Eindhoven University of Technology Department of Mathematics and Computer Science Performance Analysis of the Clinical Chemistry Laboratory Waterland Hospital Purmerend Author: Maike Op het Veld Supervisors: Dr. J.A.C Resing TU/e Ir. M.S. van den Broek, Dr.ir. M. van Vuuren CQM Eindhoven I. Estany-Stoelwinder, P. Hofman Waterlandziekenhuis Purmerend August, 2011
Abstract This thesis contains the performance analysis of the clinical chemistry laboratory in the Waterland Hospital in Purmerend. The object is to improve the processes at the laboratory. The system is modeled as a large network of queues. Due to the size of the network, only the part of the laboratory at which all samples arrive and are prepared for testing (SAP) is investigated in detail. The analysis is mainly done by simulation and approximative methods, as the processes are too complex for exact analysis. The simulation reveals that the throughput times are good in the current situation and the occupation rate of the employees is relatively low. The simulation also shows that the occupation rate cannot be increased while keeping the throughput times at an acceptable level in the current situation, because the samples mainly arrive in batches. It is also found that there are many options for decreasing throughput times. Two machines at the SAP serve the customers in batches. To investigate the effect of the machine batch policy on the throughput times, a simplified model of the machines is analyzed by exact and approximative methods. The analysis shows that machines with a low workload should be started already when there are only a few samples present, in order to achieve optimal throughput times. The analysis also shows that the minimal batch size for which the waiting time is minimal increases when the workload of the system increases.
Acknowledgements With this thesis I complete the master Industrial and Applied Mathematics, with the specialization Statistics, Probability and Operations Research, at the University of Technology in Eindhoven. I am greatly indebted to a number of people, from whom I have received support during the nine months of this project, and during the rest of my study. First of all, I would like to thank Jacques Resing, Monique Van den Broek and Marcel van Vuuren. The weekly discussions with Jacques at the TU/e, and with Marcel and Monique at CQM have guided me through this project. I am also grateful for the support and enthusiasm from Ilonka Estany and Peter Hofman from the Waterland hospital in Purmerend. The other employees of the clinical chemistry laboratory, and Ilona den Besten in particular, have always been very helpful and eager to introduce me into the laboratory world as well, for which I am very thankful. Further, I am very grateful for the enthusiasm, interest, and support of everyone at CQM, which has contributed very much to the pleasure I found in performing this project. As this project also ends my study period, I would also like to give a special thanks to my parents and brother, who have always supported me in everything I did and do. Last but not least, I would also like to thank Ruud, and my other friends just for being there. Maike Op het Veld, August 2011 ii
Contents 1 Introduction 1 1.1 Waterland Hospital Purmerend................. 1 1.2 Clinical Chemistry Laboratory................. 1 1.3 Current developments in health care and lean thinking.... 2 1.4 Problem description....................... 3 1.5 Thesis outline........................... 5 2 Clinical Chemistry Laboratory 6 2.1 Laboratory structure....................... 6 2.1.1 Sample arrival and preparation............. 6 2.1.2 Test execution...................... 8 2.1.3 Administration...................... 9 2.2 Result administration...................... 9 2.3 Priorities............................. 10 2.4 Employee behavior........................ 10 2.5 Model............................... 11 3 Data analysis 13 3.1 Data format............................ 13 3.2 Arrival patterns.......................... 14 3.2.1 General description.................... 14 3.2.2 Arrival types....................... 15 3.3 Routing patterns in the laboratory............... 22 3.4 Process times........................... 23 3.5 Throughput times........................ 24 3.6 Data conclusions......................... 25 3.7 Research conclusions....................... 26 iv
CONTENTS v 4 Sample arrival and preparation 29 4.1 Arrival types........................... 29 4.2 Servers............................... 29 4.3 Priorities............................. 30 4.4 Tasks at the sample arrival and preparation area....... 30 4.5 Routing patterns......................... 32 4.6 Conclusion............................ 33 5 Simulation model 35 5.1 Simulation set up......................... 35 5.2 Simulation input......................... 38 5.2.1 (Inter) Arrival times................... 38 5.2.2 Batch sizes........................ 45 5.2.3 Cito tests......................... 50 5.2.4 Process times....................... 50 5.2.5 Disturbances....................... 51 5.2.6 Task priorities...................... 51 5.3 Verification and validation.................... 52 5.4 Simulation output........................ 52 5.4.1 Key performance indicators............... 53 5.4.2 Waiting times....................... 54 5.5 Conclusions............................ 55 6 Simulation scenarios 58 6.1 Basic scenarios.......................... 58 6.2 Basic scenario results....................... 60 6.2.1 Cito shorter........................ 60 6.2.2 No disturbing factors................... 62 6.2.3 Move outpatient clinic.................. 62 6.2.4 Blood withdrawal round................. 63 6.2.5 Move sorting activities.................. 63 6.2.6 BWO 2x.......................... 63 6.2.7 Batch size outpatient clinic train............ 64 6.2.8 One employee....................... 64 6.2.9 No cito type....................... 69 6.2.10 Preanalyzer........................ 70 6.3 Scenario combinations...................... 70 6.4 Sensitivity analysis........................ 71 6.4.1 Sensitivity to arrival parameters............ 71 6.4.2 Sensitivity to task priority setting........... 73
CONTENTS vi 6.5 Conclusions............................ 75 6.5.1 Scenarios......................... 75 6.5.2 Sensitivity......................... 78 7 Analysis 80 7.1 Machine batch policy....................... 80 7.2 M/G a,n /1............................. 81 7.2.1 Model description.................... 82 7.2.2 Results.......................... 89 7.3 M X /D a,n /1........................... 93 7.3.1 Model description.................... 94 7.4 M/D a,n /c............................. 95 7.4.1 Model description.................... 96 7.4.2 Performance measures.................. 100 7.4.3 Results.......................... 108 7.5 Conclusions and suggestions for further research....... 110 7.5.1 Conclusions........................ 110 7.5.2 Suggestions for further research............. 113 8 Conclusions 115 8.1 Conclusions............................ 115 8.1.1 Laboratory........................ 115 8.1.2 Simulation........................ 116 8.1.3 Analysis.......................... 117 8.2 Suggestions for further research................. 117 8.2.1 Laboratory........................ 118 8.2.2 Analysis.......................... 118 A Simulation Input and Output 120 A.1 (Inter) Arrival distributions................... 120 A.2 Batch size distributions..................... 121 A.3 Cito probabilities......................... 121 A.4 Process times........................... 121 A.5 Task priority setting....................... 122 A.6 Validation by sampling...................... 124 B Goodness-of-fit tests 125 B.1 Continuous distributions..................... 125 B.2 Discrete distributions....................... 126
CONTENTS vii C Results from the imbedded Markov chain for M/G a,n /1 127
Chapter 1 Introduction This research is performed for the clinical chemistry laboratory of the Waterland Hospital in Purmerend. This chapter gives some background information about the hospital (Section 1.1) and the clinical chemistry laboratory (Section 2), explains the developments that have led to this research, (Section 1.3), describes the problem and solution approach, (Section 1.4) and gives an outline of this thesis, (Section 1.5). 1.1 Waterland Hospital Purmerend The Waterland Hospital is the result of a fusion between two hospitals in the region Waterland in 1984. The current location in Purmerend is in use since 1988 and the name of the hospital was Streekziekenhuis Waterland until January 1992. Since 2002, the hospital also has a secondary location in Volendam called Waterland-Oost. The Waterland hospital counts 359 beds, which makes it a small to middle-sized hospital. Approximately 25.000 inpatients are treated and 80.000 outpatients visit the hospital each year. Slightly more than 1.200 employees and 160 volunteers work in the hospital. 1.2 Clinical Chemistry Laboratory The clinical chemistry laboratory is the department in the hospital in which all body fluids are tested. These tests show for example if a patient is contaminated with a disease, which blood group a patient has, if medicines are working or if a patient is pregnant. There are nearly 1000 different tests that can be performed. Body fluids are tested each day for nearly every 1
CHAPTER 1. INTRODUCTION 2 inpatient and many outpatients come to the hospital for blood withdrawal or to bring body fluid samples that have to be investigated. This means that over 3.000 tests are performed per day with more than 800 body fluid samples. Most of the tests are done by a machine, and several tests are done by hand. On a week day, eleven or twelve employees work in the laboratory, in the weekend two or three employees are present and during the evening and night one employee runs the tests that are urgent. There are two types of requests; regular requests and urgent requests. The results of the tests that are marked as urgent should be available within an hour after requesting. The results of regular requests are generally available within one day, except for tests that are done by external institutions. The laboratory consists of three departments; a sample arrival and preparation department, a department in which all tests are executed and an administration department. Most analysts can work at any place in the laboratory, and each day the analysts are assigned to work in one of the departments. 1.3 Current developments in health care and lean thinking Currently, many developments concerning health care are taking place in the Netherlands. Hospitals are facing a shortage in staff, privatization, and budget cuts. This has led to more awareness for the efficiency, service and quality of the processes in hospitals. The Waterland Hospital also faces the same problems and introduced lean thinking in 2009 to reach improvements in efficiency, quality and service of the processes in the hospital. Lean manufacturing stems from the car manufacturer Toyota and concerns the efficiency of processes. The theory focuses on improving flow and eliminating waste, every process step that does not add value to the end product for the consumer is considered to be wasteful. The consumer plays a central role in lean theory, because the most important goal is a satisfied customer. There are five essential steps in lean thinking [11]: 1. Identify which features create value. 2. Identify the sequence of activities called the value stream. 3. Make the activities flow. 4. Let the customer pull products or service through the system.
CHAPTER 1. INTRODUCTION 3 5. Pursue perfection. The theory provides several tools to take these steps, such as value stream mapping, 5S and kanban systems. For further information about lean thinking and the tools it provides, the reader is referred to [11]. The goal of introducing lean thinking in the hospital can be formulated as follows: Transform the organization from an output controlled organization to a process minded and possibly process controlled organization. Before lean thinking was introduced in the hospital, the main focus for evaluating the efficiency of a process was the result of the process, such as costs, the number of treated patients and the number of complaints from patients. By introducing lean thinking, the hospital tries to realize a switch to a focus on the processes itself. This switch cannot be made quickly, it is a time-consuming process that involves all employees of the hospital; it is expected to take 5 to 10 years. At the moment, the implementation of lean thinking is still in an initial phase. A lean manager is employed to regulate the activities concerning lean thinking and education projects about lean thinking for employees to become a lean coach in his or her department have started. A lean coach is expected to function as an accelerator for the introduction of lean thinking in his or her department by introducing changes and motivating and guiding the employees. The first two rounds of lean education projects are nearly finished and each lean coach has to create a lean improvement project in his or her department. Next to the lean education projects, much information about the processes in the hospital is gathered. This information is gathered by data analysis and actual measurements. For example, at the emergency department, the operating rooms and the radiology department measurements concerning process times and throughput times have been performed. There are still many departments for which the processes have to be mapped and improvements concerning quality, service and efficiency can be reached. 1.4 Problem description The clinical chemistry laboratory is a large and busy department and as nearly every patient that comes to the hospital also needs body fluid tests, it is valuable for nearly all other departments of the hospital. The developments mentioned in the previous section also apply to the laboratory. Therefore the quality, service and efficiency of the processes are a main topic
CHAPTER 1. INTRODUCTION 4 in the laboratory and the quality officer of the laboratory is educated to become a lean coach. One change initiated by the lean coach is to rearrange the machines, such that employees can easily work together and help each other when necessary and the work flows better through the laboratory. This is only the beginning, and there are many other aspects in the laboratory that can be improved, therefore this research is performed at the laboratory. The next list gives an overview of a few explicit reasons to investigate the processes in the clinical chemistry laboratory: 1. No good overview of the processes in the laboratory exists. There is no thorough knowledge about for example the actual number of body fluid samples that are investigated per day, the work load of the machines, the throughput time of test results or which tests are done most frequently. 2. Complaints about throughput times for test results. The laboratory sometimes receives complaints about throughput times, but no statistical information about throughput times is available. 3. The workload varies over the day. At some moments, the work load is very high, while no work is available at other moments. 4. The laboratory has to shrink by 3 fte. Due to budget cuts, most departments of the hospital have to shrink. 5. New division of workplaces. Machines and workplaces are rearranged, as a result of a previous lean project. 6. Many urgent request that are not really urgent. Each request can be marked as urgent by the doctor that is requesting it. This should only be done if the result should be available within an hour, however many doctors make a request urgent if they only need it on the same day. 7. New machines can be purchased. For example a new machine that takes over some activities in the arrival and preparation area can be purchased. This has led to the following research goal and approach:
CHAPTER 1. INTRODUCTION 5 Research goal: Investigate and improve the processes in the clinical chemistry laboratory. Research approach: 1. Process mapping and data analysis Create an overview of the processes in the laboratory and investigate throughput times of tests, the number of performed tests, the origin of requests, process step times etcetera. 2. Find improvement possibilities in the processes Find a part of the laboratory that appears to have possibilities for improvement. 3. Investigate improvement possibilities Investigate improvement possibilities with mathematical tools. 1.5 Thesis outline In Chapter 2, the structure and characteristics of the laboratory are discussed and the laboratory is modeled as a network of queues. Because the network is too large and complex to analyze entirely, a part of the laboratory is analyzed in detail. To investigate which part of the laboratory is the most interesting to analyze, and to obtain insight in the network concerning arrival streams, routing patterns and processing times, Chapter 3 contains a data analysis of the laboratory. With the information from the data analysis and from consultation with the laboratory staff, it is chosen to analyze the part of the laboratory at which all samples arrive and are prepared for testing. Chapter 4 explains the structure of this part of the laboratory, and models it as a queueing network. Because the network is too complex for exact analysis, Chapter 5 develops a simulation model. In Chapter 6, test scenarios and the results from the scenarios are discussed, and a sensitivity analysis is performed. An exact and approximative analysis concerning the influence of the machine batch policy on the throughput times is performed in Chapter 7. The final chapter contains conclusions and recommendations for further research.
Chapter 2 Clinical Chemistry Laboratory As mentioned in Section 2, more than 3000 tests with over 800 samples are performed on an average weekday, all these tests are done in the laboratory and all samples find their way through the laboratory. This chapter explains the structure and the processes in the laboratory. The laboratory structure is clarified in Section 2.1, the procedure for processing the results is explained in Section 2.2, the different request priorities are discussed in Section 2.3 and the employee behavior is the subject of Section 2.4. 2.1 Laboratory structure The clinical chemistry laboratory consists of three main areas: 1. Sample arrival and preparation 2. Test execution 3. Administration. 2.1.1 Sample arrival and preparation The sample arrival and preparation area (SAP) is the area at which all body fluids arrive in the laboratory and the samples are prepared for the tests. Two employees receive, register, sort and centrifuge the body fluid samples such that the samples are ready to go to the test execution area. The samples arrive from several origins: 6
CHAPTER 2. CLINICAL CHEMISTRY LABORATORY 7 Inpatient care Pneumatic mail There exists a transportation network for body fluid samples from emergency departments such as the intensive care unit (ICU), cardiac care unit (CCU) and the emergency unit (SEH). Each morning at approximately 7:00, the nurses or doctors from the ICU and CCU send body fluid samples from their patients to the laboratory. During the day, any sample from these three departments is sent by pneumatic mail as well. Some other departments also send their samples to the laboratory by pneumatic mail. Inpatient blood withdrawal Each morning, all employees of the laboratory, except for the administrative employee and one or two analysts that have to stay in the laboratory to handle the urgent test requests, go into the hospital to withdraw blood from the patients in all departments except the ICU, CCU and SEH. During the rest of the day, analysts can also be requested to withdraw blood. Brought samples During the day, nurses or doctors from the hospital units physically bring body fluid samples to the laboratory. Outpatient clinic Waterlandziekenhuis The outpatient clinic is located in the hospital and opened from 8:00 until 17:00 on week days, only on Tuesdays, the clinic is open until 20:00. Patients come to this clinic to withdraw blood or hand in body fluid samples. It is located in the hospital, but at a different floor than the laboratory. The clinic sends the body fluid samples to the laboratory with a small train that arrives at the sample arrival and preparation area. Outpatient clinic Waterland Oost This clinic is located in Volendam and is only opened from 8:00 until 12:30 on each week day. The body fluid samples are collected after 12:30 and brought to the laboratory by a carrier. External arrivals The laboratory from the Waterland hospital cooperates with other laboratories by exchanging tests, so each day samples from other laboratories arrive in Purmerend. Each Tuesday, an analyst goes to a
CHAPTER 2. CLINICAL CHEMISTRY LABORATORY 8 psychiatric clinic and takes the body fluid samples of these patients to the laboratory. Figure 2.1 gives an overview of the arrivals of body fluid samples in the sample arrival and preparation area. Inpatient: Pneumatic mail Inpatient: Blood withdrawal Inpatient: Brought samples Outpatient clinic WLZ Sample arrival and preparation area Outpatient clinic W-O External Figure 2.1: Arrivals at Sample Arrival and Preparation Area 2.1.2 Test execution After processing the samples at the arrival and preparation area, the samples are ready for the test execution phase. The tests can be split into seven types: 1. Blood gas 2. Coagulation 3. Haematology 4. Transfusion 5. Chemistry 6. Urine 7. External
CHAPTER 2. CLINICAL CHEMISTRY LABORATORY 9 The blood gas machine is located at the sample arrival and preparation area, because these tests can only be conducted shortly after blood withdrawal. The other test types all have a separate area in the laboratory at which one or more machines are located, except the external tests, as these are done in other laboratories. The analysts have to operate the machines, check the results and do manual tests. When a machine is finished with a test, an analyst should confirm the result. If the result is too abnormal, the clinical chemist or the team leader has to confirm the result. The samples are stored in the laboratory for a few days, after which they are eliminated. For an overview of the test execution area, see Figure 2.2. Samples Results Blood gas Coagulation Sample arrival and preparation area Haematology Transfusion Chemistry Confirmation Urine External Sample arrival and preparation Test execution Figure 2.2: Test Execution Area 2.1.3 Administration The administration activities consist of handling the external tests. This consists of preparing, registering and sending the requests and receiving and processing the results. Also other small administrative activities are handled by the administration. 2.2 Result administration Each inpatient and outpatient is registered in a digital information system called Labosys. All qualified employees of the hospital can enter the digital
CHAPTER 2. CLINICAL CHEMISTRY LABORATORY 10 information system and request information about patients. Body fluid test requests and results are also registered in this system. The machines at the clinical chemistry laboratory are linked with the information system. The machine can recognize the patient that belongs to the body fluid sample by the code on the sample and puts the result in the information system immediately. The laboratory staff only has to confirm the results, after which the doctor that requested the test for the patient can see the confirmed result in Labosys. 2.3 Priorities Three different priority types for the test requests exist: 1. Blood gas determination request This is the most urgent request type, because this test should be performed immediately after blood withdrawal, so it is given priority over all other tests. 2. Cito request The result of a cito request should be available within one hour, so it is given priority over all other requests, except for blood gas determination tests. 3. Regular request This type contains all other requests. The standard for these requests is that the result is available within one day. Among the regular type requests, one can still observe some priority handling, as inpatients are generally prioritized over outpatient requests. 2.4 Employee behavior Each day, the employees of the laboratory are assigned to a work spot. This work spot generally differs each day, so nearly all employees can work at any place in the laboratory. At 7:00, one or two employees from the morning shift start their work day and handle all cito requests, set up the machines and prepare the blood withdrawal round. The rest of the employees start their working day with the inpatient round at 7:45, and after this round, everyone starts working at the work spot he or she is assigned to for that day. This means that the morning shift employees also start working at their spot. At 16:00 the morning shift employees end their working day,
CHAPTER 2. CLINICAL CHEMISTRY LABORATORY 11 while the employee from the evening and night shift starts at either 14:00 or 17:00. At 17:15, the normal shift employees end their day and the evening shift employee is the only one left in the laboratory. This employee prepares the inpatient round for the next day and handles all cito requests during the evening and night. He or she is allowed to leave when the employees for the next day arrive at 7:00. In the weekend, there are much less requests than on a week day, so two or three employees handle all requests. Each day, every employee has two short breaks of 15 minutes and a long break of 30 minutes. The night shift has a dinner break, and he or she can go to sleep in between cito requests during the night. 2.5 Model Based on the information in the previous sections, the processes in the laboratory can be modeled as a network of queues. The sample arrival and preparation area and the test execution area together form a network of queues in which the body fluid samples are the customers. The administration area exists separately from this network, because only paper work is done here. The network formed by the sample arrival and preparation area and the test execution area is displayed in a global way in Figure 2.3. Each block in the figure consists again of more detailed process steps. Samples Samples are stored Results Inpatient: Pneumatic mail Blood gas Inpatient: Blood withdrawal Coagulation Haematology Inpatient: Brought samples Sample arrival and preparation area Transfusion Confirmation Outpatient clinic WLZ Chemistry Outpatient clinic W-O Urine External External Sample arrival and preparation area Test execution area Figure 2.3: Sample arrival and test execution network The network contains some complicating factors that differentiate it from a general queueing network: Many different arrival types, mainly in batches
CHAPTER 2. CLINICAL CHEMISTRY LABORATORY 12 Three different customer priorities Servers have multiple tasks At many places in the laboratory, an employee has to perform more than one task. This means that the tasks do not have a server available all the time, and the server has to choose which task to perform. The network is also quite large, Figure 2.3 already shows six different arrival types and eight different process blocks. Some of the arrival types are again split in different streams and each of the blocks contains different jobs and routings again, so it is hard to model the complete network in detail. Therefore, this research focuses on a part of the laboratory. To investigate which part of the laboratory is the most interesting to investigate, and to obtain input for the network concerning arrival streams, routing patterns and processing times, the next chapter contains a data analysis of the laboratory.
Chapter 3 Data analysis This chapter discusses data concerning the laboratory, to find which part of the laboratory is most interesting to investigate, and to obtain input for the queueing network model. First, in Section 3.1, the data format is discussed, after which the arrival patterns are investigated in 3.2, the routing patterns in 3.3, the process times in 3.4 and finally the throughput times in 3.5. The conclusions concerning the data are discussed in 3.6 and the consequences for the research are explained in Section 3.7. 3.1 Data format The laboratory has a digital information system, called Labosys, in which all requested tests are registered and the results are saved. Many details are registered for each test, such as the test type, the urgency type of the test, the time the request form is read into the system, the time the result is available, the time the result is confirmed and the origin of the request. Unfortunately, much information is not registered, for example the throughput time per part of the laboratory, the actual time of arrival in the laboratory, or the process times. In this chapter, a data set containing laboratory data from March 2010 until February 2011 is used. Weekdays are structured differently than the days in the weekends, so they should be investigated separately. It would become too extensive to investigate both day structures separately, and the laboratory has the most interest in improving weekdays, so it is chosen to focus on weekdays in this research. There are three dimensions in the data: 1. Lab numbers: Each time tests are requested for a patient, a lab number is assigned 13
CHAPTER 3. DATA ANALYSIS 14 to the patient. 2. Body fluid samples: Per patient, and thus lab number, generally more than one body fluid sample has to be investigated. The number of samples depends on the tests that are requested. Some tests need a preparation substance, and each machine receives a separate sample, such that tests can be done simultaneously. 3. Tests: More than one test is performed per body fluid sample in general, every test that can be done on one machine is performed with the same sample. There are nearly 1000 different tests that can be requested. 3.2 Arrival patterns In this section, a general description of the arrivals of body fluid samples in the laboratory is given first (Section 3.2.1), after which each arrival stream is discussed in detail (Section 3.2.2) 3.2.1 General description The arrival time of body fluid samples in the laboratory is not available, but the registration time in Labosys does give an impression of the arrival times for many samples. Figure 3.1 gives an impression of the mean number of registrations of body fluid samples per half hour on a weekday for all arrival types in the investigated year, except for the samples from the outpatient clinic in Volendam (BWO), and the samples from the blood withdrawal round. The registration times for these two types differ very much from the arrival times. BWO samples are registered at withdrawal in Volendam in the morning, while they only arrive in the afternoon in Purmerend. The samples from the blood withdrawal round are registered the day and night before the round, while they are only withdrawn and arrive in the laboratory in the morning. Therefore, these sample types are filtered and gathered in one time slot, 13:30-14:00 for BWO and 8:00-8:30 for the blood withdrawal round. Figure 3.1 shows that the peak moments are caused by BWO and the blood withdrawal round, and that the morning is the busiest part of the day. Figure 3.2(a) shows that the outpatient clinic in Purmerend and the inpatient care provide the most samples, but the outpatient clinic in Volendam and the external arrivals also provide a significant amount of
CHAPTER 3. DATA ANALYSIS 15 Body fluid samples 0 50 100 150 Body fluid samples over time on a weekday 0:00 06:00 12:00 18:00 24:00 Time Figure 3.1: Mean number of body fluid sample arrivals per half hour on a weekday samples. It is also interesting to see whether each week day is equally busy, or if a trend exists in the week. Figure 3.3 shows that the mean number of body fluid samples per day differs between approximately 800 on Friday to 950 on Tuesday. The mean number of body fluid samples appears to decrease over the week. The urgent samples arrive through the same arrival streams as the regular samples. On a weekday, on average 116 of the 876 samples that arrive in the laboratory are cito samples, and 17 samples need blood gas determination. The blood gas samples mainly originate from inpatient care, because this is a very urgent test and it is mainly done for the observation of patients. The outpatient clinic in Purmerend occasionally receives a blood gas sample as well, but the samples from the outpatient clinic in Volendam and from external arrivals never concern a blood gas request. Figure 3.2(b) shows the mean number of cito body fluid samples per origin on a week day. It shows that the most cito samples are provided by inpatient care, because most patients that need urgent tests are hospitalized. The outpatient clinic in Purmerend also provides a significant amount of cito samples, but these samples mainly concern requests from doctors that need the result on the same day, instead of within one hour. 3.2.2 Arrival types Figure 2.1 distinguishes six arrival types, but within some of these arrival types, different streams can be distinguished, these are also described in
CHAPTER 3. DATA ANALYSIS 16 Mean number of body fluid samples per origin on a weekday Body fluid samples 0 100 200 300 400 Outpatient clinic WLZ Inpatient care External Outpatient clinic BWO (a) All samples Mean number of cito samples per origin on a weekday Cito body fluid samples 0 20 40 60 80 Outpatient clinic WLZ Inpatient care External Outpatient clinic BWO (b) Cito samples Figure 3.2: Mean number of body fluid samples per origin on a weekday Section 2.1.1. 1. Inpatient care The body fluid samples can again be split in three categories: (a) Pneumatic mail i. Samples from IC and CCU at 7:00. ii. Samples from IC, CCU and SEH during the day. iii. Samples from other departments during the day. (b) Blood withdrawal i. Round at 7:45 at all departments except IC, CCU and SEH. ii. Samples during the day.
CHAPTER 3. DATA ANALYSIS 17 Body fluid samples 0 200 400 600 800 1,000 Mean number of body fluid samples per day Monday Tuesday Wednesday Thursday Friday Figure 3.3: Average amount of body fluid samples on a week day per day (c) Brought samples from all departments in the hospital except CCU, IC and SEH. 2. Outpatient clinic Waterlandziekenhuis 3. Outpatient clinic Waterland Oost 4. External arrivals The previous section shows that the largest amount of cito samples stems from inpatient care. Within inpatient care, the cito samples are divided over the different arrival types. All lab numbers from IC, CCU and SEH contain cito samples, because these are the emergency departments. The blood withdrawal round generally only contains a small number of cito requests, 1 or 2 samples. 1(a)iii, 1(b)ii, and 1c concern cito samples more often, approximately 14% of the time. The number of cito samples per day for the other arrival types is already displayed in Figure 3.2(b). Each of the arrival types has its own characteristics. A characteristic that all arrival types share is that the body fluid samples arrive in the laboratory in batches per lab number. The number of body fluid samples in a lab number is determined by the tests that are requested for the lab number. In general, each machine type in the laboratory requires a separate sample, because the machines require different pre-processing steps (for example centrifugation, or a certain temperature), and this makes simultaneous testing possible. Therefore, the number of body fluid samples per lab number is generally equal to the number of machine types required
CHAPTER 3. DATA ANALYSIS 18 to perform the tests for the lab number. Table 3.1 gives some descriptive statistics concerning the number of body fluid samples per lab number. Mean St.dev. Min Max Body fluid samples per lab number 2.41 1.32 1 11 Table 3.1: Body fluid samples per lab number Body fluid samples per lab number Fraction 0.1.2.3 1 2 3 4 5 6 7 8 9 10 11 Number of body fluid samples Figure 3.4: Body fluid samples per lab number The arrival types can be split in two groups, arrivals that occur once a day around an expected time, and arrivals that occur more often during the day with stochastic interarrival times. The following subsections describe more characteristics of the arrival types per group. Once a day arrivals The samples from the outpatient clinic BWO, the blood withdrawal round in the morning, and the ICU and CCU at 7:00 belong to this type of arrivals. The samples from these origins arrive in batches of lab numbers; Table 3.3 gives some statistics concerning the number of lab numbers per arrival per type, and Figure 3.5 displays the distribution of the batch sizes. The employees of the laboratory know when to expect a batch of samples from these origins. The actual arrival times are not registered, but it is wellknown that the samples from the ICU and CCU arrive a few minutes after 7:00, and the samples from BWO arrive around 13:30. The samples from the blood withdrawal round generally arrive in the laboratory between 8:00 and 9:30, but no specific arrival time is known. The arrival time of the samples from the blood withdrawal round depends on the number of patients (i.e.
CHAPTER 3. DATA ANALYSIS 19 lab numbers) from which blood has to be withdrawn, the department type (blood withdrawal for children takes longer), and the number of employees that walk the round. Information concerning these parameters should be collected to find an estimate for the arrival time of the samples from the blood withdrawal round. Mean St.dev. Min Max BWO 45.46 11.65 10 79 Blood withdrawal round 44.25 14.75 10 74 ICU & CCU 7:00 6.87 2.75 1 14 Table 3.2: Lab numbers per arrival - Once a day arrivals Fraction 0.01.02.03.04.05 Arrival batch size BWO 0 20 40 60 80 Number of lab numbers Fraction 0.02.04.06 Arrival batch size from blood withdrawal round 0 20 40 60 80 Number of lab numbers Fraction 0.05.1.15.2 Arrival batch size from ICU&CCU at 7:00 0 5 10 15 Number of lab numbers (a) BWO (b) Withdrawal round (c) ICU & CCU 07:00 Figure 3.5: Histogram of lab numbers per arrival - Once a day arrivals Continuous arrivals The arrival types 1(a)ii, 1(a)iii, 1(b)ii, 1c, 2, and 4 belong to this group. It is not possible to distinguish between 1(a)iii, 1(b)ii, and 1c in the data, so these are considered to be one group for now. The lab numbers from these groups do not always arrive individually, Table 3.3 gives some descriptive statistics for the batch sizes, except for the outpatient clinic in Purmerend. The outpatient clinic has some specific characteristics, so it is treated separately later in this section. Figure 3.6 depicts the distribution of the arrival batch sizes. The mean number of lab number registrations per half hour per weekday from ICU/CCU/SEH is displayed in Figure 3.7(a). The figure shows that the number of arrivals is low during the night, relatively high during the day, and it goes down in the evening. The arrivals from external origins are displayed in 3.7(b). The information concerning external arrivals is limited,
CHAPTER 3. DATA ANALYSIS 20 Mean St.dev. Min Max ICU/CCU/SEH (1(a)ii) 1.28 0.62 1 6 External (4) 5.14 6.39 1 24 Rest (1(a)iii, 1(b)ii, 1c) 1.37 2.13 1 13 Table 3.3: Lab numbers per arrival - Continuous arrivals Arrival batch size from ICU&CCU&SEH Arrival batch size from external Arrival batch size from rest Fraction 0.2.4.6.8 0 2 4 6 8 10 Number of lab numbers Fraction 0.1.2.3 0 10 20 30 40 50 Number of lab numbers Fraction 0.2.4.6.8 0 5 10 15 Number of lab numbers (a) ICU/CCU/SEH (b) External (c) Rest Figure 3.6: Histogram of lab numbers per arrival - Continuous arrivals because one cannot distinguish between the different external origins. The different origins all have specific characteristics, but this is ignored here and the external arrivals are considered to be one group. The figure shows that there might be a group of lab numbers that arrives typically around noon, as there exists a higher peak in Figure 3.7(b). The rest of the lab numbers from inpatient care, 1(a)iii, 1(b)ii, 1c, are displayed in Figure 3.7(c). Note that the number of lab numbers equals 0 between 6 and 9. This is due to the data filtering for the blood withdrawal round, it is assumed that all lab numbers from the non-urgent departments that are activated between 6 and 9 are taken in the blood withdrawal round. The figure shows a clear decrease of lab number registrations from this type over the day. The peak is in the morning, which may be caused by lab numbers that were forgotten in the blood withdrawal round. The later it gets on a day, the likelier it is to wait for the blood withdrawal round on the next day if the tests are not cito, so the number of lab numbers decreases over the day. Outpatient clinic WLZ The arrival time at the laboratory differs a lot from the registration times of the lab numbers at the outpatient clinic WLZ, so the arrival process at the laboratory cannot be obtained from this information. Because it is too time-
CHAPTER 3. DATA ANALYSIS 21 Lab numbers from ICU, CCU, and SEH over time on a weekday Lab numbers 0.5 1 1.5 0:00 06:00 12:00 18:00 24:00 Time (a) ICU/CCU/SEH External lab numbers over time on a weekday Lab numbers 0 2 4 6 0:00 06:00 12:00 18:00 24:00 Time (b) External Rest of lab numbers over time on a weekday Lab numbers 0.5 1 1.5 2 2.5 0:00 06:00 12:00 18:00 24:00 Time (c) Rest Figure 3.7: Lab number arrivals per type consuming to obtain accurate data for the arrival times at the laboratory,
CHAPTER 3. DATA ANALYSIS 22 and the process of withdrawal at the outpatient clinic and the transport to the laboratory is quite clear, the processes at the outpatient clinic are modeled separately in Section 5.2.1. The output of this process is equal to the arrival process at the laboratory. The arrivals at the outpatient clinic are input for the model of the outpatient clinic. Figure 3.8 displays the average number of registrations at the outpatient clinic during a weekday. It is clear from this figure that the outpatient clinic is the busiest in the morning. During lunch time, the arrival intensity goes down, then after lunch, the intensity increases slightly again, after which it decreases again towards the end of the day. Lab numbers per half hour from outpatient clinic WLZ Lab numbers 0 5 10 15 0:00 06:00 12:00 18:00 24:00 Time Figure 3.8: Arrivals Outpatient Clinic WLZ 3.3 Routing patterns in the laboratory All samples for the laboratory arrive at the sample arrival and preparation area. After the pre-process steps at this area, the samples proceed to the test execution step. Figure 2.2 shows that there are seven different test types. Each sample is destined for one of the test execution areas, depending on the tests that have to be done with the sample. Figure 3.9(a) displays the mean number of body fluid samples per test type on a weekday. It is clear that the haematology (302 samples) and chemistry department (344 samples) process most of the samples, and the other departments process between 20 and 50 samples per weekday. Unfortunately, the data also contains on average 80 samples per day from which the test type is unknown, it is not registered. Part of the samples in Figure 3.9(a) concern cito samples, not all machines can process cito samples, only chemistry, coagulation and tests can be cito. Figure 3.9(b) shows the distribution of cito samples over the different
CHAPTER 3. DATA ANALYSIS 23 test types. It shows that the haematology and chemistry department also test the most cito samples. Number of body fluid samples per test type on a weekday Body fluid samples 0 100 200 300 400 Coagulation Transfusion Haematology Chemistry Urine Blood gas External (a) Regular samples Cito samples per test type on a weekday Cito body fluid samples 0 10 20 30 40 50 Coagulation Haematology Chemistry (b) Cito samples Figure 3.9: Average number of body fluid samples per test type/machine on a weekday 3.4 Process times The process times are not registered. For some machines, the process times are known, these are mainly deterministic. The process times for the human process steps are not known, only estimates by experience can be given.
CHAPTER 3. DATA ANALYSIS 24 3.5 Throughput times The exact throughput times for the laboratory are not available, but an estimate can be obtained by subtracting the registration time from the result confirmation time. As explained earlier, the registration time does not coincide with the arrival time in the laboratory, but it does give an estimate for most samples. For the blood withdrawal round and BWO, the registration times are adjusted because they differ too much from the arrival times. Even though each machine has different process times, the throughput times are only considered per test type (see Section 2.1.2). This is done because there are too many different machines. Not only the observed throughput times are interesting, but also the sum of the individual process step times, i.e. the theoretical throughput times. It is then interesting to see whether the theoretical throughput times differ much from the observed throughput times, and for which test types the largest deviations occur. Each block in Figure 2.3 consists again of several process steps and/or machines; the process times of these steps and machines are not registered. Therefore, an overview of all process steps in the blocks is created and estimates for process times are made in consultation with the laboratory staff. Theoretical throughput times are then created by taking the sum of the estimated process times. Figure 3.10(a) shows the observed throughput times and the theoretical throughput times for regular samples and blood gas samples. The figure shows that the largest deviation between the observed and theoretical throughput times occurs for the transfusion tests. After investigating the throughput times for transfusion in detail, and consulting the laboratory staff, it can be concluded that this is mainly caused by the fact that many transfusion tests are done on the day after arrival at the laboratory. If the samples arrive in the afternoon, it is often decided to store the samples and do the tests on the next day. The chemistry tests also have a large deviation between theoretical and observed throughput times, the reason for this the same as for the transfusion tests, some tests are only done on the next day. Cito tests are only done on a few machines, so for cito tests, the throughput times are considered per machine. Also for cito tests, the observed throughput times are compared with theoretical throughput times. Figure 3.10(b) shows the results. The D-dimere and APTT machine perform tests of the coagulation test type, the Sapphire performs tests from the Haematology type and the Cobas6000 and the Axsym perform Chemistry tests. The Sapphire and Cobas6000 do approximately 90% of all cito tests, and these machines have small deviations between theoretical and observed through-
CHAPTER 3. DATA ANALYSIS 25 put times. Therefore, it can be concluded that the cito throughput times appear to be quite good. The throughput times only differ much from the theoretical times for samples that are tested on the Axsym, this is partially caused by the fact that this machine has no urgency entrance. When a cito sample arrives, the sample has to wait until all samples in the machine are finished. The process times for this machine are quite long, approximately 30 minutes, so the waiting times can become quite large. The other machines all have a separate entrance for cito tests. 3.6 Data conclusions It can be concluded that there are many different arrival types, of which a part arrives at fixed moments in large batches of lab numbers, and another part arrives in smaller batches or singly continuously over the day. All samples arrive in a batch of body fluid samples per lab number, on average 2.4 body fluid samples belong to one lab number. Figure 3.11 gives an overview of the mean number of lab number arrivals on a weekday per arrival type. The most samples arrive during the day, between 7:00 and 17:15. The haematology and chemistry department test 74% of all samples, the other samples are divided over the other 5 departments. Figure 3.11 also shows the mean number of samples per laboratory department on a weekday. Cito samples mainly stem from inpatient care and the outpatient clinic in the WLZ, and on average 13% of all samples is cito. The cito samples arrive through the same channels as the normal samples, but the pneumatic mail is the most common way for cito samples to arrive in the laboratory. The haematology and chemistry department also test the most cito samples, 90% of the cito samples goes to these departments, the rest is processed at the coagulation department. Only estimates of observed and theoretical throughput times can be evaluated. The throughput times appear quite good, especially for cito samples. The regular samples have long throughput times at the transfusion and chemistry department, but this is mainly caused by the policy of testing samples a day later than the arrival in the laboratory. These departments have not experienced any complaints about this.
CHAPTER 3. DATA ANALYSIS 26 3.7 Research conclusions The data results have been discussed with the laboratory staff. Many results have given more insight, and the throughput times have not been evaluated as dramatically bad. It does not appear that one of the test type areas causes the most problems, and it is perceived that the machines in the test execution area have more than enough capacity to handle the samples. The idea lives that the sample arrival and preparation area is an area at which much improvement may be possible, due to the following reasons: The sample arrival and preparation area consists of very many different activities, which all have to be performed by two employees. These employees are disturbed by phone calls and people entering the laboratory, because the sample arrival and preparation area is located at the entrance of the laboratory. The large number of different activities also causes that the employees experience this work place as a busy place, whilst the clinical chemist thinks the activities can be performed by one employee instead of two employees. The work load fluctuations are also experienced most at the sample arrival and preparation, which is mainly caused by the batch arrivals. There are many moments at which no work is available, but also many moments at which many samples arrive at once. Currently, there are some plans for changing the laboratory that also affect the sample arrival and preparation area. The outpatient clinic may be moved next to the laboratory and the sample and arrival preparation area may get closer to the test execution area. The effect of these plans are not investigated yet, so there is much interest for this. The throughput times of all samples benefit from improvements at the sample arrival and preparation area, because all samples arrive at the sample arrival and preparation area. A machine that takes over some of the activities at the sample arrival and preparation area is available, and the laboratory staff is interested in buying this. Therefore it is interesting for them to see what the effect of this machine would be. For all these reasons, it is concluded that the research continues with investigating the sample arrival and preparation area. The next chapters first describe the sample arrival and preparation area in detail, and then investigate improvement possibilities.