hhd

)( ijdijr ccijij

r12 = 2/(6+2) =0.25

C

D

B

A

A

B

D

E

010

100

020

0111210

1110210

12012101H

000

002

2202H

The Similarity Measure - Relationships

The Sensitivity of the Similarity Measure

The similarity measure is sensitive to:

• The absence of an activity or to additional activities a resource is expected to perform.

• The absence of a relationship or to an additional relationship between activities.

The similarity measure is not sensitive to:

• The order in which activities are expected to be performed.

Clustering the Patient Processes

Average Similarity Level – 0.44

1I

1 O

1 S

1 FT

2 I

2O

2S

3I

3 O_W

3 S_W

3 I_W

3T

4I_S

4O

4 I_A

5I

5 O

5 S

5 FT

1 I 1 O

1 S 1 FT

2 I 2 O 2 S

3 I 3 O_W 3 S_W

3 I_W3 T

4 I_S 4 O

4 I_A 5 I 5 O 5 S

5 FT

43 52 80 64335259 32 2332 43894670 6624 55 88 66 40 40897414 60 3712 59358636 3277 62 53

61 49597431 58 4731 68586139 3742 89 79 56325144 37 2928 45675743 4823 56 94

445363 25 1839 38592573 8923 40 66 67943 236 45307150 3272 51 46

31 45 3832 62465545 3751 71 64 10 9 27 2757751 531 23 52 8416 88285215 1425 51 46

30 10016315 52 41 37 3629326 230 19 45

344624 2322 64 54 3972 6127 54 79

26 1853 56 57 7732 27 59

1625 55 5232

65

• Full enumeration and ranking was used to determine the best way to divide the processes into:

Three clusters Four clustersTwo clusters


Clustering the Processes Into Two Groups

• The first group included all the internal patient types from all 5 hospitals: 1Int, 1FT, 2Int, 3Int, 3W_Int, 4Int_S, 4Int_A, 5Int, 5FT.

• The best combined average similarity value for two clusters (0.579, 0.571) was 0.575.




• The best combined average similarity value for three clusters was 0.638.

• The chosen clustering option was ranked as number 17 with a combined average similarity value of (0.656, 0.746, 0.544) 0.623.

Clustering the Processes Into Three Groups

“When good is better than best” (Petroski 1994)

1I

1 O

1 S

1 FT

2I

2O

2S

3I

3 O_W

3 S_W

3 I_W

3T

4I_S

4O

4 I_A

5I

5 O

5 S

5 FT

1 I 1 O

1 S 1 FT

2 I 2 O 2 S

3 I 3 O_W 3 S_W

3 I_W3 T

4 I_S 4 O

4 I_A 5 I 5 O 5 S

5 FT

43 528064335259 32 2332 43894670 6624 55 88 664040897414 60 3712 59358636 3277 62 53 6149597431 58 4731 68586139 3742 89 79

56325144 37 2928 45675743 4823 56 94 445363 25 1839 38592573 8923 40 66 67943 236 45307150 3272 51 46

31 45 3832 62465545 3751 71 64 10 9 27 2757751 531 23 52 8416 88285215 1425 51 46

30 10016315 52 41 37 3629326 230 19 45

344624 2322 64 54 3972 6127 54 79

26 1853 5657 7732 27 59

1625 55 5232

65




Combined Average Similarity Level – 0.623




Clustering the Processes Into Four Groups

• The best combined average similarity value for four clusters was 0.683.

• The chosen clustering option was ranked as number 76 with a combined average similarity value of (0.669, 0.746, 0.654, 0.558) 0.666.

• The first group included all acute internal patient types: 1Int, 2Int, 3Int, 4Int_S, 4Int_A, 5Int.

• The second group included most orthopedic patients types: 1O, 2O, 4O, 5O.

• The third group included most surgical patients types: 1S, 2S, 3O_W, 3S_W, 3T, 5S.

• The forth group included all ambulatory patients types: 1FT, 3Int_W, 5FT.


Three clusters Four clusters

• The clustering options chosen were compared to the best similarity result of 1000 random clustering solutions into 4 groups

• For a selection probability (0.25, 0.25, 0.25, 0.25) the best combined average similarity value was 0.554.

• For a selection probability (0.315, 0.21, 0.315, 0.16) the best combined average similarity value was 0.56.

Two clusters


Based on this analysis it is safe to argue that in the

hospitals that participated in this study, patient type has

a higher impact in defining the operation process than

does the specific hospital in which the patients are

treated.

Conclusions






• Simple to use

The Relative Precision of the Time Elements

• Since a time study is basically a statistical sampling process, it is important to estimate the precision of the gathered data.

ipip ,ˆ

ipm

Average Duration and Standard Deviation over all observed elements i for patient type p at all the hospitals

The number of times element i was observed for each patient type p

p The maximum number of times patient type p goes through an element that is only performed once during the ED process

ipip

ipip

m

zd

ˆ

ˆ21

Precision as a proportion of the gathered element

The Relative Precision of the Time Elements

i

ipipp wddThe relative precision for patient type p

p

ipipip

mt

ˆ~

The contribution of element i to the total process time of patient type p

iipipip ttw ~~

The relative weight of element i for patient type p

ii

ii

m

zd

ˆ

ˆ21

The relative precision of element i

Over 20,000 process elements were observed and recorded.

Element Precision

Patient Types

Fast-TrackTraumaOrthopedicSurgicalInternalElement2.2%3.2%6.7%8.9%5.7%3.6%Vital Signs

3.0%9.7%13.1%16.0%11.3%3.6%E.C.G. Check

3.9%15.6%10.8%11.1%12.6%5.5%Treatment Nurse

7.9%50.1%19.7%43.0%47.5%10.1%Follow-up Nurse

11.9%43.2%25.2%29.1%30.7%16.5%Instructions Prior to Discharge

2.8%10.2%7.4%4.4%6.3%4.6%First Examination

4.3%30.2%11.8%8.0%11.4%6.7%Second or Third Examination

5.4%----32.9%26.0%27.8%5.9%Follow-Up Physician

7.5%15.0%32.9%19.3%13.0%11.0%Hospitalization /Discharge

4.6%18.4%9.5%9.3%15.9%6.5%Handling Patient and Family

7.1%49.9%21.2%15.4%12.9%11.3%Treatment Physician

7.6%9.5 %8.1%9.4%5.2%Patient Precision

Precision of the Different Time Elements

id

pd

The combined precision values indicate, that

aggregating element duration regardless of patient type

and the hospital in which the patients are treated,

improves the precision levels of all the different

elements.

Conclusions





It is possible and it makes sense to develop a simulation tool That is based on a generic unified process






• Simple to use

ARENA’s Simulation

Model

Graphical User Interface based on the Generic Process

Mathematical Models

Decision Support System

The Structure of the Simulation Tool

Imaging Center

Specialists

Scheduling Medical Staff


Model


Mathematical Models



• Staff’s walking time

• Patient Arrivals at the Imaging Center

• Patient arrivals to the ED

The following mathematical models were developed based on the gathered information:

Mathematical Model Development

• Let Xpihd be a random variable normally distributed with a mean of that represents the square-root of the number of patients of type p who arrive at the ED of hospital i at hour h on day d.

• The gathered data reveals that the number of patients arriving at the ED differs from hour to hour and from day to day

• Statistical tests reveal that the square-root of the patients' arrival process can be described by a normal distribution.

Estimating the Patient Arrival Process

pihd


The number of patients of type p who arrive during hour h on day d

- pihdwn

- ˆ pi

- ,HW

- ˆpiF

- ˆapihdwn

- ˆ phd

The square-root of the number of patients of type p who arrive at the ED of hospital i at hour h on day d in week w

The average square-root estimator of the number of patients of type p arriving at hospital i per hour

Number of data weeks received from the hospitals' information systems and number of hospitals

The patient arrival factor

The estimated adjusted arrival data values of patients of type p who arrive at hospital i at hour h on day d in week w

The patient arrival process is similar for all the hospitals surveyed therefore it was decided to combine the gathered data from all hospitals


2pihdpihd x

247ˆ1

7

1

24

1

Wn

W

w d hpihdwpi

HF

ipi

pipi

ˆ

ˆˆ

pipihdwapihdw Fnn ˆˆ

WHnH

i

W

w

apihdwphd

1 1ˆ̂

piphdpihd F̂ˆˆ 6.0 ,ˆ~ pihdpihd NX

The number of patients of type p who arrive at hospital i at hour h on day d

Patient Type

OrthopedicSurgicalInternalHospital

1.1871.2931.1801

0.8401.0380.9582

0.9740.6690.8624

It is clear from these factors that hospital 1 is larger than the other two hospitals


In the case a new hospital whishes to use the simulation tool all that is needed are the values obtained from the hospital's computerized information systems.

pihdwn

The rest of the process, which includes calculating the formulas, is performed automatically by the simulation tool.

0

2

4

6

8

10

12

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

Hospital 1

Hospital 2

Hospital 3

Hospital 1

Hospital 2

Hospital 3

Patients

Hour

Actual patient arrivals - Solid tick marksExpected patient arrivals - Open tick marks

0

1

2

3

4

5

6

7

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

Hospital 1

Hospital 2

Hospital 3

Hospital 1

Hospital 2

Hospital 3

Patients

Hour


Internal Patients on Saturday

Internal Patients on Monday

Validating The Model

Surgical Patients on Wednesday

0

1

2

3

4

5

6

7

8

9

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

Hospital A

Hospital E

Hospital F

Hospital A

Hospital E

Hospital F

Patients

Hour



MomentsMean 0.0000844Std Dev 0.6003367Std Err Mean 0.0025241upper 95% Mean 0.0050316lower 95% Mean -0.004863N 56571

The distribution of the residuals between the predicted patient arrivals and the actual patient arrivals.

Shapiro-Wilk goodness of fit tests reveal that the residuals can be described by a normal distribution with a mean close to 0, and a standard deviation of 0.6.







The Patient Arrival Process to the Imaging Center

• To accurately estimate the turnaround time ED patients experience at the imaging center it is important to estimate the following:‐ patients' walking time

‐ Waiting time at the imaging center

‐ the time it takes to perform an X-ray

‐ the time it takes the radiologist to view the X-ray to return a diagnose

• Imaging centers (X-ray, CT and ultrasound) are not always ED-dedicated. In some cases these centers serve the entire hospital patient population.

The Patient Arrival Process to the Imaging Center

• In these cases two different patient types are sent to the imaging center for service:‐ patients who come from the ED

‐ patients who come from all other hospital wards

• These two streams interact and interfere with each other and compete for the same resources

• In these case it is imperative to estimate the hospital patient arrival process.

• The gathered data reveals that the number of hospital patients arriving at the imagining center differs from hour to hour and from day to day and from month to month

• Statistical tests reveal that the square-root of the hospital patients' arrival process can be described by a normal distribution.

Estimating The Imaging Center Arrival Process

• A linear regression model was used to estimate the stream of hospital patients. In order to maintain the model's linearity, four separate regression sub-models were developed.


‐ A sub-model to estimate the arrivals between 6 AM and 12 midnight on weekdays.

‐ A sub-model to estimate the arrivals between 6 AM and 12 midnight on weekends.

‐ A sub-model to estimate the arrivals between 12 midnight and 6 AM on weekdays and weekends.

‐ A sub-model to estimate the arrivals between 12 noon and 5 PM in the cases the central imaging center only operates part of the day.


- ̂

- i

- d- h

- m

The square-root of the average number of patients arriving to the imaging center

The hospital effect

The hour effect

The day effect

The month effect,

mdhiihdm ˆˆ

2ihdmihdm The number of hospital patients of type p who

arrive at imagining center of hospital i at hour h on day d and on month m

0

5

10

15

20

25

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

Hospital 1

Hospital 2

Hospital 3

Hospital 1

Hospital 2

Hospital 3

Patients

Hour


Hospital Patient Arrivals to the Imaging Center on A Tuesday


The distribution of the residuals between the predicted patient arrivals and the actual patient arrivals.

Shapiro-Wilk goodness of fit tests reveal that the residuals can be described by a normal distribution with a mean close to 0, and a standard deviation of 0.8.

MomentsMean -1.62e-14Std Dev 0.8030956Std Err Mean 0.0075429upper 95% Mean 0.0147854lower 95% Mean -0.014785N 11336







• Observations show that the medical staff spends a considerable amount of time, during each shift, walking between the different activity points in the ED.

Estimating the Staff’s Walking Time

‐ patient beds

‐ medicine cabinet

‐ nurse's station

‐ ED main counter

• The estimation model is based on the following parameters:

‐ The distances between the different activity points

‐ The number of beds each staff member is in charge of

‐ The ED space dimensions each staff member operates in.


- ˆ DpT

- ˆ NpT

- ,LW

- cd

- rd

- md

- sd

- N

Physician's mean walking time when treating patient type p (sec)

Nurse's mean walking time when treating patient type p (sec)

Width, Length of the space in which the medical staff operates (cm)

Walking distance from the area's centroid to the ED counter (cm)

Walking distance from the area's centroid to the procedure room (cm)

Walking distance from the area's centroid to the medicine cabinet (cm)

Walking distance from the area's centroid to the nurse's station (cm)

Number of patient beds in the ED room

NWd

WdddWT

r

crcDp

2150,05.5968125.204300034.0

5.5965.70300047.0 13354.012628.050041.037127.461

Physician’s Walking Model

WLN

WdWd

ddWT

mm

msNp

2150,0

66667.80666667.117600875.0 66667.80644444.49902921.0

50267.11936.561123.681994.7695

Nurse’s Walking Model



• The fit of the above models as indicated by R2 is 0.737 for the physician's walking model and 0.675 for the nurse's walking models.

• The variance analysis shows the both models and all their parameters are significant.

• The residual analyses of the physicians' and nurses' estimation walking models reveal that in both cases residuals are normally distributed with a mean of 0.

• The models have been used in a setting different from the ones that were used in the initial development.


• The single factor ANOVA in both cases reveals that the null hypothesis, (there is no statistical difference between the model and observation results) can not be rejected.

• P-value for the physicians’ model was 0.28

• P-value for the nurses’ model was 0.74


Model


Mathematical Models








• Simple to use

The Decision Support Module

The validation process is comprised of two stages:

• Five simulation models were created using the developed tool in conjunction with the suggested default values and the other specific values for each of the five EDs that participated in the study.

• Ten 60-day simulation runs were performed for each of the five EDs.

• The performance of each of these models was compared to the actual data that was obtained from each of hospital's information systems (250,000 data entries that represent around 2.5 years of data).

Model Validation

• Statistical significance of the differences between the simulation and the averages obtained from the information system.

Model Validation

Time

Practical Difference

Statistical Significance

Information Systems

Simulation

Frequency

Frequency

Time

• Practical significance of the differences between the information system's and simulation averages.

Comparison of the Results Obtained for the ED in Hospital 1

Patient TypeDatabaseAverage (2 years)

SimulationAverage (10 runs)

SimulationStd.


P-Value

Internal195182136.7%0.33

Surgical198211106.6%0.18

Orthopedic15715074.5%0.28

Model Validation




SimulationStd.


P-Value

Internal408399202.2%0.67

Surgical236240111.7%0.75


Model Validation


PatientType

DatabaseAverage(2 years)

SimulationAverage (10runs)

SimulationStd.

PracticalDifference

P-Value

Internal279261186.5 %0.31

Surgical1461251314.4%0.09

Orthopedic134142156.0%0.59


PatientType

DatabaseAverage(2 years)


SimulationStd.

PracticalDifference

P-Value

Internal1611781710.6%0.32

Surgical158149165.7%0.59


Model Validation



SimulationStd.


P-Value

Fast-Track134143136.7%0.48

Internal1721971914.5%0.14

Surgical9510388.4%0.06



Internal Patients During a Weekday in the ED of Hospital 1

0

2

4

6

8

10

12

14

01_1 02_3 04_1 05_3 07_1 08_3 10_1 11_3 13_1 14_3 16_1 17_3 19_1 20_3 22_1 23_3

Hour

Nu

mb

er

of

Pa

tie

nts

Orthopedic Acute & Walking - Weekend

Orthopedic Acute & Walking Weekend - Database

Lower Bound

Upper Bound

Orthopedic Patients During a Weekend day in the ED of Hospital 3

0

5

10

15

20

25

30

01_1 02_3 04_1 05_3 07_1 08_3 10_1 11_3 13_1 14_3 16_1 17_3 19_1 20_3 22_1 23_3

Hour

Nu

mb

er

of

Pa

tie

nts

Internal & FT - Weekday

Internal & FT Weekday - Database

Lower BoundUpper Bound

Model Validation

Internal Patients During a Weekday in the ED of Hospital 4

0

5

10

15

20

25

01_1 02_3 04_1 05_3 07_1 08_3 10_1 11_3 13_1 14_3 16_1 17_3 19_1 20_3 22_1 23_3

Hour

Nu

mb

er

of

Pa

tie

nts

Internal & Acute - Weekday

Internal & Acute Weekday - Database

Lower Bound

Upper Bound

Model Validation




SimulationStd


P-Value

Internal147161169.5%0.36

Surgical154149113.2%0.67

Orthopedic116132713.8%0.09

• A sixth ED was chosen and data on its operations was gathered from the hospital's information systems and through observations.

• A simulation model was created using the tool's default values augmented by some of the gathered data and ten 60-day simulation runs were performed.

Model Validation

0

5

10

15

20

25

30

Hour

Nu

mb

er

of

Pa

tie

nts

Internal Acute & Walking - Weekday

Internal Acute & Walking Weekday - Database

Lower Bound

Upper Bound

0

2

4

6

8

10

12

14

01_1 02_3 04_1 05_3 07_1 08_3 10_1 11_3 13_1 14_3 16_1 17_3 19_1 20_3 22_1 23_3

HourN

um

be

r o

f P

ati

en

ts

Surgical - WeekdaySurgical Weekday - DatabaseLower BoundUpper Bound

Surgical Patients During a Weekday in the ED of Hospital 6

Internal Patients During a Weekend day in the

ED of Hospital 6

Model Validation

If we use the statement

Conclusions

“The suggested unified generic process can be used to model any arbitrary ED"

as a scientific hypothesis and try to find a system for which the statement is not true, each failure increases our confidence in the model.

So far we have failed to reject the statement eight times

To the Israeli National Institute for Health Policy and Health Services Research NIHP

To all the students from the IE&Mgmt. Faculty and the Research Center for Human Factors and Work Safety which assisted in gathering the data and analyzing it and especially to Almog Shani and Ira Goldberg

Acknowledgment

Date post:	13-Jan-2016
Category:	Documents
Upload:	patsy
View:	21 times
Download:	0 times

Faculty of Industrial Engineering and Management Technion – Israel Institute of Technology

Documents