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 115 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. 116 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. [1] J. Dyro “Clinical Engineering Handbook”, issue 2003. [2] Victoria, Auditor General, “Managing Medical Equipment in Public Hospitals,” government printer for the state of Victoria, Australia, 2003. [ 3 ] D. Rajasekaran, “Development of an Automated Medical Equipment Replacement Planning System in Hospitals,” Bioengineering Conference, Proceeding of the IEEE 31st Annual Northeast, April, 2005, pp. 52–53. [4] A. Miguel Cruz, E. Rodriguez Denis, M.C. Sanchez Villar and L.M. Lic Gonzalez, “An Event Tree-Based Mathematical Formula for the Removal of Biomedical Equipment from a Hospital Inventory,” Journal of Clinical Engineering, winter 2002, pp. 63–71. [5] B. K. Ouda, A.S.A. Mohamed and N. K. Saleh “A Simple Quantitative Model for Replacement of Medical Equipment Proposed for Developing Countries,” the IEEE 5th Cairo International Biomedical Engineering Conference, Cairo, Egypt, Dec 2010, pp.188-191. [6] W.E. Vesely and F.F. Goldberg, “Fault Tree Handbook,” U.S. Nuclear Regulatory Commission, NUREG-0492, U.S.A., 1981. [7] Life Expectancy Projection Benchmarks: A How-to Guide for Medical Equipment Replacement Programs, American Society for Healthcare Engineering of the American Hospital Association, 1996. [8] Michael Stamatelatos, “Fault Tree Handbook with Aerospace Applications,” NASA office of safety and mission assurance, version 1.1, 2002. Fig. 6. The replacement score and useful life ratio relationship for medical equipment, based on the proposed FTA model. 117