Analysis of Outpatient Waiting Times for Penalty Points Accrued by Hospital

This project analyzes the outpatient waiting times for penalty points accrued by a hospital due to patients waiting longer than the maximum waiting time set by the government. The expected minimum, maximum and mean number of penalty points are determined using Risk Solver on Excel. The appropriate probability distribution that governs the wait time is determined using the Distribution Fitting Facility. A 1000 iteration simulation of the waiting times is performed to estimate the probability distribution of the additional penalty points.

Enterprise Risk Modelling

Table of Contents
Project Description..............................................................................................................................1
Question 1............................................................................................................................................1
Question 2............................................................................................................................................2
Question 3............................................................................................................................................4
References............................................................................................................................................6

Project Description
This project is analysis the outpatient waiting times for provided quantitative data.
The provided data is based on the patients because basically patients are come to the local
hospital accidents and emergency department or treatment. But, the patients are wait until a
doctor or nurse is available to the treat them. Basically, the government has set the maximum
length of waiting time for each patient must been have treated. The maximum waiting time is
12o minutes. So, if patients are wait longer than this maximum, it will result in the hospital
being awarded penalty points at the rate of 10 points per minute over the maximum. So, this
project is needs to determine the total number of penalty points the hospital accrues over the
year by using the Risk solver on Excel. These are will be discussed and analysed in detail.
Question 1
First, we are determine the expected minimu, maximum and mean number of the
penalty points. It is represented as below.

Question 2
Here, we are using the Distribution Fitting Facility to determine an appropriate probability
distribution that appears to govern the wait time. It is represented as below (solver, 2018).

Name Patient # Length of wait (minutes)
Range Quantitative_Data!
A2:A502
Quantitative_Data!B2:B502
Best Fit
(Ranked by
AIC)
RiskUniform(0,501) RiskBetaGeneral(1.7739,1.8887,107.6
59,146.585)
Function 40.29133078 127.9479047
AIC 6220.6302 3569.8466
Minimum 0 107.6593
Maximum 501 146.585
Mean 250.5 126.5126
Mode 0 125.7793
Median 250.5 126.3908
Std. Deviation 144.6262 9.009
Graph
Correlation Patient # Length of wait (minutes)
Patient # 1.000
Length of wait 0.059 1.000

(minutes)
Question 3
Here, we hare perform the 1000 iteration simulation of the waiting times to estimate
the probability distribution of the additional penalty points. It is represented as below
(Albright et al., 2011).

Name
Ce
ll
Function
Min Mea
n
Max
Correlation Matrix: Location: 'Fit Summary '!$B$20:$C$21
Size: 2 X 2
Function /
RiskUniform(0,501)
B
9
RiskUniform(0,501,RiskCorrmat($B$20:$C$2
1,1))
0 250.
5
501
Function /
RiskBetaGeneral(1.7739,1.8
887,107.659,146.585)
C
9
RiskBetaGeneral(1.7739,1.8887,107.659,146.
585,RiskCorrmat($B$20:$C$21,2))
107.
659
126.
512
146.
585
5.0% 90.0% 5.0%
4.9% 90.0% 5.1%
112.03 141.31
105 110 115 120 125 130 13
0.000
0.005
0.010
0.015
0.020
0.025
0.030
0.035
0.040
Function / RiskBetaGeneral(1.7739,1.8887,107.659,146.585)
Comparison with BetaGeneral(1.7739,1.8887,107.659,146.585)
References
Albright, S., Winston, W., Zappe, C. and Broadie, M. (2011). Data analysis, optimization,
and simulation modeling. Australia: Cengage Learning.
solver. (2018). Risk Solver® Platform. [online] Available at: https://www.solver.com/risk-
solver%C2%AE-platform [Accessed 29 Dec. 2018].