2012 Cairo International Biomedical Engineering Conference (CIBEC)
Cairo, Egypt, December 20-21, 2012
The Effect of Useful Life and Vendor Performance on
Replacement Decision of Medical Equipment
Bassem K. Ouda and Neven S.K. Saleh
Ahmed S.A. Mohamed
Biomedical Engineering and Systems Dept.
Faculty of Engineering, Cairo University
Giza, 12613, Egypt
e-mail: bkouda@k_space.org
Engineering Mathematics and Physics Dept.
Faculty of Engineering, Cairo University
Giza, 12613, Egypt
e-mail: aashiry@ieee.org
Abstract—Medical equipment management life cycle considers
various stages ranging from planning to disposal or replacement.
Replacement decision is critical and essential stage of medical
equipment. A variety of criteria contributes to make an
intelligent replacement decision. We enhance the Fault Tree
Analysis (FTA) model for replacement of medical equipment,
considering a combination of technical, financial, and safety
criteria. The considered criteria are; hazard and alerts, cost,
useful life, and vendor support. Throughout this model, we
classify medical equipment life status into four groups;
replacement, test, surveillance and keep. According to the final
event score, the replacement decision is approved or not.
Neonatal Intensive Care Unit (NICU) equipment of 12 different
types for 3 hospitals, along three years, is utilized to investigate
the proposed model. Our model proposes a priority list of
equipment that should be replaced. According to the analysis to
the proposed factors, the useful life factor is found to be the
dominant factor. In addition, a high correlation between vendor
performance and expended costs is realized.
Keywords— FTA, medical equipment, replacemnt decision,
useful life, vendor preformance.
I.
INTRODUCTION
Healthcare systems everywhere face the steep test of being
safe, timely, effective, efficient, and patient-centred. Therefore,
medical management is one of the most important segments of
the health care system.
The medical equipment management is a process through
which hospitals are guided to develop, monitor, and manage
their equipment to promote the safe, effective, and economical
use of equipment [1]. Medical equipment management life
cycle considers nine stages; planning, acquisition, incoming
inspection, inventory, installation, user training, monitoring,
maintenance, and replacement [2]. Disposal or replacement of
medical equipment must follow safety procedures in order to
protect people and environment.
The ideal healthcare technology replacement planning
system would be facility-wide covering all clinical equipment.
It would utilize accurate, objective data for analysis and would
be flexible enough to incorporate non-equipment factors. It
also would be futuristic by including strategic planning
relating to clinical market place trends and hospital strategic
initiatives relating to technology [1].
There are different criteria by which the medical equipment
replacement decision should be considered. Firstly, technical
criteria; that include indicators such as useful life time ratio,
978-1-4673-2801-2/12/$31.00 ©2012 IEEE
114
utilization, downtime, technological change, vendor support,
etc... Secondly, financial criteria; that may include the service
and operating costs, availability of backup, etc... Finally,
safety criteria; that include factors such as hazards/alerts and
user/technician errors. According to these criteria, one of the
most significant indictors of the technical criteria is the vendor
support that can be taken into account in the replacement
decision making process especially in developing countries.
The support can be introduced by different ways according to
vendor qualification. Also, useful life time of medical
equipment is an important worldwide factor that should be
considered as replacement factor.
Various techniques were developed to demonstrate when a
piece of medical equipment should be replaced. One method
performs replacement prioritization according to a
combination of criteria utilizing software program which
produces relative replacement number (RRN) for each
equipment [3]. An interesting quantitative model employed the
Fault Tree Analysis (FTA) for replacement of medical
equipment was introduced in [ 4 ] and modified in [ 5 ] to
incorporate the vendor performance. Although this
modification considers an important factor, it suffers from
redundancy due to unnecessary utilization of the availability of
spare parts twice. In this proposed model, we modify the
construction to avoid factors redundancy. It guarantees a
warning when a piece of medical equipment needs to be
replaced. Also the data set is expanded to cover more
equipment data and types for different hospital sizes and for a
longer time span. Moreover, useful analysis about the
correlation between the replacement decision and technical
and financial criteria are included.
II.
METHODOLOGY
Fault Tree Analysis (FTA) is a deductive failure analysis
which focuses on one particular undesired event and which
provides a method for determining causes of this event [6].
The fundamental concept of fault tree analysis is the
translation of the failure behaviour of a physical system into a
visual diagram and logic model. As mentioned, the popular
way to model using FTA considers four steps [5]:
‚
‚
‚
‚
Definition of the Undesired Event (UE)
Identification of events that cause UE
Construction of the fault tree
Evaluation of the fault tree
B. Determination of Final Replacement Score
To determine final replacement score, the mathematical
model of FTA should be analyzed. It is necessary to substitute
the logical gates from up to down, by resolving the FT shown
in Fig. 1 to evaluate the replacement R as follows:
The FTA model for replacement of medical equipment
considering a set of criteria is developed for this purpose [4-5].
This study aims to modify the model to improve replacement
process. The previous FTA model reveals redundancy of SP
(spare parts availability) parameter in the model [5]. To
overcome this problem, we suggest modifying the model by
replacing SP parameter by USP parameter as described in the
next section. The model considers four major events (criteria).
Hazards and alerts (HA), useful life ratio (UL), the cost, which
can be characterized by the service and operating costs (SC)
and unavailability (U), and vendor support. Vendor support is
a powerful factor that impacts the replacement decision,
especially in developing countries. In this model, vendor
support criterion can be measured by three indicators,
unavailability of spare parts (USP), time consumed in repair
compared to down time (RD) and call response ratio (CR).
(1)
From Eq. 1, there are 7 cut sets which are (HA, UL, SC, U,
CR, USP ,and RD) where HA, UL and USP are the first order
cut sets but SC, U, CR, and RD are the second order cut sets.
Each separate term in Eq. (1) is considered minimal cut sets.
The factor w in Eq. (1) is considered to weight the effect of
spare parts unavailability. FTA is a qualitative model that can
be evaluated quantitatively and often is [8]. The quantitative
evaluation is performed in a sequential manner; first the
component failure probabilities are determined, then the
system top event probability is evaluated [8]. If the sum of all
these factors is greater than 1, it means that at least one factor
has a great effect on equipment life and this equipment must
be replaced. The probabilities can be calculated as follow:
1) Hazards and Alerts:
based on the manufacturer
recommendations and/or accidents, the probability can be
expressed as 1 in case of existence; and 0 otherwise.
2) Useful Life ratio: it compares the age of the equipment to
the expected useful life time (in hours or years).
A
(2)
UL ?
EL
UL: useful life time ratio,
A: age from purchasing year to the point of evaluations,
EL: the expected life time, according to manufacturers’
recommendations, local experience, and international data.
3) Cost: it can be measured by two ratios, the service and
operating costs to acquisition cost (SC) ratio, which is
widely reported and standardized, and the unavailability
(U) ratio. The SC can be formulated as
A. Model Description
We start FTA model by defining the undesired event,
replacement of medical equipment and identification of events
lead to the occurrence of UE. It is constructed as in Fig. 1.
HA: hazard &Alert
SC: service costs
U: unavailability ratio
UL: useful life time ratio
CR: call response ratio
RD: repai to downtime ratio
USP :unavailable spare parts
Medical Equipment
Replacement
HA
Cost
SC
UL
Vendor Support
U
USP
CR
RD
Fig.1. The proposed Fault Tree Analysis (FTA) model for replacement of
medical equipment considering vendor support.
As shown in Fig. 1, the medical equipment replacement will
take place if one or more of the following occur:
‚ Hazards and alerts (HA), that threat the safe use of
equipment.
‚ The equipment age exceeds its expected useful life time
(UL).
‚ High service cost ratio (SC) and unavailability (U) events
that together lead to high cost and less revenue.
‚ Long call response (CR), long repair time-to-downtime
(RD) and unavailable spare parts (USP) events that
together lead to poor vendor support.
SC ?
TC
AC
(3)
SC: service and operating costs ratio,
TC: total cost includes operating, maintenance and repair,
AC: acquisition cost.
The service cost-to-acquisition cost ratio is accepted
worldwide in the range of 2.3-12 % [4].
The unavailability can be calculated as a ratio of the
downtime intervals to periodic interval:
ÂD
n
The Neonate Intensive Care Unit (NICU) equipment is
selected due to its diversity of equipment categories. Three
different size hospitals are considered, and take into account
only 3-years interval (2007-2009) for investigation on fifty
pieces of NICU equipment. The data include equipment name;
purchasing date; expected life time [ 7 ]; operating costs;
maintenance and repair costs, spare parts availability, failure
rate and downtime. A statistical analysis of the factors
affecting the model is performed to investigate whether the
data followed statistic behavior according to any cumulative
distribution or probabilistic density functions. Those factors
include: age-to-expected lifetime ratio, service costs-toacquisition cost ratio, unavailability ratio, spare parts
unavailability, call response ratio, repair time ratio and the
replacement as a function of all factors.
U ?
i ?1
i
;i ? 1, 2 ,...,n
(4)
T
U: unavailability ratio,
Di: downtime in interval i in days,
T: total interval (1095 days),
n: number of periodic intervals (3 years in our case)
4) Vendor Support: this term can be quantified through three
indicators; the unavailability of spare parts (USP), the call
response (CR) ratio and repair time-to-downtime (RD) ratio.
The spare parts indicator reflects the discontinuation of any
medical equipment where the availability of spare parts can
maximize the usage of medical equipment. In this model, USP
probability is taken as 1 in case of unavailability and 0 in case
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ratio has the highest R score among the rest of medical
equipment. This is an indication of the great effect of spare
parts availability and the age of any medical equipment for
replacement decision.
Table I
of availability. The unavailability of spare parts in some cases
does not lead to replacement because of existence of
equivalent spare parts that can do the same functions.
The CR ratio reflects the response of the vendor to
maintain and repair the medical equipment when it is needed,
the shortest response time the better the call response and
better vendor support. It can be formulated as [5]
n
Ts
CR ? Â i ;i ? 1, 2 ,...,n
(5)
i ?1 D i
CR: call response ratio
Tsi: average response time in interval i in days,
Di: downtime in interval i in days,
n: number of periodic intervals (3 years)
SAMPLE DATA OF INVESTIGATED EQUIPMENT FOR REPLACEMENT
Equipment
name
BGA (Roche)
Incubator
(Caleo)
Bilirubin meter
(dragger,
cutaneous)
Infusion
Pump(Atom)
Ventilator,
Bennett, 840
Monitor, drager
The RD ratio is the time consumed in repair with respect to
downtime, the shortest RD ratio the better vendor support. It
can be formulated as [5]
n
Tr
RD ? Â i ;i ? 1, 2 ,...,n
(6)
i ?1 D i
RD: repair time-to-downtime ratio
Tri: average repair time in interval i in days,
Di: downtime in interval i in days,
n: number of periodic intervals (3 years)
Substitute Eq. (2) to Eq. (6) in Eq. (1), it becomes:
UL
SC
U
USP
CR
RD
R
0.25
0.72
0.03
0
0.4
0.5
0.47
0.5
0.38
0.48
0
0.63
0.24
0.83
1.13
0.46
0.27
1
0.16
0.16
1.7
0.5
0.54
0.1
0
0.1
0.35
0.6
0.3
0.1
0.003
0
0
0
0.3
0.5
0.29
0.16
0
0.35
0.4
0.68
(7)
The weighting factor w is considered to reflect the effect of
unavailability of spare parts on the possibility of repair and
maintenance for different equipment types, e.g., blood gas
analyzer, w~1.0, ventilators, w~0.8, and others, w~0.5. As
shown from Eq. (7), the spare parts availability is presented
only in one term not in two terms as stated in the previous
work [5]. Therefore, the modified model avoids redundancy of
spare parts availability in the model.
Fig.2. Histograms of replacement, cost, useful life time, vendor support,
service cost, unavailability ratio, call response ratio, repair to downtime ratio
factors.
III.
RESULTS AND DISCUSSION
The proposed model is applied on fifty NICU equipment
data of 12 different types for 3 hospitals. Due to limited access
to trustable data along equipment life cycle and variety of
equipment; the model is focused on NICU equipment only for
now. Table I shows sample data of various types of the
investigated equipment along with the replacement values.
The statistical analysis is performed using MATLAB program.
HA factor is taken 0 for all equipment as no hazards or alerts
are reported. The weighting factor w is taken 1.0 for blood gas
analyzer (BGA), 0.8 for ventilators and 0.5 for the other
equipment.
Based on this analysis, the equipment life status can be
classified into four groups. The equipment in group I must be
replaced if the final event score is greater than 1. In group II,
the equipment should be tested if the score in the range 0.75 to
1. Group III contains the equipment that should be under
surveillance and it should be tested in the next year if the score
within range 0.5 to 0.75. Finally group IV contains the
equipment that could be kept with no need for test if the score
is less than 0.5. Here, the scale ratio of equipment life status is
stretched comparing with [5] to enhance the categorization
process. From Table I, it can be found that, the ventilator
which has no spare parts (USP = 1), in addition to its high UL
Factors CDF
ffunctions
nctions of UL ((--),
) SC ((-^),
^) U ((.-),
) CR (-.),
(
Fig.3. The cumulative distribution fu
RD (-+) and R (-*).
The analysis also suggests arranging R value for different
equipment, hence, the equipment test and surveillance can be
prioritized. Fig. 2 shows the histograms obtained by
MATLAB program for each analyzed factor. These
histograms show that the replacement function and useful life
time factor have both approximate normal distributions while
the other factors have various distributions.
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Regression analysis is performed based on this linear
correlation. The equation of straight line that best fits the
given data is presented by
Y = 1.071 × X + 0.144
(8)
where Y is the replacement score and X is the useful life ratio.
Employing Eq. (8), the replacement score can be calculated for
any device by knowing the device useful life ratio which could
guide the decision makers for replacement decision quickly.
Applying Eq. (8), the medical equipment can be classified as:,
28% of equipment should be replaced, 4% need to be tested,
42% is under surveillance and 26% could be kept.
The proposed model assures the fact that the age and cost
factors have a direct impact on replacement decision as shown
in Fig. 3. The cumulative distribution function for replacement
score, useful life ratio, total cost factor and vendor support
factor is illustrated in Fig.4. According to the proposed model:
32.5% of equipment should be replaced, 25% need to be
tested, 32.5% is under surveillance and 10% could be kept
(See Fig. 5).
III.
Factors CDF
Fig.4. Cumulative distribution functions of R (-*), UL (-^), total cost factor (--)
and vendor support factor (.-) according to equipment data set.
%32.5 Replacement
%25 Test
%32.5 Surveillance
%10 Keep
10%
32.5%
32.5%
25%
CONCLUSION AND FUTURE WORK
We update the FTA model to include the vendor support
effect to enhance the medical equipment disposal decision.
The new model provides the decision makers with the
necessary tools that help in monitoring medical equipment
status and remove/replace it from inventory at the right time.
We employ, for the first time, the unavailability of spare parts
with a suitable weighting factor according to the medical
equipment type. Our model suggests the classification of the
equipment life status into 4 groups according to reliable
quantitative measures based on the Fault Tree Analysis.
Regression analysis shows the linear dependency of the
replacement score and the useful life ratio. Also, the proposed
model highlights the impact of the poor vendor performance
on the replacement decision and the high correlation between
vendor performance and maintenance cost.
The performed analysis in this study, highly recommends
the existence of detailed and updated hospital documentations
that significantly affect the scraping decision.
In future, model could include more vendor support
indicators such as warranty, service contract features, training
qualification and stock availability. Also, the proposed model
could be adapted to different categories such as laboratories
and radiology equipment.
Fig. 5. The investigated NICU medical equipment life status according to the
proposed FTA model.
REFERENCE
The result states that when the equipment reaches its useful
time end, replacement should be considered and when the
service costs increases, it is alarming for disposal.
The linear correlation between replacement score and
useful life ratio is shown in Fig.6.
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Fig. 6. The replacement score and useful life ratio relationship for medical
equipment, based on the proposed FTA model.
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