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Basic Tools for Process Improvement
2 RUN CHART
What is a Run Chart?
A Run Chart is the most basic tool used to display how a process performs over time.It is a line graph of data points plotted in chronological order—that is, the sequence inwhich process events occurred. These data points represent measurements, counts,or percentages of process output. Run Charts are used to assess and achieveprocess stability by highlighting signals of special causes of variation (Viewgraph 1).
Why should teams use Run Charts?
Using Run Charts can help you determine whether your process is stable (free ofspecial causes), consistent, and predictable. Unlike other tools, such as ParetoCharts or Histograms, Run Charts display data in the sequence in which theyoccurred. This enables you to visualize how your process is performing and helpsyou to detect signals of special causes of variation.
A Run Chart also allows you to present some simple statistics related to the process:
Median: The middle value of the data presented.You will use it as the Centerline on your Run Chart.
Range: The difference between the largest and smallest values in the data.You will use it in constructing the Y-axis of your Run Chart.
You can benefit from using a Run Chart whenever you need a graphical tool to helpyou (Viewgraph 2)
Understand variation in process performance so you can improve it.
Analyze data for patterns that are not easily seen in tables or spreadsheets.
Monitor process performance over time to detect signals of changes.
Communicate how a process performed during a specific time period.
RUN CHART VIEWGRAPH 1
What is a Run Chart?
A line graph of data points plotted in
chronological order that helps detect
special causes of variation.
RUN CHART VIEWGRAPH 2
Why Use Run Charts?
• Understand process variation
• Analyze data for patterns
• Monitor process performance
• Communicate processperformance
Basic Tools for Process Improvement
RUN CHART 3
Basic Tools for Process Improvement
4 RUN CHART
What are the parts of a Run Chart?
As you can see in Viewgraph 3, a Run Chart is made up of seven parts:
1. Title: The title briefly describes the information displayed in the Run Chart.
2. Vertical or Y-Axis: This axis is a scale which shows you the magnitude ofthe measurements represented by the data.
3. Horizontal or X-Axis: This axis shows you when the data were collected. It always represents the sequence in which the events of the process occurred.
4. Data Points: Each point represents an individual measurement.
5. Centerline: The line drawn at the median value on the Y-axis is called theCenterline. (Finding the median value is Step 3 in constructing a Run Chart.)
6. Legend: Additional information that documents how and when the data werecollected should be entered as the legend.
7. Data Table: This is a sequential listing of the data being charted.
How is a Run Chart constructed?
Step 1 - List the data. List the data you have collected in the sequence in which it occurred. You may want to refer to the Data Collection module for information ondefining the purpose for the data and collecting it.
Step 2 - Order the data and determine the range (Viewgraph 4). To order the data, list it from the lowest value to the highest. Determine the range—thedifference between the highest and lowest values.
Step 3 - Calculate the median (Viewgraph 4). Once the data have been listed from the lowest to the highest value, count off the data points and determine themiddle point in the list of measurements—the point that divides the series of datain half.
If the count is an odd number, the middle is an odd number with an equalnumber of points on either side of it. If you have nine measurements, forexample, the median is the fifth value.
If the count is an even number, average the two middle measurements todetermine the median value. For example, for 10 measurements, the medianis the average of the fifth and sixth values. To determine the average, just addthem together and divide by two.
RUN CHART VIEWGRAPH 3
1 TITLE 3 X-AXIS 5 CENTERLINE 7 DATA TABLE
2 Y-AXIS 4 DATA POINT 6 LEGEND
Parts of a Run Chart
Centerline = .3325
1
3
2
4
5
Durham Bulls’Team BattingAvg. recorded onMon. of everyweek during the1994 season byRob Jackson,team statistician
October 15, 1994
6
WEEK 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
AVG 300 333 325 332 340 345 350 340 341 345 349 354 350 344 333 325 318 305 298 306 310 315 310 318
7
24232221201918171615141312111098765432100.290
0.300
0.310
0.320
0.330
0.340
0.350
0.360
TEAM BATTING AVERAGE (1994)
Weeks of the Season
Bat
tin
g A
vera
ge
RUN CHART VIEWGRAPH 4
How to Construct a Run ChartStep 2 - Order data & determine rangeStep 3 - Calculate the median
RANK AVG RANK AVG RANK AVG
1 .298 9 .318 17 .341
2 .300 10 .325 18 .344
3 .305 11 .325 MEDIAN: 19 .345
4 .306 12 .332 (.332 + .333) / 2 20 .345
5 .310 13 .333 = .3325 21 .349
6 .310 14 .333 22 .350
7 .315 15 .340 23 .350
8 .318 16 .340 24 .354
RANGE: .354 - .298 = 0.56
Basic Tools for Process Improvement
RUN CHART 5
Basic Tools for Process Improvement
6 RUN CHART
Now let’s continue with the remaining steps (Viewgraph 5).
Step 4 - Construct the Y-Axis. Center the Y-Axis at the median. Make the Y-axis scale 1.5 to 2 times the range.
Step 5 - Draw the Centerline. Draw a horizontal line at the median value and labelit as the Centerline with its value. The median is used as the Centerline, ratherthan the mean, to neutralize the effect of any very large or very small values.
Step 6 - Construct the X-axis. Draw the X-axis 2 to 3 times as long as the Y-axis to provide enough space for plotting all of the data points. Enter all relevantmeasurements and use the full width of the X-axis.
NOTE: One of the strengths of a Run Chart is its readability, so don't risk makingit harder to interpret by putting too many measurements on one sheet. If youhave more than 40 measurements, consider continuing the chart on anotherpage.
Step 7 - Plot the data points and connect them with straight lines.
Step 8 - Provide a Title and a Legend. Give the chart a title that identifies theprocess you are investigating and compose a legend that tells:
The period of time when the data were collected
The location where the data were collected
The person or team who collected the data
How do we interpret a Run Chart?
Interpreting a Run Chart requires you to apply some of the theory of variation. Youare looking for trends, runs, or cycles that indicate the presence of special causes.But before we examine those features of Run Charts, a word about variation. Expectto see it. Just remember that process improvement activities are expected toproduce positive results, and these sometimes cause trends or runs, so the presenceof special causes of variation is not always a bad sign.
A Trend signals a special cause when there is a sequence of seven ormore data points steadily increasing or decreasing with no change indirection. When a value repeats, the trend stops. The example in Viewgraph 6shows a decreasing trend in lower back injuries, possibly resulting from a new"Stretch and Flex" exercise program.
When your Run Chart shows seven or more consecutive ascendingor descending data points, it is a signal that a special cause may beat work and the trend must be investigated.
RUN CHART VIEWGRAPH 5
How to Construct a Run Chart
Step 4 - Construct the Y-axis
Step 5 - Draw the Centerline
Step 6 - Construct the X-axis
Step 7 - Plot and connect the data points
Step 8 - Provide a title and a legend
RUN CHART VIEWGRAPH 6
Trend Example
Data taken from OSHA Reports andCA-1 forms by Bob Kopiske. Compiledand charted on 15 January 1994.
Signal of special cause variation:7 or more consecutive ascendingor descending points
Centerline = 23
1992 - 1993J F M A M J J A S O N D J F M A M J J A S O N D
0
4
8
12
16
20
24
28
32
36
40MONTHLY REPORTED BACK INJURIES
Nu
mb
er o
f In
juri
es
Stretch & Flex Started: January 1993
Basic Tools for Process Improvement
RUN CHART 7
Basic Tools for Process Improvement
8 RUN CHART
A Run consists of two or more consecutive data points on one side of thecenterline. A run that signals a special cause is one that shows nine ormore consecutive data points on one side of the centerline. In theexample in Viewgraph 7, you can see such a run occurring between 15 and 28March. Investigation revealed that new software was responsible for theincrease in duplication. This was corrected on 29 March with the introductionof a software "patch." Whenever a data point touches or crosses thecenterline, a run stops and a new one starts.
When your Run Chart shows nine or more consecutive data pointson one side of the centerline, it is an unusual event and should always be investigated.
A Cycle, or repeating pattern, is the third indication of a possible specialcause. A cycle must be interpreted in the context of the process thatproduced it. In the example in Viewgraph 8, a housing office charted data onpersonnel moving out of base housing during a four-year period anddetermined that there was an annual cycle. Looking at the 1992-1993 data,it's evident that there were peaks during the summer months and valleysduring the winter months. Clearly, understanding the underlying reasons whya cycle occurred in your process enables you to predict process results moreaccurately.
A cycle must recur at least eight times before it can be interpretedas a signal of a special cause of variation.
When interpreting a cycle, remember that trends or runs might also bepresent, signaling other special causes of variation.
NOTE: The absence of signals of special causes does not necessarily mean that aprocess is stable. Dr. Walter Shewhart suggested that a minimum of 100 observa-tions without a signal is required before you can say that a process is in statisticalcontrol. Refer to the Control Chart module for more information on this subject.
RUN CHART VIEWGRAPH 7
Run Example
Signal of special cause variation:9 or more consecutive data pointson the same side of the centerline
Data taken from manual daily countof incoming messages, entered onchecksheet by L. Zinke, NAVEURFleet Quality Office.
DUPLICATE MESSAGES
3130292827262524232221201918171615141312111098765432100
10
20
30
40
March 1994 - Weekdays only plotted
Nu
mb
er o
f M
essa
ges
Centerline = 15
RUN CHART VIEWGRAPH 8
Cycle Example
Signal of special cause variation:Repeating patterns
Data from Housing Office recordsfor 1992-93. Compiled and chartedon 1 FEB 94 by Gail Wylie.
J F M A M J J A S O N D J F M A M J J A S O N D0
10
20
30
40
HOUSING MOVE-OUTS
1992-1993
Centerline= 10
Nu
mb
er o
f U
nit
s
Basic Tools for Process Improvement
RUN CHART 9
Basic Tools for Process Improvement
10 RUN CHART
How can we practice what we've learned?
The following exercises are provided to help you sharpen your skills in constructing and interpreting Run Charts.
EXERCISE 1 has two parts based on this scenario:
Maintenance personnel in a helicopter squadron were receiving complaints from within the squadron and from its external customersbecause of valve overhaul backlogs which kept some aircraft grounded. To overcome the complaints and satisfy their customers, they realizedthey needed to reduce valve overhaul time without lessening reliability.
EXERCISE 1 - PART A: They collected data from their process for 14 days, placingtheir measurements in a table (Viewgraph 9). The table told them that it took thembetween 170 and 200 minutes to complete one valve overhaul. Although theworkload assignment for the 14-day period was 20 overhauls, their process allowedthem to complete only 1 per day. This meant that they were adding 6 valves to thebacklog every 2 weeks.
They decided to display their data in a Run Chart which they could analyze forsignals of special cause variation. To do this, they put their data in numerical orderand calculated the centerline as follows:
1 200 2 191 3 190 4 190 5 187 6 185 7 184Centerline (184 + 183) / 2 = 183.5 8 183 9 17510 17511 17512 17413 17314 170
Draw a Run Chart of the overhaul time for the 14 valves shown in Viewgraph 9.Viewgraph 10 is an answer key.
RUN CHART VIEWGRAPH 9
EXERCISE 1A DATAOverhaul TimesFirst 14 Valves
VALVE 1st 2nd 3rd 4th 5th 6th 7thTIME 174 190 185 170 191 187 183DAY 1 2 3 4 5 6 7
VALVE 8th 9th 10th 11th 12th 13th 14thTIME 175 200 175 173 184 190 175DAY 8 9 10 11 12 13 14
Basic Tools for Process Improvement
RUN CHART 11
RUN CHART VIEWGRAPH 10
EXERCISE 1A RUN CHARTFirst 14 Valves
Centerline = 183.5
Valve 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th 11th 12th 13th 14th
Time 174 190 185 170 191 187 183 175 200 175 173 184 190 175
Day 1 2 3 4 5 6 7 8 9 10 11 12 13 14
14131211109876543210160
170
180
190
200
210
Days
Min
ute
s
Basic Tools for Process Improvement
12 RUN CHART
Basic Tools for Process Improvement
RUN CHART 13
In the Run Chart constructed from the data in Part A of Exercise 1 (Viewgraph 10),there are no patterns or indications of special causes of variation. However, itappears that the process is not meeting customers’ expectations in terms of thenumber of valves that can be repaired within a given period of time.
The helicopter maintenance team realized that they needed to decrease the timerequired to overhaul each valve so that they could increase the number of overhauledvalves produced. Using tools such as Flowcharts, Pareto Charts, and Cause-and-Effect Diagrams, they analyzed their process and made some changes.
Basic Tools for Process Improvement
14 RUN CHART
EXERCISE 1 - PART B: The team collected data from the overhaul of the next 14valves and placed them in a table (Viewgraph 11). The table told them that the newrange of the overhaul process was 95 to 165 minutes.
Perform the centerline calculation for the two sets of data. Viewgraph 12 isan answer key.
Draw a new Run Chart showing the overhaul times for all 28 valves. Viewgraph 13 is an answer key.
Interpret the Run Chart. As you plot the data for all 28 valves, answer thesequestions:
What can we tell about the performance of this process?
What has occurred?
How do we know?
RUN CHART VIEWGRAPH 11
EXERCISE 1B DATAOverhaul Times
Second 14 Valves
VALVE 15th 16th 17th 18th 19th 20th 21stTIME 165 140 125 110 108 105 100DAY 15 16 17 18 19 20 21
VALVE 22nd 23rd 24th 25th 26th 27th 28thTIME 95 108 115 120 105 100 95DAY 22 23 24 25 26 27 28
Basic Tools for Process Improvement
RUN CHART 15
RUN CHART VIEWGRAPH 12
EXERCISE 1B
Centerline Calculations
Starts
Starts
Old Process
New Process
Ends
Ends
1200
2191
3190
4190
5187
6185
7184
8183
9175
10175
11175
12174
13173
14170
15165
16140
17125
18120
19115
20110
21108
22108
23105
24105
25100
26100
2795
2895
}
Centerline (184 + 183)/2 = 183.5
}
Centerline (108 + 108)/2 = 108
RUN CHART VIEWGRAPH 13
EXERCISE 1B RUN CHART
All 28 Valves
Valve Time Day
1st 2nd 3rd 4th174 190 185 170
1 2 3 4
5th 6th 7th 8th191 187 183 175
5 6 7 8
9th 10th 11th 12th200 175 173 184
9 10 11 12
13th 14th 15th 16th190 175 165 140
13 14 15 16
17th 18th 19th 20th125 110 108 105
17 18 19 20
21st 22nd 23rd 24th100 95 108 115
21 22 23 24
25th 26th 27th 28th120 105 100 95
25 26 27 28
TREND
28272625242322212019181716151413121110987654321060
80
100
120
140
160
180
200
220
240
Days
Min
ute
s
Centerline= 108
Centerline = 183.5
Basic Tools for Process Improvement
16 RUN CHART
Basic Tools for Process Improvement
RUN CHART 17
Looking at Viewgraph 12, you can see that there are now two distinct processes,each with its own centerline. The Run Chart plotted in Viewgraph 13 clearly showsthat the new process has significantly improved the throughput by reducing the valveoverhaul time.
Basic Tools for Process Improvement
18 RUN CHART
EXERCISE 2: A team was tasked with reducing the time required to launch theship's motor whaleboat during man-overboard drills. Their analysis identified startingthe motor as the factor having the greatest affect on time to launch. The teamcollected data on the time, measured in minutes, required to start the motor during 10drills using the current process. The data table they prepared is shown in Viewgraph14.
The team then brainstormed factors that might contribute to the amount of time it tookthe engine to start. Fuel injector fouling was cited numerous times. The team investigated and learned that the engine started promptly on four earlier occasionswhen the injectors were removed and cleaned or completely replaced. They thenused a technique know as “the five whys” to investigate further:
Q: Why were the injectors getting fouled?A: There was oil in the cylinders.
Q: Why was there oil in the cylinders?A: The piston rings were worn.
Q: Why were the piston rings worn?A: They were old and needed replacement.
Q: Why weren't they replaced?A: Spare parts were not readily available.
Q: Why weren't spare parts readily available?A: The engine manufacturer recently lost all stock of spare parts in
a devastating fire. Parts will be available in about two months.
The team was able to develop a plan for improvement based on the answers thismethod of inquiry produced. To deal with the fouling problem, they (1) initiated aschedule for cleaning or replacing the fuel injectors, (2) made long-term plans toreplace the worn piston rings, and (3) reviewed the maintenance schedule to ensurethat the rings would be replaced routinely at particular maintenance intervals. Afterthese changes in the process were instituted, the team collected data on the next 10drills. The data table they prepared is shown in Viewgraph 15.
Draw a Run Chart of the data from the 20 drills. Don’t forget to perform thecenterline calculations. An answer key is provided in Viewgraph 16.
Interpret your Run Chart.
Are there any signals of special cause variation?
If so, what are they?
RUN CHART VIEWGRAPH 14
EXERCISE 2 DATAMinutes to Start Engine
First 10 Drills
DRILL 1st 2nd 3rd 4th 5th
TIME 15.3 12.1 14.4 16.8 17.3
DRILL 6th 7th 8th 9th 10th
TIME 16.6 14.2 12.0 11.3 13.9
RUN CHART VIEWGRAPH 15
EXERCISE 2 DATAMinutes to Start Engine
Second 10 Drills
DRILL 11th 12th 13th 14th 15th
TIME 8.1 7.6 7.2 5.1 4.4
DRILL 16th 17th 18th 19th 20th
TIME 4.0 2.6 2.2 4.5 5.3
Basic Tools for Process Improvement
RUN CHART 19
RUN CHART VIEWGRAPH 16
EXERCISE 2 RUN CHARTMinutes to Start Engine
Drill 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Time 15 .3 12 .1 14 .4 16 .8 17.3 16 .6 14.2 12 .0 11.3 13 .9 8 .1 7.6 7.2 5 .1 4 .4 4.0 2.6 2.2 4.5 5.3
Drill
Centerline = 4.2
20
15
10
5
0
Min
ute
s
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Centerline = 14.3
TREND
Basic Tools for Process Improvement
20 RUN CHART
Basic Tools for Process Improvement
RUN CHART 21
When you interpret the Run Chart in Viewgraph 16, you’ll see that there is indeed asignal of a special cause of variation—a trend. This trend charts the dramaticreduction in the number of minutes required to start the engine during the second tendrills. The efforts of the team described in Exercise 2 were rewarded with animprovement in the process.
Basic Tools for Process Improvement
22 RUN CHART
REFERENCES:
1. Brassard, M. (1988). The Memory Jogger, A Pocket Guide of Tools forContinuous Improvement, pp. 30 - 35. Methuen, MA: GOAL/QPC.
2. Department of the Navy (November 1992). Fundamentals of Total QualityLeadership (Instructor Guide), pp. 6-52 - 6-56. San Diego, CA: Navy PersonnelResearch and Development Center.
3. Department of the Navy (September 1993). Systems Approach to ProcessImprovement (Instructor Guide), pp. 7-13 - 7-43. San Diego, CA: OUSN TotalQuality Leadership Office and Navy Personnel Research and DevelopmentCenter.
4. U.S. Air Force (Undated). Process Improvement Guide - Total Quality Tools forTeams and Individuals, pp. 52 - 53. Air Force Electronic Systems Center, AirForce Materiel Command.
RU
N C
HA
RT
VIE
WG
RA
PH
1
Wh
at is a Ru
n C
hart?
A line graph of data points plotted in
chronological order that helps detect
special causes of variation.
RU
N C
HA
RT
VIE
WG
RA
PH
2
Wh
y Use R
un
Ch
arts?
•U
nderstand process variation
•A
nalyze data for patterns
•M
onitor process performance
•C
omm
unicate process
performance
RU
N C
HA
RT
VIE
WG
RA
PH
3
1 TIT
LE
3 X-A
XIS
5 C
EN
TE
RL
INE
7 D
AT
A T
AB
LE
2 Y-A
XIS
4 D
AT
A P
OIN
T6 L
EG
EN
D
Parts o
f a Ru
n C
hart
Cen
terline = .3325
1
3
2
4
5
Durham
Bulls’
Team B
attingA
vg. recorded onM
on. of everyw
eek during the1994 season byR
ob Jackson,team
statistician
October 15, 19946
WE
EK
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
AV
G 300 333 325 332 340 345 350 340 341 345 349 354 350 344 333 325 318 305 298 306 310 315 310 318
7
2423
2221
2019
1817
1615
1413
1211
109
87
65
43
21
00.290
0.300
0.310
0.320
0.330
0.340
0.350
0.360
TEA
M B
ATTIN
G A
VE
RA
GE
(1994)
Weeks o
f the S
eason
Batting Average
RU
N C
HA
RT
VIE
WG
RA
PH
4
Ho
w to
Co
nstru
ct a Ru
n C
hart
Step
2 - Order data &
determine range
Step
3 - Calculate the m
edianR
AN
KA
VG
RA
NK
AV
GR
AN
KA
VG
1.298
9.318
17.341
2.300
10.325
18.344
3.305
11.325
ME
DIA
N:
19.345
4.306
12.332
(.332 + .333) / 220
.345
5.310
13.333
= .332521
.349
6.310
14.333
22.350
7.315
15.340
23.350
8.318
16.340
24.354
RA
NG
E: .354 - .298 = 0.56
RU
N C
HA
RT
VIE
WG
RA
PH
5
Ho
w to
Co
nstru
ct a Ru
n C
hart
Step
4 - Construct the Y
-axis
Step
5 - Draw
the Centerline
Step
6 - Construct the X
-axis
Step
7 - Plot and connect the data points
Step
8 - Provide a title and a legend
RU
N C
HA
RT
VIE
WG
RA
PH
6
Tren
d E
xamp
le
Data taken from
OS
HA
Reports and
CA
-1 forms by B
ob Kopiske. C
ompiled
and charted on 15 January 1994.
Sig
nal o
f special cau
se variation
:7 o
r mo
re con
secutive ascen
din
go
r descen
din
g p
oin
ts
Centerline = 23
1992 - 1993J
FM
AM
JJ
AS
ON
DJ
FM
AM
JJ
AS
ON
D0 4 8 12 16 20 24 28 32 36 40
MO
NTH
LY R
EP
OR
TED
BA
CK
INJU
RIE
SNumber of Injuries
Stretch &
Flex Started: January 1993
RU
N C
HA
RT
VIE
WG
RA
PH
7
Ru
n E
xamp
le
Sig
nal o
f special cau
se variation
:9 o
r mo
re con
secutive d
ata po
ints
on
the sam
e side o
f the cen
terline
Data taken from
manual daily count
of incoming m
essages, entered onchecksheet by L. Zinke, N
AV
EU
RFleet Q
uality Office.
DU
PLIC
ATE
ME
SS
AG
ES
3130
2928
2726
2524
2322
2120
1918
1716
1514
1312
1110
98
76
54
32
10
0
10 20 30 40
March
1994 - Weekd
ays on
ly plo
tted
Number of Messages
Centerline
= 15
RU
N C
HA
RT
VIE
WG
RA
PH
8
Cycle E
xamp
le
Sig
nal o
f special cau
se variation
:R
epeatin
g p
atterns
Data from
Housing O
ffice recordsfor 1992-93. C
ompiled and charted
on 1 FEB
94 by Gail W
ylie.
JF
MA
MJ
JA
SO
ND
JF
MA
MJ
JA
SO
ND
0
10 20 30 40
HO
US
ING
MO
VE
-OU
TS
1992-1993
Cen
terline
= 10
Number of Units
RU
N C
HA
RT
VIE
WG
RA
PH
9
EX
ER
CIS
E 1A
DA
TAO
verhau
l Tim
esF
irst 14 Valves
VA
LVE
1st2nd
3rd4th
5th6th
7thTIM
E174
190185
170191
187183
DAY
12
34
56
7
VA
LVE
8th9th
10th11th
12th13th
14thTIM
E175
200175
173184
190175
DAY
89
1011
1213
14
RU
N C
HA
RT
VIE
WG
RA
PH
10
EX
ER
CIS
E 1A
RU
N C
HA
RT
First 14 Valves
Cen
terline
= 183.5
Valve 1st 2n
d 3rd
4th 5th
6th 7th
8th 9th
10th 11th
12th 13th
14th
Tim
e 174 190 185 170 191 187 183 175 200 175 173 184 190 175
Day 1 2 3 4 5 6 7 8 9 10 11 12 13 14
1413
1211
109
87
65
43
21
0160
170
180
190
200
210
Days
Minutes
RU
N C
HA
RT
VIE
WG
RA
PH
11
EX
ER
CIS
E 1B
DA
TAO
verhau
l Tim
esS
econ
d 14 V
alvesV
ALV
E15th
16th17th
18th19th
20th21st
TIME
165140
125110
108105
100D
AY
1516
1718
1920
21
VA
LVE
22nd23rd
24th25th
26th27th
28thTIM
E95
108115
120105
10095
DA
Y22
2324
2526
2728
RU
N C
HA
RT
VIE
WG
RA
PH
12
EX
ER
CIS
E 1B
Centerline C
alculations
Starts
Starts
Old P
rocess
New
Process
Ends
Ends
12002191
31904190
51876185
71848183
917510175
11175
12174
13173
14170
15165
16140
17125
18120
19115
20110
21108
22108
23105
24105
25100
26100
27952895
}
Cen
terline (184 + 183)/2 = 183.5
}
Cen
terline (108 + 108)/2 = 108
RU
N C
HA
RT
VIE
WG
RA
PH
13
EX
ER
CIS
E 1B
RU
N C
HA
RT
All 28 V
alves
Valve
Tim
e D
ay
1st2n
d3rd
4th174
190185
1701
23
4
5th6th
7th8th
191187
183175
56
78
9th10th
11th12th
200175
173184
910
1112
13th14th
15th16th
190175
165140
1314
1516
17th18th
19th20th
125110
108105
1718
1920
21st22n
d23rd
24th100
95108
11521
2223
24
25th26th
27th28th
120105
10095
2526
2728
TRE
ND
2827
2625
2423
2221
2019
1817
1615
1413
1211
109
87
65
43
21
060 80
100
120
140
160
180
200
220
240
Days
Minutes
Cen
terline
= 108
Cen
terline = 183.5
RU
N C
HA
RT
VIE
WG
RA
PH
14
EX
ER
CIS
E 2 D
ATA
Min
utes to
Start E
ng
ine
First 10 D
rills
DR
ILL1st
2nd3rd
4th5th
TIME
15.312.1
14.416.8
17.3
DR
ILL6th
7th8th
9th10th
TIME
16.614.2
12.011.3
13.9
RU
N C
HA
RT
VIE
WG
RA
PH
15
EX
ER
CIS
E 2 D
ATA
Min
utes to
Start E
ng
ine
Seco
nd
10 Drills
DR
ILL11th
12th13th
14th15th
TIME
8.17.6
7.25.1
4.4
DR
ILL16th
17th18th
19th20th
TIME
4.02.6
2.24.5
5.3
RU
N C
HA
RT
VIE
WG
RA
PH
16
EX
ER
CIS
E 2 R
UN
CH
AR
TM
inutes to Start E
ngine
Drill 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Tim
e 15 .3 12 .1 14 .4 16 .8 17.3 16 .6 14.2 12 .0 11.3 13 .9 8 .1 7.6 7.2 5 .1 4 .4 4.0 2.6 2.2 4.5 5.3
Drill
Centerline = 4.2
201510 50
Minutes
1 2
3 4
5 6
7 8
910
1112
1314
1516
1718
1920
Centerline = 14.3
TRE
ND