analysis of the pneumatic tube system in the university of...

1

Team 4

Analysis of the Pneumatic Tube System in the University of Michigan Hospital

Programs and Operations Analysis

Final Report December 12, 2008

To:

Joseph Stchur, Facility Operations Director Sam Clark, Senior Management Engineer

Prepared by:

Matthew Bostwick, Industrial and Operations Engineering, University of Michigan Tom Guttenberger, Industrial and Operations Engineering, University of Michigan

Christine McAllister, Industrial and Operations Engineering, University of Michigan

2

Contents Table of Figures ..................................................................................................................................................... 3Executive Summary .............................................................................................................................................. 4Introduction ............................................................................................................................................................ 5Background ............................................................................................................................................................. 5

Key Issues ............................................................................................................................................................ 5Methodology ........................................................................................................................................................... 6

Interviews ............................................................................................................................................................ 6Transaction and Error Data Collection .................................................................................................... 6

Qualitative Findings ............................................................................................................................................. 6Interviews with Key Users ............................................................................................................................ 6Interviews with Technicians ........................................................................................................................ 6Interview with Training Specialist Senior .............................................................................................. 7

Quantitative Findings .......................................................................................................................................... 7Overall Traffic Trends ..................................................................................................................................... 8Wait and Travel Times ................................................................................................................................. 10

Identifying Problem Stations ................................................................................................................ 15Zone Traffic Trends ....................................................................................................................................... 15

Zone A ............................................................................................................................................................ 16Zone C ............................................................................................................................................................ 20

Causes of High Wait Times ......................................................................................................................... 24Conclusions .......................................................................................................................................................... 30

Errors and Transaction Times .................................................................................................................. 30Carrier Availability ........................................................................................................................................ 30Wait Times in Central Distribution ......................................................................................................... 30

Recommendations ............................................................................................................................................. 30Error Reduction .............................................................................................................................................. 30Carrier Availability ........................................................................................................................................ 31Reduction of Wait Times in Central Distribution .............................................................................. 31

Appendix A – Additional Analysis .............................................................................................................. A-1Zone E Volume Analysis ............................................................................................................................ A-2Zone N Volume Analysis ........................................................................................................................... A-4Other Zones Volume Analysis ................................................................................................................. A-6

Appendix B – Training Document .............................................................................................................. B-1Appendix C – Carriers Needed ..................................................................................................................... C-1

3

Table of Figures Figure 1: Weekly Volume over Time ............................................................................................................. 8Figure 2: Total Volume by Day of Week ....................................................................................................... 9Figure 3: Average Daily Traffic by Hour .................................................................................................... 10Figure 4: Total Daily Volume versus Average Daily Wait Times ..................................................... 11Figure 5: Daily Number of Errors versus Average Wait Times ........................................................ 11Figure 6: Number of Blowers versus Average Travel Time .............................................................. 12Figure 7: Number of Blowers versus Average Travel Time - 0 Errors .......................................... 13Figure 8: Number of Blowers versus Average Travel Time - 1 to 3 Errors ................................. 13Figure 9: Number of Blowers versus Average Travel Time - 4 or more Errors ........................ 14Figure 10: Average Daily Traffic by Zone ................................................................................................. 16Figure 11: Average Zone A Volume Sent by Hour ................................................................................. 17Figure 12: Average Volume Sent by Hour, by Station - Zone A ........................................................ 18Figure 13: Average Volume Received by Hour, by Station - Zone A ............................................... 19Figure 14: Average Wait Time by Hour – Carriers Sent from A02 .................................................. 19Figure 15: A02 Average Wait Time by Hour - Carriers Sent to A02 ............................................... 20Figure 16: Average Zone C Volume Sent by Hour .................................................................................. 21Figure 17: Average Volume Sent by Hour, by Station - Zone C ........................................................ 22Figure 18: Average Volume Received by Hour, by Station - Zone C ............................................... 22Figure 19: Average Wait Time by Hour – Sent from C08 ................................................................... 23Figure 20: Average Wait Time by Hour – Received by C08 ............................................................... 23Figure 21: Average Wait Time by Hour - C09 as Source ..................................................................... 24Figure 22: A02 Average Wait Times and Average Volume Received by Hour ........................... 25Figure 23: C08 Average Wait Times and C08 Average Volume Received by Hour .................. 25Figure 24: C09 Average Wait Times and Zone C Average Volume Received by Hour ............ 26Figure 25: A02 Average Wait Times vs Average Volume Received ................................................ 27Figure 26: C08 Average Wait Times vs Average Volume Received ................................................ 27Figure 27: C09 Average Wait Times vs Zone C Average Volume Received ................................. 28Figure 28: A02 Average Wait Times vs Average Volume Sent ......................................................... 28Figure 29: C08 Average Wait Times vs Average Volume Sent ......................................................... 29Figure 30: C09 Average Wait Times vs Average Volume Sent ......................................................... 29Figure 31: Daily Volume over Time .......................................................................................................... A-1Figure 32: Average Daily Traffic by Hour and Day ............................................................................. A-1Figure 33: Average Zone E Volume ........................................................................................................... A-2Figure 34: Average Hourly Volume Sent by Station - Zone E .......................................................... A-3Figure 35: Average Hourly Volume Received by Station - Zone E ................................................ A-3Figure 36: Average Zone N Volume .......................................................................................................... A-4Figure 37: Average Hourly Volume Sent by Station - Zone N ......................................................... A-5Figure 38: Average Hourly Volume Received by Station - Zone N ................................................ A-5Figure 39: Total Daily Traffic By Hour and Day - Zone B ................................................................. A-6Figure 40: Total Daily Traffic By Hour and Day - Zone D ................................................................. A-6Figure 41: Total Daily Traffic by Hour and Day - Zone J ................................................................... A-7Figure 42: Total Daily Traffic by Hour and Day - Zone K .................................................................. A-7Figure 43: Total Daily Volume by Hour and Day - Zone L ................................................................ A-8

4

Executive Summary The team performed a study of the University of Michigan Hospital Pneumatic Tube System (PTS). To analyze the system, the team conducted interviews and obtained data records from August and September of 2008. Using extensive data analysis, the team was able to make recommendations to reduce wait and travel times through the reductions of errors, improve the availability of carriers in the system, and significantly reduce wait times in problem areas of the system. The data showed a correlation between the number of errors per day and the average transaction time per day. Interviews revealed that there is currently no formal training required for employees to use the PTS. The team concluded that a training program should be implemented to reduce the average number of daily errors. If the average number of daily errors was reduced from the current average of 3.16 per day to less than one per day, the average transaction time per carrier would be reduced by about 15 seconds. The interviews provided information about carrier availability. In units where more carriers are sent than received each day, there is difficulty in obtaining an empty carrier to send. Currently, there are runners from each of these departments who travel to Central Distribution (where many empty carriers are stored) and gather carriers to bring back to their own departments. By sending multiple people to do the same job, the hospital is wasting employees’ time. The team recommends that one runner be assigned to this task at the start of each shift. Existing employees who already act as runners should take turns collecting and distributing the carriers. The distribution of carriers should be determined by the expected number of carriers sent per shift. The data showed that the Central Distribution department (also known as pathology) receives 29.24% of the total system volume between its three stations. This is much higher than any other station’s portion of overall volume. It also experiences relatively high wait times for carriers that are sent from these stations. The team concluded that the wait times are an affect of the high volume of carriers coming in. The team also concluded that by using stations C08 and C09 exclusively for receiving, and station A02 exclusively for sending wait times for carriers sent from central distribution could be significantly reduced. However, this will result in higher wait times for other stations sending from Zone C. Additionally, the team is unsure of the effects on other departments in the system due to the unprecedented volume directed to Zone C. The team recommends further study is performed on the affects of this change.

5

Introduction A pneumatic tube system (PTS) runs throughout the University of Michigan Hospital connecting departments with a network of hollow tubes. The tubes provide a highway for the transfer of small carriers. Various departments use the carriers and the PTS to transport documents, specimens, and other objects to departments located elsewhere in the hospital. The Facility Operations Director reported concerns about the traffic levels and transfer times for carriers in the system. The team was hired by the Facility Operations Director to study the system, by examining the activity levels and patterns of use, and to make any recommendations that will ensure reliable and efficient use of the PTS. The purpose of this document is to provide an explanation of the project’s analysis and findings.

Background The PTS has thirteen zones, each with several stations for sending and receiving carriers. The stations and zones are connected by tubes which serve as a network of one-way paths for transport. As a result, if a tube is occupied by a carrier going one direction, another carrier scheduled to go the opposite direction must wait for the first carrier to clear the tube. This setup can create large backups that could potentially bog down the PTS and increase the time required to move a carrier. The hospital has hired an outside vendor, Swisslog, to design a new PTS to replace the current system. However, Swisslog’s project is not expected to be completed for the next several years. To assess the situation in the meantime, the project discussed in this report is intended to ensure efficient use of the current system until the completion of Swisslog’s project. The team has used interviews, observation, simulation, and data analysis to study the use of the PTS and make any necessary recommendations to ensure the reliability and efficiency of carrier transport.

Key Issues The following are key issues reported by users of the system:

• The PTS is sensitive to user errors. If the user places a carrier in the station and enters the destination code for sending, but then decides not to send the carrier or removes the carrier from the tube, the system jams and a technician must reset it.

• Spills can occur when users do not properly insulate specimens. When a specimen

spills in the PTS, the technicians must clean out and disinfect the affected tubes. To clean the tubes, the technicians send a carrier filled with disinfectant, which adds to the heavy traffic in the PTS.

• To avoid unnecessary carrier traffic, some departments have stopped sending

empty return carriers. This situation has led to the “hoarding” of carriers and has created a need for someone to push a cart between departments to collect and redistribute empty carriers.

6

• Some departments choose to send carriers in batches rather than one at a time as

the need occurs. This batching causes fluctuations in traffic patterns.

Methodology This section of the report covers the approach to the analysis of the PTS.

Interviews The team interviewed two technicians, eight high volume users in various departments, and two training specialists. The users’ departments included Central Distribution, Blood Bank, Blood Draw, Pharmacy, Central Reception, and Central Staffing Resource Department.

Transaction and Error Data Collection The team received data ran queries to view source station, destination station, and route. The team used this data to identify areas of the PTS with high volume or long wait times.

Qualitative Findings Interviews provided qualitative data that helped define the current state of the system.

Interviews with Key Users Interviews with users showed that six of the eight users interviewed were pleased with the speed and reliability of the PTS; however, there were some who reported mistrust of the system. The team interviewed three users in Central Distribution. These interviews informed the team that the majority of carriers sent from central distribution are empty carriers requested by other departments. They occasionally send supplies to the ED emergency lab.

Interviews with Technicians During the interviews, the technicians provided schematics of the PTS and data for errors, transactions, and historical volume of usage. The data received from the technicians was in a format unreadable without the software created by Swisslog. Therefore, the technicians provided a contact at Swisslog who converted the data to a standard Excel format. The data received covered the period of August 1st, 2008 to September 17th, 2008, and included 93,536 individual transactions. Included in the file were data for source station, destination station, wait time, travel time, total time, and time of day. Technicians provided the team with information on system errors. These errors are usually a result of improper use by the sender and can have any of the following results:

7

• If the sender places a carrier in the station and enters the destination code for sending, but then decides not to send the carrier or removes the carrier from the tube, the system jams and a technician must reset it.

• Spills can occur when users do not properly insulate specimens. When a specimen spills in the PTS, the technicians must clean out and disinfect the affected tubes. To clean the tubes, the technicians send a carrier filled with disinfectant, which adds to the heavy traffic in the PTS.

• When a carrier is not properly closed, pieces of paper can come out. The paper then

covers the blower and obstructs suction in the tube, prohibiting other carriers from being sent in that section of the system.

• When senders fail to inspect the carrier before sending, carrier defects can cause them to get jammed in the system. When this occurs, technicians first try sending a brick in a carrier to force the jammed carrier out of the way. If the brick doesn’t solve the problem, the system must be shut down and the technicians will cut open the tube to remove the jammed carrier.

Interview with Training Specialist Senior The team was informed by the client that several key users travelled to Clarion Hospital in Indianapolis, Indiana to observe their PTS which is known for its efficiency. The Training Specialist Senior was one of these key users. There is currently no formal employee training program in place for use of the PTS. Clerks receive instruction on the job which causes bad habits to proliferate. This contrasts greatly with the program in place at Clarion Hospital, where employees must go through extensive training before using the system. As a result, there are almost no user errors which cause the system to shut down at Clarion. It became apparent that carrier availability is an issue. Because departments aren’t returning empty carriers, it leads to hoarding which makes it difficult for some stations to find a carrier to send when needed. At one time, there was a runner employed to distribute empty carriers to stations. This setup ultimately failed and was abandoned because individuals followed the runner and took carriers that had just been restocked for other stations. This led to a disproportionate supply of available carriers. The Training Specialist Senior explained the trends in the volume of carriers being sent throughout the day. These trends will be discussed in the quantitative analysis.

Quantitative Findings The 93,536 data points were analyzed to examine the use of the system. The following sections provide the results of this analysis.

8

Overall Traffic Trends The historical data provided by the technicians covered dates from December 2006 through September 2008. The trends show that the overall level of use of the PTS has been decreasing over time. A large drop in volume occurred in the spring of 2008, the same time period that CareLink, a computerized order entry system, was implemented. These trends can be seen below in Figure 1.

Figure 1: Weekly Volume over Time

Data provided by Brian Luttermoser, Collected December 2006 through September 2008 Transactional level data was provided for the time period from August 1, 2008 through September 18, 2008. This data was analyzed first for trends in volume. Figure 31 in Appendix A shows a cyclic pattern in volume from week to week with the highest volumes on weekdays and the lowest volumes on weekends. Figure 2 shows the total volume per day of week for the same time period as Figure 31.

8000

10000

12000

14000

16000

18000

20000

12/2

9/20

06

1/29

/200

7

3/1/

2007

4/1/

2007

5/1/

2007

6/1/

2007

7/1/

2007

8/1/

2007

9/1/

2007

10/1

/200

7

11/1

/200

7

12/1

/200

7

1/1/

2008

2/1/

2008

3/1/

2008

4/1/

2008

5/1/

2008

6/1/

2008

7/1/

2008

8/1/

2008

9/1/

2008

Tota

l Vol

ume

Date

9

Figure 2: Total Volume by Day of Week

Data collected from Lamson/Airlink Pneumatic Tube System by Brian Luttermoser and Team 4. Data collected on September 19, 2008.

Data Covers August 1, 2008 through September 18,2008. Sample size of 93536. The data was then broken down by the total daily traffic by hour of day from midnight to midnight. Figure 32 in Appendix A shows these results separated by day of the week. After noticing similar patterns between weekdays and weekends, the data was plotted by the average traffic by hour separated by weekdays and weekends. This can be seen in Figure 3.

9000

10000

11000

12000

13000

14000

15000

Tota

l Vol

ume

Day of Week

10

Figure 3: Average Daily Traffic by Hour


Data Covers August 1, 2008 through September 18,2008. Sample size of 93536. The spikes in the graph correspond to shift changes as pointed out in the interview with the Training Specialist Senior. At the end of shifts, specimens must be prepared and sent to the pathology department for testing. This practice ensures that test results will be available at the start of the next shift when doctors arrive.

Wait and Travel Times A regression analysis was performed to determine a correlation between average wait time per day and total carrier volume per day. Figure 4 indicates that there is only a weak relationship between daily volume and average wait time for that day.

0.00

20.00

40.00

60.00

80.00

100.00

120.00

1 3 5 7 9 11 13 15 17 19 21 23

Ave

rage

Vol

ume

Hour of Day

Weekday

Weekend

11

Figure 4: Total Daily Volume versus Average Daily Wait Times


Data Covers August 1, 2008 through September 18,2008. Sample size of 93536. Additionally, a regression analysis was performed to find a correlation between the number of errors and wait time. The analysis in Figure 5 shows a moderate correlation between these factors.

Figure 5: Daily Number of Errors versus Average Wait Times


Data Covers August 1, 2008 through September 18,2008. Sample size of 93536.

y = 0.0178x + 4.3037R² = 0.377

0

10

20

30

40

50

60

1000 1200 1400 1600 1800 2000 2200 2400

Ave

rage

Wai

t Ti

me

(sec

)

Total Volume

y = 2.2875x + 29.36R² = 0.4796

0

10

20

30

40

50

60

0 2 4 6 8 10 12

Ave

rage

Wai

t Ti

me

(sec

)

Daily Number of Errors

12

Another regression analysis was performed to investigate a relationship between the travel times for a carrier as it relates to the number of blowers passed en route. The results in Figure 6 confirm that the two are strongly correlated.

Figure 6: Number of Blowers versus Average Travel Time


Data Covers August 1, 2008 through September 18,2008. Sample size of 93536. To determine if the number of errors had an effect on travel time, the data was stratified by the number of errors in a day. Figure 7 shows an analysis of the number of blowers passed en route versus travel time when there are no errors in the system. Figure 8 shows the same analysis with one to three errors while Figure 9 shows four or more errors.

y = 34.656x + 79.468R² = 0.8708

0

50

100

150

200

250

300

350

0 1 2 3 4 5 6 7

Ave

rage

Tra

vel T

ime

(sec

)

Number of Blowers

13

Figure 7: Number of Blowers versus Average Travel Time - 0 Errors



Figure 8: Number of Blowers versus Average Travel Time - 1 to 3 Errors



y = 32.574x + 77.079R² = 0.8762

0

50

100

150

200

250

300

350

0 1 2 3 4 5 6 7

Ave

rage

Tra

vel T

ime

(sec

)

Number of Blowers

y = 33.688x + 85.419R² = 0.8177

0

50

100

150

200

250

300

350

0 1 2 3 4 5 6 7

Ave

rage

Tra

vel T

ime

(sec

)

Number of Blowers

14

Figure 9: Number of Blowers versus Average Travel Time - 4 or more Errors


Data Covers August 1, 2008 through September 18,2008. Sample size of 93536. The results of these studies suggest that when errors are present, travel time is increased slightly. This is also seen as a function of the number of blowers passed. The number of errors has a smaller effect on travel times than wait times, but an effect is still apparent.

y = 37.155x + 83.197R² = 0.8017

0

50

100

150

200

250

300

350

400

450

0 1 2 3 4 5 6 7 8

Trav

el T

ime

(sec

)

Number of Blowers

15

Identifying Problem Stations Throughout the entire system the average wait time was found to be 37.2 seconds with a standard deviation of 22 seconds. The data in Table 1 shows the highest volume stations according to their volume received and their respective average wait times. Stations C09, A02, and C08 were identified as problem stations to be further analyzed due to their relatively high wait times and volumes. These stations are all associated with the Central Distribution department which is also known as pathology and are located right next to each other. When these three stations are considered as a group, the mean wait time is 79.5 seconds, far above the mean of the system.

Table 1: Highest Volume Stations with Average Wait Times Data collected from Lamson/Airlink Pneumatic Tube System by Brian Luttermoser and Team 4.

Data collected on September 19, 2008. Data Covers August 1, 2008 through September 18,2008. Sample size of 93536.

Source Station Average Wait Time (sec)

Avg Daily Volume

Received % of System

Volume Received

Avg Daily Volume Sent

% of System Volume Sent

E02 – Blood Bank 16.0 111 5.80 135 7.09

A15 – ED Emergency Lab 37.3 22 1.14 111 5.80 C09 – Central Distribution 81.4 5 0.27 91 4.77

K04 – Pharmacy Sat 6 12.8 67 3.53 90 4.70

A02 – Central Distribution 56.0 345 18.07 88 4.61

C08 – Central Distribution 102.4 208 10.90 82 4.31 D10 – MSC 12.8 8 0.44 61 3.21

B08 – Central Pharmacy 31.8 43 2.26 59 3.08

N10 – Pharmacy 5

th 33.8 Floor 41 2.13 54 2.84

N04 – Mott Admitting 39.4 47 2.49 48 2.50

N09 - NICU 30.7 45 2.36 46 2.43

Zone Traffic Trends Figure 10 shows the average daily incoming and outgoing traffic, broken down by zone. This data was used to identify high volume zones to be further analyzed.

16

Figure 10: Average Daily Traffic by Zone


Data Covers August 1, 2008 through September 18,2008. Sample size of 93536. The data showed that zones A, C, E, and N are high volume zones and zones B, D, J, K, and L are moderate volume zones. Zones F, G, H, P, R and S are considered low volume zones and are outside of the scope of this analysis. Because Zones A and C contain the identified problem stations, they were chosen for deeper analysis. These analyses are described in the following sections. The analysis for other high volume and moderate volume zones can be found in Appendix A.

Zone A Figure 11 shows the traffic originating in Zone A tends to be higher during early morning and late night hours.

0

100

200

300

400

500

600

700

A B C D E F G H J K L N P R S

Ave

rage

Vol

ume

Sent

/Rec

eive

d

Zone

17

Figure 11: Average Zone A Volume Sent by Hour


Data Covers August 1, 2008 through September 18,2008. Sample size of 93536. To investigate these changes in volume, the hourly data for sending volume was broken down by station in Zone A. The individual station breakdown for Zone A can be seen in Figure 12. Station A02 has a large spike in volume in the 10:00 PM hour and steadily decreases until a large drop occurs between 5:00 and 8:00 AM. This pattern dictates the overall Zone A source volume trends seen in Figure 11. The spikes seen here also correspond to the spikes observed in the overall system, shown in Figure 3.

0

5

10

15

20

25

30

1 2 3 4 5 6 7 8 9 101112131415161718192021222324

Ave

rage

Vol

ume

Sent

Hour of Day

Sunday

Monday

Tuesday

Wednesday

Thursday

Friday

Saturday

18

Figure 12: Average Volume Sent by Hour, by Station - Zone A


Data Covers August 1, 2008 through September 18,2008. Sample size of 93536. A similar analysis was done for Zone A as a receiving station. The resultant breakdown by station is shown in Figure 13. As depicted below, station A02 accounts for 74.5% of the total carriers sent to Zone A within the time period covered by this analysis. The station’s volume received peaks at 6 am, but stays high throughout the day and night. Because of A02 large volumes and variability the team further analyzed the data at A02.

0

5

10

15

20

25

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

Ave

rage

Vol

ume

Sent

Hour of Day

A01

A02

A08

A11

A12

A13

A14

A15

19

Figure 13: Average Volume Received by Hour, by Station - Zone A



A02 The average wait times by hour for carries sent by and received in station A02 can be seen in Figure 14 and Figure 15 respectively.

Figure 14: Average Wait Time by Hour – Carriers Sent from A02



0

5

10

15

20

25

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Ave

rage

Vol

ume

Rece

ived

Hour of Day

A01

A02

A06

A07

A08

A11

A12

A13

A14

A15

0

20

40

60

80

100

120

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Ave

rage

Wai

t Ti

mes

(sec

)

Hour of Day

20

Figure 15: A02 Average Wait Time by Hour - Carriers Sent to A02


Data Covers August 1, 2008 through September 18,2008. Sample size of 93536. These results show that when A02 is sending, the peak wait time averages more than two standard deviations above the system mean, and there is a great deal of variability based on the time of day. When A02 is receiving, the peak times are well above the system mean, but the majority of points are within control.

Zone C Similar to Zone A, the overall sent traffic pattern in Zone C is lower during daytime hours and higher during early morning and late night hours. Zone C also experiences a peak during the 10:00 PM hour. These trends are shown in Figure 16.

0

10

20

30

40

50

60

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Ave

rage

Wai

t Ti

mes

(sec

)

Hour of Day

21

Figure 16: Average Zone C Volume Sent by Hour


Data Covers August 1, 2008 through September 18,2008. Sample size of 93536. To investigate the variation in volume of carriers sent from Zone C, the data was broken down by station as seen in Figure 17. Stations C08 and C09 account for the largest volumes in Zone C. The patterns are similar to each other and dictate the overall Zone C pattern for carriers sent, as seen in Figure 16.

0

5

10

15

20

25

1 2 3 4 5 6 7 8 9 101112131415161718192021222324

Ave

rage

Vol

ume

Sent

Hour of Day

Sunday

Monday

Tuesday

Wednesday

Thursday

Friday

Saturday

22

Figure 17: Average Volume Sent by Hour, by Station - Zone C


Data Covers August 1, 2008 through September 18,2008. Sample size of 93536. When the stations are viewed as destinations rather than sources, C08 has by far the highest volume throughout the day and night. A peak in C08 can be seen in the early morning; traffic remains high during business hours and moderately high during the night.

Figure 18: Average Volume Received by Hour, by Station - Zone C



0

2

4

6

8

10

12

14

16

18

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

Ave

rage

Vol

ume

Sent

Hour of Day

C08

C09

C10

C11

C12

C13

C14

C15

0

2

4

6

8

10

12

14

16

18

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Ave

rage

Vol

ume

Rece

ived

Hour of Day

C03

C04

C05

C06

C08

C09

C10

C11

C12

C13

C14

23

C08 The average wait times by hour, both for carriers sent from and received by station C08 can be seen in Figure 19 and Figure 20 respectively.

Figure 19: Average Wait Time by Hour – Sent from C08



Figure 20: Average Wait Time by Hour – Received by C08


Data Covers August 1, 2008 through September 18,2008. Sample size of 93536. When C08 sends carriers, there is a peak average wait time between 4 AM and 5 AM. Currently, the average wait times are more than six standard deviations above the system mean. The smallest average wait times by hour were still well above the system mean, so wait times from station C08 need to be addressed. When C08 receives carriers, there is a

020406080

100120140160180200

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Ave

rage

Wai

t Ti

me

(sec

)

Hour of Day

0

20

40

60

80

100

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Ave

rage

Wai

t Ti

mes

(sec

)

Hour of Day

24

large spike in wait times of carriers sent to C08 during the 10 PM hour, but most points are similar to the mean of the entire system.

C09 The average wait times by hour of station C09 were analyzed next. The results are shown in Figure 21.

Figure 21: Average Wait Time by Hour - C09 as Source


Data Covers August 1, 2008 through September 18,2008. Sample size of 93536. The average wait time by hour for station C09 peaks at 135 seconds which is more than four standard deviations above the system mean. The lowest average wait times by hour for C09 were similar to the mean wait times of the entire system, the causes of this variability will be further analyzed later in this report.

Causes of High Wait Times The most significant wait times were observed in the central distribution stations A02, C08, and C09, so hourly breakdowns of wait times were analyzed for each of the three stations. These wait time patterns closely match the patterns in hourly volume received as shown in Figure 22, Figure 23, and Figure 24. For stations A02 and C08 the wait times were plotted along with the volume of carriers being sent to that station, and in C09 were plotted along with the volume of carriers being sent to Zone C (because volume in C09 alone is so low, it was combined with the volume of carriers sharing the same blower).

0

20

40

60

80

100

120

140

160

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Ave

rage

Wai

t Ti

me

(sec

)

Hour of Day

25

Figure 22: A02 Average Wait Times and Average Volume Received by Hour



Figure 23: C08 Average Wait Times and C08 Average Volume Received by Hour



0

5

10

15

20

25

0

20

40

60

80

100

120

1 3 5 7 9 11 13 15 17 19 21 23

Ave

rage

Vol

ume

Rece

ived

Ave

rage

Wai

t Ti

me

(sec

)

Hour of Day

Wait Time

Destination Volume

0

2

4

6

8

10

12

14

16

18

0

20

40

60

80

100

120

140

160

180

200

1 3 5 7 9 11 13 15 17 19 21 23

Ave

rage

Vol

ume

Rece

ived

Ave

rage

Wai

t Ti

me

(sec

)

Hour of Day

Wait Times

Destination VolumeVolume Received

Volume Received

26

Figure 24: C09 Average Wait Times and Zone C Average Volume Received by Hour


Data Covers August 1, 2008 through September 18,2008. Sample size of 93536. To explore these correlations, a regression analysis was performed between volume received and wait time for carriers sent. These data are strongly correlated. In stations A02, C08, and C09 the wait time for carriers departing these stations increased by 4.2 seconds, 9.4 seconds, and 6.6 seconds respectively for each carrier per hour sent there. Figure 25, Figure 26, and Figure 27 show these relationships.

0

5

10

15

20

25

0

20

40

60

80

100

120

140

160

1 3 5 7 9 11 13 15 17 19 21 23

Ave

rage

Vol

ume

Rece

ived

Ave

rage

Wai

t Ti

me

(sec

)

Hour of Day

Wait Times

Destination VolumeVolume Received

27

Figure 25: A02 Average Wait Times vs Average Volume Received



Figure 26: C08 Average Wait Times vs Average Volume Received



y = 4.2411x - 6.3989R² = 0.4488

0

20

40

60

80

100

120

0 5 10 15 20 25

Ave

rage

Wai

t Ti

me

(sec

)

Average Volume Received per Hour

y = 9.4x + 21.595R² = 0.7435

0

20

40

60

80

100

120

140

160

180

200

0 2 4 6 8 10 12 14 16 18

Ave

rage

Wai

t Ti

me

(sec

)


28

Figure 27: C09 Average Wait Times vs Zone C Average Volume Received


Data Covers August 1, 2008 through September 18,2008. Sample size of 93536. The relationship between volume sent and average wait times are shown in Figure 28, Figure 29, and Figure 30.

Figure 28: A02 Average Wait Times vs Average Volume Sent



y = 6.5823x - 2.1082R² = 0.6468

0

20

40

60

80

100

120

140

160

0 5 10 15 20 25

Ave

rage

Wai

t Ti

me

(sec

)


y = 0.7115x + 51.956R² = 0.0121

0

20

40

60

80

100

120

0 2 4 6 8 10 12

Ave

rage

Wai

t Ti

me

(sec

)

Average Volume Sent per Hour

29

Figure 29: C08 Average Wait Times vs Average Volume Sent



Figure 30: C09 Average Wait Times vs Average Volume Sent


Data Covers August 1, 2008 through September 18,2008. Sample size of 93536. From these results, it is clear that volume sent has no effect on average wait times in their respective stations. However, there is a very significant relationship between the number of carriers received at a station and the average wait time for carriers being sent from that station.

y = -1.0273x + 106.64R² = 0.002

0

20

40

60

80

100

120

140

160

180

200

0 1 2 3 4 5 6 7

Ave

rage

Wai

t Ti

me

(sec

)


y = -3.2392x + 96.188R² = 0.0312

0

20

40

60

80

100

120

140

160

0 1 2 3 4 5 6 7 8

Ave

rage

Wai

t Ti

me

(sec

)


30

Conclusions

Errors and Transaction Times Through regression analysis, the team found that reduction of errors would decrease both wait and travel times throughout the system. If errors were reduced from their current average level of 3.16 per day to less than 1 per day, the expected system wait time would be decreased by approximately 8 seconds and the travel time would be decreased by approximately 7 seconds.

Carrier Availability Through the interviews with users in the nursing units, the team found that carrier availability is an issue and different units send a person to retrieve carriers for their department. The team has determined that sending multiple people throughout the day to do the same job is a waste of employee time because one person could be sent to retrieve all of the carriers for these departments.

Wait Times in Central Distribution Based on the data from the regression analyses, the team concluded that wait times for carriers sent from a given station are determined by the volume of carriers received at that station for a given time period. By reducing the volume arriving at a station, the wait times for carriers departing the station can be improved. The exact amount of improvement depends on the current volumes and the volume after the reduction. For station A02, the relationship between wait time and volume received is described by Equation 1, where y is wait time and x is carriers received per hour. Additionally, Equations 2 and 3 describe stations C08 and C09, respectively.

𝒚𝒚 = 𝟒𝟒.𝟐𝟐𝟒𝟒𝟐𝟐𝟐𝟐𝒙𝒙 − 𝟔𝟔.𝟑𝟑𝟑𝟑𝟑𝟑𝟑𝟑 Equation 1

𝒚𝒚 = 𝟑𝟑.𝟒𝟒𝒙𝒙 + 𝟐𝟐𝟐𝟐.𝟓𝟓𝟑𝟑𝟓𝟓 Equation 2

𝒚𝒚 = 𝟔𝟔.𝟓𝟓𝟑𝟑𝟐𝟐𝟑𝟑𝒙𝒙 − 𝟐𝟐.𝟐𝟐𝟏𝟏𝟑𝟑𝟐𝟐 Equation 3

These equations can be used to estimate the improvement in wait time based on the reduction of volume received. However, further study is needed to determine the exact effect because the equations are specific to the system’s current traffic trends.

Recommendations

Error Reduction Through data analysis the team was able to determine that errors in the system increased both wait and travel time in the system. Errors are most frequently caused by users improperly using the system. To reduce the wait and travel time throughout the system the team recommends having an employee training program for a standardized method of packing and sending carriers. This would include instruction on inspecting the carrier before use, double bagging and properly insulating specimens, closing the carrier securely,

31

and correctly typing the destination code. The team will work with the hospital to create and implement the recommended training program. If the program is implemented, the team expects errors to be reduced from an average of 3.16 per day to 0. Through our regression analysis the team estimates the elimination of errors would decrease the average transaction time by approximately 15 seconds. A standardized training model has been developed by a training specialist. This will be used to train new clerks who will interact with the PTS. This model can be found in Appendix B. The team recommends that a similar training model be used for all users of the PTS.

Carrier Availability To ensure the appropriate stations have a sufficient amount of carriers the team suggests that a runner system be implemented. This system would entail a person manually distributing carriers at the beginning of each shift. With this system carriers would be allotted based on the sending volumes of each station. The required volumes for high volume stations are shown below in Table 2. Additional volumes can be found in Appendix C.

Table 2: Carriers Needed per Shift in Top Ten Stations

Between 7 am and 3 pm Between 3pm and 11 pm Between 11pm and 7 am

Station Carriers Needed Station Carriers Needed Station Carriers Needed

A15 34.7 A15 37.2 C09 40.8

D10 27.7 C09 27.8 A15 21.9

E02 27.0 D10 19.9 K04 11.4

C09 19.6 E02 9.9 D10 7.8

D04 14.2 K04 6.6 N10 7.0

H09 14.0 H09 5.9 A08 5.6

B08 11.6 B08 4.5 A14 5.3

P03 6.7 A08 3.1 A11 5.2

J10 6.2 B04 2.8 B04 5.0

K04 4.8 D05 2.7 A12 4.6

Reduction of Wait Times in Central Distribution The team suggests further study regarding the sending of carriers to and from Central Distribution. If station A02 is used exclusively for sending, and stations C08, and C09 are reserved exclusively for receiving, overall wait times for carriers departing Central Distribution will be reduced. The carriers sent from central distribution account for 13.69% of the total system volume, but are usually empty so they should be considered a lower priority. Stations A02, C08, and C09 are physically located next to each other, so the change is feasible. With this recommendation stations sending specimens in Zone C will likely see an increase in wait times due to the large volume of carriers redirected to the shared blower C. Carrier

32

volume sent from other stations in Zone C is currently significantly lower, but the contents of the carriers are likely a higher priority than the empty carriers leaving Central Distribution. The hospital should consider whether the reduction of wait times for empty carriers is worth the increase wait times for specimens leaving the other departments in Zone C. Additionally, if the change is implemented, the system will experience unprecedented volumes of carriers sent to Zone C. This could have other unforeseen effects that should be investigated.

A-1

Appendix A – Additional Analysis

Figure 31: Daily Volume over Time



Figure 32: Average Daily Traffic by Hour and Day



0

500

1000

1500

2000

2500

3000

3500

4000

4500

8/1/2008 8/8/2008 8/15/2008 8/22/2008 8/29/2008 9/5/2008 9/12/2008

Tota

l Vol

ume

Date

0

100

200

300

400

500

600

700

800

900

1 2 3 4 5 6 7 8 9 101112131415161718192021222324

Ave

rage

Vol

ume

Hour of Day

Sunday

Monday

Tuesday

Wednesday

Thursday

Friday

Saturday

A-2

Zone E Volume Analysis The overall source volume patterns in Zone E contrasts the patterns in Zones A and C. In Zone E, a steady rise and fall in volume is observed throughout the day, reaching its greatest level around noon.

Figure 33: Average Zone E Volume


Data Covers August 1, 2008 through September 18,2008. Sample size of 93536. When the data is broken down by station, station E02 seems to control the overall source volume for the zone. This station level data can be seen in Figure 34.

0

5

10

15

20

25

1 3 5 7 9 11 13 15 17 19 21 23

Ave

rage

Vol

ume

Hour of Day

Sunday

Monday

Tuesday

Wednesday

Thursday

Friday

Sunday

A-3

Figure 34: Average Hourly Volume Sent by Station - Zone E


Data Covers August 1, 2008 through September 18,2008. Sample size of 93536. As a destination, E02 remains the highest volume station. Hourly destination volume by station can be seen in Figure 35.

Figure 35: Average Hourly Volume Received by Station - Zone E



0

2

4

6

8

10

12

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Ave

rage

Vol

ume

Sent

Hour of Day

E02

E03

E04

E06

E07

E10

E11

E12

E13

E14

0

2

4

6

8

10

12

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Ave

rage

Vol

ume

Rece

ived

Hour of Day

E02

E03

E04

E06

E07

E10

E11

E12

E13

E14

A-4

Zone N Volume Analysis Zone N has a pattern unlike any of the other high volume zones; peaking between 5:00 and 6:00 AM and remaining fairly steady during the remainder of the day.

Figure 36: Average Zone N Volume


Data Covers August 1, 2008 through September 18,2008. Sample size of 93536. Stations N09 and N12 have large peaks in the morning defining the overall pattern in Zone N. For all other hours the volume is relatively evenly shared between the stations. This can be seen in Figure 37.

0

5

10

15

20

25

30

1 2 3 4 5 6 7 8 9 101112131415161718192021222324

Ave

rage

Vol

ume

Hour of Day

Sunday

Monday

Tuesday

Wednesday

Thursday

Friday

Saturday

A-5

Figure 37: Average Hourly Volume Sent by Station - Zone N


Data Covers August 1, 2008 through September 18,2008. Sample size of 93536. Zone N as a destination is fairly constant among all stations, with several stations spiking around 11:00 PM. This can be seen in Figure 38.

Figure 38: Average Hourly Volume Received by Station - Zone N



0

1

2

3

4

5

6

7

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Ave

rage

Vol

ume

Sent

Hour of Day

N04

N07

N09

N10

N12

N13

N15

0

1

2

3

4

5

6

7

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Ave

rage

Vol

ume

Rece

ived

Hour of Day

N04

N07

N09

N10

N12

N13

N14

N15

A-6

Other Zones Volume Analysis

Figure 39: Total Daily Traffic By Hour and Day - Zone B



Figure 40: Total Daily Traffic By Hour and Day - Zone D



0

2

4

6

8

10

12

1 2 3 4 5 6 7 8 9 101112131415161718192021222324

Ave

rage

Vol

ume

Hour of Day

Zone B

Sunday

Monday

Tuesday

Wednesday

Thursday

Friday

Saturday

0

2

4

6

8

10

12

14

1 2 3 4 5 6 7 8 9 101112131415161718192021222324

Tota

l Vol

ume

Hour of Day

Zone D

Sunday

Monday

Tuesday

Wednesday

Thursday

Friday

Saturday

A-7

Figure 41: Total Daily Traffic by Hour and Day - Zone J



Figure 42: Total Daily Traffic by Hour and Day - Zone K



0

2

4

6

8

10

12

14

1 3 5 7 9 11 13 15 17 19 21 23

Tota

l Vol

ume

Hour of Day

Zone J

Sunday

Monday

Tuesday

Wednesday

Thursday

Friday

Saturday

0

2

4

6

8

10

12

14

1 3 5 7 9 11 13 15 17 19 21 23

Tota

l Vol

ume

Hour of Day

Zone K

Sunday

Monday

Tuesday

Wednesday

Thursday

Friday

Saturday

A-8

Figure 43: Total Daily Volume by Hour and Day - Zone L



0

2

4

6

8

10

12

1 3 5 7 9 11 13 15 17 19 21 23

Tota

l Vol

ume

Hour of Day

Zone L

Sunday

Monday

Tuesday

Wednesday

Thursday

Friday

Saturday

B-1

Appendix B – Training Document

Using the Pneumatic Tube System Job Aid

Overview:

The purpose of this aid is to explain the Pneumatic Tube system that runs thru out UMHS and its proper usage. UMHS departments use a pneumatic Tube system (much like a banking system, but bigger) to facilitate the quick and efficient movement of:

1) Blood products 2) Medicines 3) Pathology samples 4) Small supplies (wrapped for sterility!) 5) Paperwork

Departments in UMHS have “stations” where the pneumatic tubes come and go. Each of

these stations is assigned a corresponding # that is selected prior to sending the tube out. Do not use the “Return Tube” button as it’s been deactivated. Movement can be delayed at times as tubes move very much like cars on a “One way street”. They can only go one way at a time!

These stations should have a bin located below where foam is kept to pack fragile items. There should be a station list posted on each Unit, here is the link to CSR’s resource site tube listing; https://ummcweb29.mcit.med.umich.edu/HOS/facilities/p-tube/ptube.cfm

Whenever sending pathology samples thru the system it is important to pack them carefully to avoid spillage or breakage. Tubes travel at a quick rate and make sudden stops and if objects are not secured they could be slammed from top to bottom of the tube causing breakage and/or potential spills. The fact alone that we do have incidents of breakage of blood vials or others should be reason enough to never “tube” food thru the system! We also never send pagers or batteries thru the tube system because of breakage or sparking potential.

Process: Any pathology samples should be in a zip top Bio Hazard bag and as stated above should be

secured with foam to ensure the sample will not move

1) Place a piece of foam in the pneumatic tube carrier

. Make sure all items are inside the tube and nothing is hanging out when closed. All samples should be labeled. Find below Pathology’s process for packing samples:

2) Distribute the bagged specimens evenly across the foam. 3) Fold the requisitions together into 1/3s and rubber band the receipt label

with them. 4) Place them on top of the specimens.

B-2

5) Place another piece of foam on top. 6) Close the carrier, making sure the clasp is tightly closed. 7) Place the carrier into the Pneumatic tube system and push the CD button.

We should be identifying any faulty tubes. They should be pulled out of service and Maintenance called to pick up any faulty carriers (65054) if:

1) They have broken or bent clasps 2) Broken hinges 3) Loose Velcro strips 4) Loose and wobbly carrier

Potential problems with packing carrier tubes: 1) Do not over load the carrier, 5 lb is the maximum. If too heavy, carrier

can break open in the pneumatic tube system and shut the system down.

2) Always use two pieces of foam. The foam should be against the walls of the carrier.

3) Always keep all specimens and requisitions inside the foam layers. 4) Do not double layer the blood specimens. They may break. 5) Carriers should be loaded in a balanced manner. Do not stuff all the

specimens in one end of the carrier. This could cause the whole system to go down.

Examples: You can’t tube an Elephant! Proper way to pack lab samples

C-1

Appendix C – Carriers Needed



A15 34.7 A15 37.2 C09 40.8

D10 27.7 C09 27.8 A15 21.9

E02 27.0 D10 19.9 K04 11.4

C09 19.6 E02 9.9 D10 7.8

D04 14.2 K04 6.6 N10 7.0

H09 14.0 H09 5.9 A08 5.6

B08 11.6 B08 4.5 A14 5.3

P03 6.7 A08 3.1 A11 5.2

J10 6.2 B04 2.8 B04 5.0

K04 4.8 D05 2.7 A12 4.6

N07 4.4 K06 2.3 K07 4.4

J08 4.0 J03 2.1 L04 2.8

N10 3.9 N10 2.0 A07 2.0

D05 3.7 J10 1.9 K03 1.9

A08 3.2 A14 1.5 D04 1.3

J11 2.8 A12 1.3 B08 1.2

N12 2.7 N04 1.3 L02 1.2

E03 2.2 S06 1.2 N09 1.1

B04 2.2 E07 1.2 K06 1.1

A03 2.1 J06 1.2 D05 0.9

C15 2.0 K03 1.0 L05 0.9

A14 1.9 A03 1.0 C14 0.9

F08 1.7 A01 1.0 E14 0.9

J12 1.5 E10 0.7 N12 0.8

H05 1.2 F08 0.6 E07 0.8

P02 1.1 F05 0.6 L03 0.6

R02 1.0 A04 0.6 R01 0.6

N06 1.0 G10 0.6 E10 0.5

H02 1.0 P03 0.5 C13 0.5

E08 0.9 A07 0.5 C12 0.4

H12 0.9 L02 0.5 N14 0.4

F13 0.9 E08 0.5 C06 0.4

K07 0.8 F07 0.4 C10 0.4

E07 0.7 D08 0.4 E12 0.4

F05 0.7 A11 0.4 L06 0.3

C12 0.6 C04 0.3 B03 0.3

E10 0.6 E12 0.3 A01 0.2

C-2



A04 0.5 G07 0.2 H02 0.2

F04 0.5 P02 0.2 C04 0.2

B05 0.5 F04 0.2 A13 0.2

R03 0.4 H08 0.2 B05 0.2

N14 0.4 F13 0.2 A06 0.1

N15 0.4 L03 0.2 D08 0.1

J03 0.3 S04 0.2 N06 0.1

S04 0.3 R05 0.2 K05 0.1

G09 0.3 C05 0.2 S06 0.1

G10 0.3 N07 0.2 K02 0.0

E05 0.2 G06 0.1 C05 0.0

P05 0.2 E13 0.1 G07 0.0

F11 0.2 H05 0.1 G09 0.0

H08 0.2 N13 0.1 B02 0.0

H11 0.2 A13 0.1 E11 0.0

G05 0.2 R02 0.1 J03 0.0

G06 0.2 R03 0.1 F13 0.0

G11 0.2 P05 0.1 A03 0.0

N09 0.2 K05 0.1 K08 0.0

H10 0.2 H03 0.1 H09 0.0

A07 0.1 N05 0.1 E08 0.0

E13 0.1 C13 0.1 F12 0.0

F09 0.1 F11 0.1 H03 0.0

N05 0.1 S07 0.1 G12 0.0

C04 0.1 H12 0.0 D07 0.0

G12 0.1 E05 0.0 R05 0.0

G02 0.0 N09 0.0 E04 0.0

H04 0.0 H10 0.0 R02 0.0

K08 0.0 S02 0.0 F04 0.0

S02 0.0 H04 0.0 E13 0.0

A06 0.0 D07 0.0 N05 -0.1

B07 0.0 G05 0.0 B07 -0.1

F12 0.0 F09 0.0 N13 -0.1

F10 0.0 B07 0.0 F07 -0.2

N13 0.0 H07 0.0 N04 -0.2

C03 0.0 G12 0.0 C03 -0.2

R04 0.0 E14 0.0 C11 -0.2

R05 0.0 G11 0.0 A04 -0.3

H03 -0.1 F10 0.0 N07 -0.4

C-3



S07 -0.1 R04 0.0 J12 -0.5

B03 -0.1 C03 -0.1 J06 -0.6

K06 -0.2 N15 -0.1 J10 -0.6

F07 -0.2 G04 -0.1 E06 -0.8

K03 -0.2 G02 -0.1 C15 -0.9

K05 -0.2 H11 -0.1 B06 -0.9

G04 -0.2 E11 -0.1 P02 -1.2

C05 -0.3 K08 -0.1 N15 -1.3

D07 -0.3 G09 -0.1 J11 -1.3

A01 -0.3 B03 -0.1 E03 -1.7

C13 -0.4 K07 -0.2 J08 -4.5

E12 -0.5 B05 -0.3 E02 -9.2

D08 -0.5 S03 -0.3 C08 -31.4

G07 -0.5 C11 -0.3 A02 -86.4

C11 -0.6 B06 -0.4

C14 -0.6 J12 -0.4

S06 -0.6 N06 -0.4

L03 -0.6 E04 -0.4

N04 -0.6 A06 -0.5

R01 -0.6 D04 -0.6

E04 -0.6 C12 -0.6

L02 -0.7 C10 -0.7

C10 -0.8 E03 -0.7

B06 -0.8 L05 -0.7

E11 -0.9 L06 -0.8

A13 -1.2 C14 -0.9

L05 -1.3 L04 -1.0

L06 -1.5 J08 -1.1

A12 -1.6 H02 -1.2

A11 -1.9 R01 -1.3

E06 -1.9 E06 -1.5

J06 -2.0 J11 -1.7

E14 -2.2 N14 -2.0

L04 -3.1 C06 -2.0

S03 -3.2 N12 -2.1

C06 -9.7 C15 -2.6

B02 -18.4 B02 -4.0

C08 -69.1 C08 -32.5

A02 -94.6 A02 -87.7

analysis of the pneumatic tube system in the university of...

Documents