Simulation 7 Project Report Spring 201 Gokhan Egilmez

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6 input data collection and analysis pg 12 6 1 arrival data pg 12 6 2 service data pg 24 7 arena simulation model pg 30 7 1 final model pg 30 7 2 animation pg 32 7 3 tools used for troubleshooting pg 32 8 model validation amp performance analysis pg 33

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PRESENTATION REPORT,TABLE OF CONTENTS Page,EXECUTIVE SUMMARY pg 3. 1 INTRODUCTION pg 3,2 PROJECT FOCUS AREA GENERAL ASSUMPTIONS pg 4. 3 PROBLEM STATEMENT pg 4,4 OBJECTIVES pg 4,5 SYSTEM ANALYSIS pg 5. 5 1 OFFICE LAYOUT EXTERNAL ENVIRONMENT pg 5,5 2 GRAPHICAL REPRESENTATION OF SYSTEM pg 6. 5 2 1 MAIN PROCESS FLOW CHART pg 6,5 2 2 SUBSYSTEMS pg 7.
5 3 VARIABLES OF THE SYSTEM pg 9,5 4 ELEMENTS OF THE SYSTEM pg 9. 5 5 PARAMETERS OF THE SYSTEM pg 10,5 6 FEEDBACK AND CASUAL RELATIONS pg 10. 5 7 SYSTEM PERFORMANCE METRICS pg 10,5 8 CONSTANTS pg 12. 5 9 CONTRAINTS pg 12,6 INPUT DATA COLLECTION AND ANALYSIS pg 12. 6 1 ARRIVAL DATA pg 12,6 2 SERVICE DATA pg 24,7 ARENA SIMULATION MODEL pg 30.
7 1 FINAL MODEL pg 30,7 2 ANIMATION pg 32,7 3 TOOLS USED FOR TROUBLESHOOTING pg 32. 8 MODEL VALIDATION PERFORMANCE ANALYSIS pg 33,8 1 MODEL PROGRESSON REVISIONS pg 33. 8 2 MODEL VALIDATION USING STATISTICS pg 34,8 3 PERFORMANCE ANALYSIS pg 36. 9 PROPOSED POLICY IMPLICATIONS pg 39,10 TEST OF POLICY IMPLICATIONS pg 39. 10 1 SCENARIO ANALYSIS USING PROCESS ANALYZER pg 39. 11 CONCLUSION pg 41,EXECUTIVE SUMMARY, In this project the Harmony Dental Group is taken as a case study for applying simulation modeling The.
Harmony Dental Group is a dental office and the hygiene practices of the office are the main focus of study. The project can be considered to be composed of two main phases the first data collection and analyzation and. the second model building validation and performance analysis Real time and real world data was collected. from three different days a week Monday Thursday and Saturday at two different times each day morning. and afternoon for three consecutive weeks 203 total data points were collected for patient arrival times and. service times were recorded for at least 43 patients for eight process steps Distributions were fitted to each of. these data sets with the fitness increasing as the data was divided into subcategories The interarrival times for. each of the three hygienists are examples of arrival data that passed the Chi Square test Check in adult. cleaning and child cleanings are examples of service data steps whose data distributions were statistically. significant Descriptive statistics and ANOVA is performed on these data sets as well to gain a better. understanding of the model that results, A simulation model is built in ARENA which mimics the entire hygiene servicing process at the Harmony. Dental Group adult cleanings adult scaling and root planeing children cleanings and children sealants. Numerous types of modules are used in the design of the model create assign decide record read write etc. The model underwent numerous revisions as its results were compared with both the data sets and real life In. the final revision of the model it runs smoothly and yields results consisted with the office s hygiene. performance Overall the office came into this project happy with its hygiene performance but curious about. the capabilities of such data analysis and modeling The model is validated using statistics such as tests of. normality homogeneity tests and Kruskal Wallis tests Next the model s performance is analyze and as. already stated proves to be consistent with expected values. 1 INTRODUCTION, The Harmony Dental Group THDG is located in Norwalk CT and has been in business since 2005 The office. employs five dentists six hygienists three dental assistants and four front desk staff They provide services in. general dentistry periodontics implantology cosmetic dentistry restorative dentistry for adults and pediatric. dentistry for children The office is fully paperless equipped with the newest technologies in 3D imaging and. also has a Cerec CNC to make porcelain dental crowns Due to the different specialists available in the practice. they rarely have to refer out patients for procedures To accommodate patients busy schedules they offer late. hours on certain days and are also open on the weekend for Saturday appointments Scheduling for a given day. of the week largely remains constant though and will be treated as such in this analysis In other words a. hygienist s schedule every Monday is mostly the same and although his or her schedule on Thursdays may. differ from Monday it is constant across Thursdays The office clearly runs on a schedule but it should also be. noted that the office rarely has a walk in patient seeking care and during the days of our data collection we. observed zero walk ins The staff also offers financial plans and assistance with insurance claim submittals. 2 PROJECT FOCUS AREA GENERAL ASSUMPTIONS, Our team seeks to analyze the daily processes at the Harmony Dental Group Although the office has a wide. variety of services performed including the several doctors employed this project focuses on standard dental. hygiene The reason for this is that the number of procedures and the wide variation between lengths of each a. doctor can perform is vast and complicated Customer arrival data and service data has been collected and will. be reviewed The arrival data is analyzed based on the service duration the inter arrival times and the patients. wait times Each of these three categories is analyzed in subgroups of the arrival data including adult versus. children appointments morning versus afternoon evening appointments hygienist 1 versus hygienist 2 versus. hygienist 3 appointments and Tuesday versus Thursday versus Saturday appointments As stated in the. introduction a total of six hygienists are employed by the office but only two or three work at a time each day. As such this analysis will focus on the schedules of three different hygienists on Tuesdays Thursdays and. Fridays An important thing to note at this time is that data collection of this type is not a typical practice at the. Harmony Dental Group As such and this will be explained further in the Objectives Section one goal of this. project is to encourage the investment of resources into data collection and analyzation methods moving. forward In other words this project is being done with the hope that the Harmony Dental Group will find. value in such analysis and want to continue collecting and analyzing larger sets of data Another benefit to. collected more data is that they will be able to take a more granular approach to the analysis For example. categories of the arrival data are examined such as adult versus child and morning versus afternoon but there. were not enough data points collected to break it down one additional level and look at childcare in the. afternoon versus childcare in the morning versus adult care in the afternoon versus adult care in the morning. etc If that level of detail was used in this analysis far less than thirty data points would exist in the majority of. the subgroups and that would likely increase the uncertainty and variation of the model and analysis Therefore. the arrival data is broken down into major categories as previously explained it is just important to note that an. even more detailed and granular approach is possible to be taken. 3 PROBLEM STATEMENT, Overall the office is happy with hygiene performance but curious about the capabilities of simulation modeling. 4 OBJECTIVES, First and foremost one goal of this project is to gain experience in simulation modeling that can be applied in.
real world career scenarios Even though the focus of this project is on a service based company the lessons. learned and concepts used can be applied directly to manufacturing environments as well Another goal of this. project is to utilize and gain experience with software modeling and statistics tools such as Arena Input. Analyzer Excel and Minitab or SPSS Arena will be used largely in the second phase of this project whereas. Input Analyzer and Excel were used largely in this initial report. Another important set of objectives deal directly with the business unit itself in other words the high level. objective of this project is that the Harmony Dental Group will learn change and apply value as a result In. order to accomplish this data was collected and analyzed with the goal of providing recommendations for. improvement in the following areas,Material and personnel allocation. Scheduling and time utilization,Communication, Making such recommendations is the goal of this entire project and not necessarily the initial report That being. said the data collection and analysis contained in this initial report surely tells some tales that will be explored. and explained later, Finally as stated previously another main goal of this project is to encourage the continued use of data. analyzation by the Harmony Dental Group The data collection and analyzation that occurred as a result of this. project is something not normally done by the Harmony Dental Group It is our belief however that much. value resides in this data and therefore it should be utilized by the office Certain computer software systems. exist to map out and time their processes and relevant steps just as was done in this report Although. implementing such practices would require capital investment and changes in culture we believe the benefits. outweigh the costs,5 SYSTEM ANALYSIS,5 1 OFFICE LAYOUT EXTERNAL ENVIRONMENT. The office has a very simple layout that is shown in Figure 1 below The areas and rooms are all. marked on the diagram and many areas also labeled with process steps that occur there to help correlate. the layout with the process flow diagram shown in Figure 2. Customers enter the office through a door towards the left of the suite and approach an L shaped front. desk The half of the desk facing the entrance is typically dedicated for patient check in whereas the. other half of the desk facing the main hallway is typically used for check out Once the customer. checks in he or she can wait if necessary in the waiting area which includes a couch television. refrigerator with water and soft beverages and a coffee maker Once ready the hygienist will call for. the patient bring them back to an operatory take x rays in the x ray room if necessary and perform the. necessary treatment Sterilization and other miscellaneous office tasks are completed in the lab while. office and procedural supplies are kept all across the office with no standard or known locations an. easy area for improvement it seems, In terms of external environment and location the office is located directly off of Exit 16 on Interstate.
95 in Norwalk Connecticut The Harmony Dental Group occupies a suite on the second floor of an. office building that they share with another dental office a dental lab a chiropractor a naturopathic. doctor an insurance broker and an architect s office With such close proximity to I 95 the office is. located on a very busy corner of East Avenue with other small office buildings and residences in the. immediate surrounding area,Figure 1 Layout of Office. 5 2 GRAPHICAL REPRESENTATION OF SYSTEM,5 2 1 MAIN PROCESS FLOW CHART. The next important step in defining and describing our system is to show a graphical. representation of it Figure 2 shows a Process Flow Diagram PFD of the focus area of the. system for this project Once the patient arrives they check in as was explained in the previous. section From there this project observes two main types of patients hygiene and restorative. Hygiene refers to basic cleaning services whereas restorative refers to more complex procedures. performed by doctors and not examined in this project As a result one will note that the. restorative path in the diagram flows directly to the doctor exam process step In reality this. leap is much more complicated and involves many different types of procedures that this project. does not cover For hygiene patients are first categorized by age adult or child and then. treatment type For children treatment types can be either a routine cleaning or sealants For. adults on the other hand the treatment can be a routine cleaning or scaling and route planeing. At that point those receiving a routine cleaning whether they are children or adults may or. may not receive x rays in a separate room based on their medical history After receiving the x. rays or not the cleaning is performed and a doctor exam is performed at the conclusion of the. appointment once a hygienist can find a doctor we found this metric to have a high variation. and therefore be a focus moving forward For children getting sealants or adults getting scaling. and route planeing those procedures are performed without preceding x rays or a following. doctor exam At the very end of the appointment the checkout It should be noted here that. although sealants and scaling and route planeing are shown here they are only included in the. service data In other words the arrival data is missing the categorization of regular cleaning. versus sealants versus scaling and route planeing,Figure 2 Main Process Flow Diagram. 5 2 2 SUBSYTEMS, For as complicated as the main process flow diagram looks at first it s quite simple to. understand once explained This project takes this graphical approach one step further as the. process is broken down into subsystems as well, The check in and check out processes for example can be found in Figure 3 and Figure 4.
below Most people are familiar with check in and check out procedures at doctor and dental. offices As seen below such subsystems include the steps of asking for the patient s name. entering data in the computer such as insurance billing scheduling and dismissal. Figure 3 PFD for Check in Subsystem,Figure 4 PFD for Check out Subsystem. The other subsystems studied and mapped out in this report include rom preparation room. cleanup and instrument sterilization Proper workplace hygiene and cleanliness are the focus of. these procedures for sure,Figure 5 PFD for Room Preparation Subsystem. Figure 6 PFD for Room Cleanup Subsystem, Figure 7 PFD for Instrument Sterilization Subsystem. While these subsystems do exist they are not applicable to the final model For example the room. preparation room cleanup and instrument sterilization process steps are all performed by the same. person in a row the hygienist Therefore the steps are combined in the model and included in the. overall cleaning process module This is how the service data was collected so that the model. would be accurate,5 3 VARIABLES, While no variables were used in the final Arena simulation model examples of some can be. considered to be, Patient arrival time duration wait time inter arrival time.
Data consist of patient arrival time patient waiting time and patient departure time. From these data we found out inter arrival time All above mentioned data are in. Weather plays vital role in our simulation model If there are any disruptions due to. weather then it would lead to delay in arrival or may be cancellation of appointment. Proportions, As adults take longer time for check up compared to children this fact will influence. our simulation model So proportion adults to children on a day will determine total. number of patients attended, It is essential to have sufficient staff at hospital to provide expedited service If delays. are avoided then more patients can be accommodated in a day. Cost also determines the number of patients arrive to the hospital If cost is less then. more patients prefer to come to hospital,Contractors. Hospital require contractors for better staffing and maintenance of hospital This. variable does not affect directly but indirectly helps to improve performance of model. 5 4 ELEMENTS, Although not all of these are included in the model elements of the system include but are not. limited to,Dentists Operatory,Dental Hygienists Sterilization Area.
Dental Assistants Inventory Storage,Financial Coordinator X Ray Machine Room. Scheduling Coordinator Instruments,Office Manager Tooling. Front Desk Staff Ultrasonic cleaning,Waiting Room machine. Computer Hardware Autoclave,Software Disposables, Our model consist of two doctors who takes care all the patients We have three hygienists who. take care of categorized patients Hygienist 1 only takes care of children and other two take care. of adults As seen in the facility layout there are three operatories for cleaning one for each. 5 5 PARAMETERS,The parameters include,o Hygienists.
In our simulation model we have 3 hygienists Of those three hygienists one. hygienist is exclusively assigned for children and other two hygienists for. o Operatory, As we have three hygienists each require one operatory to take care of. patients So we have three operatories,Scheduled appointment length. Hospital schedules 30 minutes appointment to children and one hour appointment. to adults This allocation of time is based on previous data available with hospital. Hours of operation, Hospital has varied working hours on different days But on an average hospital. operate for 9 hours,Inventory storage locations,5 6 FEEDBACK CAUSAL RELATIONS. Several causal relations exist in the process steps previously shown and explained To start patient age. is a big determining factor As was already explained briefly children can and often do receive. different treatments than an adult For example the process flow diagram showed that a child can. receive sealants whereas an adult can receive scaling and route planeing In addition children are. allotted thirty minutes for a standard cleaning or sealants appointment whereas an adult is allotted sixty. minutes for a typical cleaning or scaling and route planeing appointment Such distinctions make the. cause and effect relationship clear with regards to patient age and the succeeding process steps Another. important major example is the initial patient type hygiene or restorative If the patient is a restorative. patient this project ignores the service data aspect If the patient is a hygiene patient this project further. This previous example brings up an important note to make with respect to causal relations that most. steps in the process flow need to occur when they are designated In other words the order of. operations matters For example in the instrument sterilization subsystem the ultrasonic bath must be. done before the autoclave,5 7 SYSTEM PERFORMANCE METRICS.
Metrics are used to measure performance over time and monitor progress towards achieving key goals. For this project metrics that will be considered consist of. Arrival Data, o Appointment duration average maximum minimum etc. o Inter arrival time average maximum minimum etc,o Patient wait time average maximum minimum etc. Service data,o Check in time average maximum minimum etc. o Take X ray average maximum minimum etc, o Scaling route planing average maximum minimum etc. o Cleaning time average maximum minimum etc,o Sealants time average maximum minimum etc.
o Data collection time average maximum minimum etc. o Time needed to find doctor for consult average maximum minimum etc. o Time needed for doctor consult average maximum minimum etc. Other variables that are touched upon or are recommended by the project group for the Harmony Dental. Group to consider include,Average number of patients per day. Proportions of,o Adult versus Children,o Cleanings versus Restorative. o Cleanings versus sealants etc,Percentage number of. o Patients who come back, o Patients who schedule services on top of cleanings. o Patients who receive fluoride with their cleaning. Customer feedback,o Check in time average maximum minimum etc.
o Take X ray average maximum minimum etc, o Scaling route planing average maximum minimum etc. o Cleaning time average maximum minimum etc,o Sealants time average maximum minimum etc. o Data collection time average maximum minimum etc. o Time needed to find doctor for consult average maximum minimum etc. o Time needed for doctor consult average maximum minimum etc. 5 8 CONSTANTS, The constants considered in this project include but are not limited to. o Number of rooms,o Number of floors,Health laws and regulations. Location is an easy to understand example of a constant as changing the location either moving or. modifying the current location would require a significant investment in capital which is not a desire. of the practice at this time,5 9 CONSTRAINTS, The constraints considered in this project include but are not limited to.
Staff availability,Insurance plans, Financial constraints are typically at the forefront of focus for any office or business They have to. manage and handle their budget and vast collection of expenses they incur This project does not dive. deep into the cost and budget control of the Harmony Dental Group but it does recognize the. importance of such matters, Schedule is typically another major constraint for companies They must work their planning around. the availability of their staff and the availability and desires of their patients or clientele in addition to. syncing their schedule with many other factors,6 INPUT DATA COLLECTION AND ANALYSIS. 6 1 ARRIVAL DATA, We collected data for nine days with 10 hours per day on Monday 10 hours per day on Thursday and 6. hours per day Saturday We noted the Inter arrival Time customer appointment time Arrival time patient. being seated time patient type scheduled departure time patient departure time scheduled duration and. actual duration time,Times of Observations,Monday February 5 2017 9am 7pm.
Thursday February 9 2017 8am 6pm,Saturday February 11 2017 8am 2 30pm. Monday February 13 2017 9am 7pm,Thursday February 16 2017 8am 6pm. Saturday February 18 2017 8am 2 30pm,Monday February 20 2017 9am 7pm. Thursday February 23 2017 8am 6pm,Saturday February 25 2017 8am 2 30pm. We collected a total 203 data points and broke down further to different categories. Raw Arrival Data Points,Adults 145,Hygeniest 1 93,Hygeniest 2 62.
Hygeniest 3 49,Morning 97,Afternoon Evening 107,Thursday 68. Saturday 57,Total Data Points 203, Figure 8 Data Point Count Summary for Raw Arrival Data Points. A screenshot of a small portion of the rows of the raw arrival data can be seen below with all of column. headers in Figure 9,Figure 9 Screenshot of Raw Arrival Data. The raw arrival data contained the following twelve columns. Patient Number Time of Day Morning or,Date Afternoon Evening day split at 1 30pm. Day Patient Type Adult or Child,Hygienist 1 2 or 3 Scheduled Departure Time.
Appointment Time Patient Departure Time,Patient Arrival Time Scheduled Duration. Time Patient Seated, From these columns an additional three columns were calculated added to the data set and served as the. primary measures of arrival data,Actual Duration,Inter Arrival Time. The process of analyzing the arrival data remained the same throughout the different categorical. breakdowns that occurred As a reminder the following four categorical studies were done as a result of. having these different classifications, Tuesday versus Thursday versus Sunday Hygienist 1 versus Hygienist 2 versus. o Actual Appointment Duration Hygienist 3, o Inter Arrival Time o Actual Appointment Duration.
o Wait Time o Inter Arrival Time,Morning versus Afternoon Evening o Wait Time. o Actual Appointment Duration Adult versus Child, o Inter Arrival Time o Actual Appointment Duration. o Wait Time o Inter Arrival Time,o Wait Time, To start the data was separated into the respective categories just mentioned Descriptive statistics were. calculated and then an outlier analysis was performed on each data set Descriptive statistics were calculated. again on the new refined data sets and then compared with the originals Finally ANOVA comparison of. means were conducted in Microsoft Excel to compare the relevant times of each subcategory If for example. the ANOVA test comparing the wait time of children versus adults proves the means of the two samples are not. statistically different those data sets were combined to create a new data set before using input analyzer Input. analyzer was then finally used to graph the distribution of the appropriate sets. Let us first take a look at the descriptive statistics before and after outlier analysis for each of the four. categorical studies,Before Outlier Analysis After Outlier Analysis. Inter Arrival min Actual Duration min Wait Time min Inter Arrival min Actual Duration min Wait Time min. Mon Thurs Sat Mon Thurs Sat Mon Thurs Sat Mon Thurs Sat Mon Thurs Sat Mon Thurs Sat. Mean 18 17 21 94 19 35 39 65 48 82 48 11 0 68 0 59 2 47 17 65 21 94 19 35 39 65 49 25 46 86 0 43 0 41 0 41. Median 19 5 22 7 5 40 52 50 0 0 0 19 22 7 5 40 52 49 5 0 0 0. Standard Deviation 13 86 17 53 20 88 12 66 10 41 14 95 1 44 1 37 9 13 13 19 17 53 20 88 12 66 9 86 11 71 0 90 0 88 1 11. Range 57 58 57 53 42 98 7 8 50 50 58 57 53 39 45 4 4 7. Max 57 58 57 62 62 118 7 8 50 50 58 57 62 62 65 4 4 7. Min 0 0 0 9 20 20 0 0 0 0 0 0 9 23 20 0 0 0, 2 5 SD 34 64 43 83 52 20 31 66 26 02 37 38 3 59 3 43 22 82 32 97 43 83 52 20 31 66 24 65 29 28 2 26 2 19 2 77.
Upper Bound 52 81 65 77 71 55 71 30 74 85 85 49 4 28 4 02 25 29 50 63 65 77 71 55 71 30 73 90 76 14 2 68 2 60 3 18. Lower Bound 0 0 0 7 99 22 80 10 73 0 00 0 00 0 00 0 0 0 7 99 24 60 17 57 0 0 0. Count 76 65 54 79 68 57 79 68 57 75 65 54 79 67 56 75 66 54. Outliers 1 0 0 0 1 1 4 2 3 0 0 0 0 0 0 0 0 0, Figure 10 Descriptive Statistics for Arrival Data Monday versus Thursday versus Sunday. Before Outlier Analysis After Outlier Analysis, Inter Arrival min Actual Duration min Wait Time min Inter Arrival min Actual Duration min Wait Time min. Morning Afternoon Morning Afternoon Morning Afternoon Morning Afternoon Morning Afternoon Morning Afternoon. Mean 20 76 18 36 47 03 42 24 0 37 2 27 20 76 18 36 46 12 42 67 0 19 0 79. Median 21 13 5 49 44 0 0 21 13 5 49 44 0 0, Standard Deviation 17 46 16 45 14 30 12 29 0 92 7 83 17 46 16 45 11 87 11 77 0 46 1 64. Range 54 58 102 53 5 50 54 58 49 43 2 8,Max 54 58 118 62 5 50 54 58 65 62 2 8. Min 0 0 16 9 0 0 0 0 16 19 0 0, 2 5 SD 43 64 41 11 35 75 30 72 2 31 19 58 43 64 41 11 29 67 29 42 1 14 4 11.
Upper Bound 64 40 59 47 82 78 72 96 2 67 21 85 64 40 59 47 75 79 72 08 1 33 4 90. Lower Bound 0 0 11 28 11 52 0 00 0 00 0 0 16 44 13 25 0 0. Count 88 107 97 107 97 107 88 107 96 106 91 104,Outliers 0 0 1 1 6 3 0 0 0 0 0 0. Figure 11 Descriptive Statistics for Arrival Data Morning versus Afternoon Evening. Before Outlier Analysis After Outlier Analysis, Inter Arrival min Actual Duration min Wait Time min Inter Arrival min Actual Duration min Wait Time min. Hyg 1 Hyg 2 Hyg 3 Hyg 1 Hyg 2 Hyg 3 Hyg 1 Hyg 2 Hyg 3 Hyg 1 Hyg 2 Hyg 3 Hyg 1 Hyg 2 Hyg 3 Hyg 1 Hyg 2 Hyg 3. Mean 21 46 18 60 14 85 36 22 51 53 51 45 1 97 1 00 0 27 21 46 18 60 13 11 35 17 51 53 51 81 0 49 0 78 0 17. Median 23 10 9 31 51 5 53 0 0 0 23 10 6 31 51 5 53 0 0 0. Standard Deviation 14 95 19 14 15 00 15 23 6 98 6 54 7 81 1 78 0 86 14 88 19 14 12 62 12 12 6 98 6 09 1 17 1 34 0 52. Range 57 58 55 109 28 28 50 8 5 57 58 51 56 28 25 7 5 2. Max 57 58 55 118 65 62 50 8 5 57 58 51 65 65 62 7 5 2. Min 0 0 0 9 37 34 0 0 0 0 0 0 9 37 37 0 0 0, 2 5 SD 37 36 47 84 37 51 38 07 17 45 16 35 19 52 4 46 2 15 37 20 47 84 31 54 30 30 17 45 15 22 2 93 3 35 1 30. Upper Bound 58 82 66 44 52 36 74 28 68 99 67 80 21 49 5 46 2 42 58 66 66 44 44 65 65 46 68 99 67 03 3 42 4 14 1 46. Lower Bound 0 0 0 0 00 34 08 35 10 0 00 0 00 0 00 0 0 0 4 87 34 08 36 60 0 0 0. Count 90 58 47 93 62 49 93 62 49 90 58 45 92 62 48 90 60 48. Outliers 0 0 2 1 0 1 3 2 1 0 0 0 0 0 0 0 0 0, Figure 12 Descriptive Statistics for Arrival Data Hygienist 1 versus Hygienist 2 versus Hygienist 3. Before Outlier Analysis After Outlier Analysis, Inter Arrival min Actual Duration min Wait Time min Inter Arrival min Actual Duration min Wait Time min.
Child Adult Child Adult Child Adult Child Adult Child Adult Child Adult. Mean 22 53 17 68 28 59 51 35 1 63 1 14 22 40 17 68 28 42 50 50 0 48 0 51. Median 23 10 5 28 52 0 0 23 10 5 28 52 0 0, Standard Deviation 14 24 16 77 6 50 10 25 6 40 5 68 14 24 16 77 4 63 6 94 1 21 1 14. Range 57 58 49 84 40 50 57 58 24 28 7 5,Max 57 58 58 118 40 50 57 58 40 62 7 5. Min 0 0 9 34 0 0 0 0 16 34 0 0, 2 5 SD 35 60 41 93 16 26 25 64 16 01 14 20 35 60 41 93 11 58 17 34 3 01 2 84. Upper Bound 58 13 59 60 44 85 76 99 17 63 15 34 58 00 59 60 40 00 67 84 3 50 3 35. Lower Bound 0 0 12 34 25 72 0 00 0 00 0 0 16 84 33 16 0 0. Count 59 136 59 145 59 145 59 136 57 144 57 144,Outliers 0 0 2 1 2 1 0 0 0 0 0 0. Figure 13 Descriptive Statistics for Arrival Data Child versus Adult. Most of the statistics for each subcategory are fairly close to one another with several exceptions that could ve. been expected For example the mean values for adult and children appointment duration are vastly different. as children are known to take less time and are therefore allotted 30 minutes less than adults Relationships like. this are why we then test the means of these subcategories using ANOVA so that we know which subcategories. are truly statistically different Those subcategories that prove to be not statistically different will be combined. back together and ultimately reflect the raw arrival data with outliers removed. For the ANOVA tests the following hypothesis test applies.

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