Basic Tools for Process Improvement
Module 9
RUN CHART
RUN CHART
1
Basic Tools for Process Improvement
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 in
which process events occurred. These data points represent measurements, counts,
or percentages of process output. Run Charts are used to assess and achieve
process 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 of
special causes), consistent, and predictable. Unlike other tools, such as Pareto
Charts or Histograms, Run Charts display data in the sequence in which they
occurred. This enables you to visualize how your process is performing and helps
you 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 help
you (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.
2
RUN CHART
Basic Tools for Process Improvement
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 1
Why Use Run Charts?
• Understand process variation
• Analyze data for patterns
• Monitor process performance
• Communicate process
performance
RUN CHART
RUN CHART
VIEWGRAPH 2
3
Basic Tools for Process Improvement
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 of
the 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 the
Centerline. (Finding the median value is Step 3 in constructing a Run Chart.)
6. Legend: Additional information that documents how and when the data were
collected 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 on
defining 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—the
difference 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 the
middle point in the list of measurements—the point that divides the series of data
in half.
If the count is an odd number, the middle is an odd number with an equal
number of points on either side of it. If you have nine measurements, for
example, the median is the fifth value.
If the count is an even number, average the two middle measurements to
determine the median value. For example, for 10 measurements, the median
is the average of the fifth and sixth values. To determine the average, just add
them together and divide by two.
4
RUN CHART
Basic Tools for Process Improvement
Parts of a Run Chart
TEAM BATTING AVERAGE (1994)
1
0.360
5
Batting Average
0.350
2
0.340
Centerline = .3325
0.330
Durham Bulls’
Team Batting
Avg. recorded on
Mon. of every
week during the
1994 season by
Rob Jackson,
team statistician
0.320
0.310
0.300
4
October 15, 1994
0.290
0
1
2
3
4
5
6
7
3
WEEK 1
AVG
2
3
4
5
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
6
Weeks of the Season
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
300 333 325 332 340 345 350 340 341 345 349 354
350 344 333
325 318
1 TITLE
3 X-AXIS
5 CENTERLINE
2 Y-AXIS
4 DATA POINT
6 LEGEND
305 298 306 310
315 310 318
7
7 DATA TABLE
RUN CHART
VIEWGRAPH 3
How to Construct a Run Chart
Step 2 - Order data & determine range
Step 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
RUN CHART
RUN CHART
VIEWGRAPH 4
5
Basic Tools for Process Improvement
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 label
it as the Centerline with its value. The median is used as the Centerline, rather
than 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 relevant
measurements 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 making
it harder to interpret by putting too many measurements on one sheet. If you
have more than 40 measurements, consider continuing the chart on another
page.
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 the
process 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. You
are 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. Expect
to see it. Just remember that process improvement activities are expected to
produce positive results, and these sometimes cause trends or runs, so the presence
of special causes of variation is not always a bad sign.
A Trend signals a special cause when there is a sequence of seven or
more data points steadily increasing or decreasing with no change in
direction. When a value repeats, the trend stops. The example in Viewgraph 6
shows 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 ascending
or descending data points, it is a signal that a special cause may be
at work and the trend must be investigated.
6
RUN CHART
Basic Tools for Process Improvement
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 5
Trend Example
MONTHLY REPORTED BACK INJURIES
40
Stretch & Flex Started: January 1993
Number of Injuries
36
32
28
24
Centerline
= 23
20
16
12
8
4
0
J
F M A M J
J
A S O N D J
F M A M J
J
A S O N D
1992 - 1993
Signal of special cause variation:
7 or more consecutive ascending
or descending points
RUN CHART
RUN CHART
Data taken from OSHA Reports and
CA-1 forms by Bob Kopiske. Compiled
and charted on 15 January 1994.
VIEWGRAPH 6
7
Basic Tools for Process Improvement
A Run consists of two or more consecutive data points on one side of the
centerline. A run that signals a special cause is one that shows nine or
more consecutive data points on one side of the centerline. In the
example in Viewgraph 7, you can see such a run occurring between 15 and 28
March. Investigation revealed that new software was responsible for the
increase in duplication. This was corrected on 29 March with the introduction
of a software "patch." Whenever a data point touches or crosses the
centerline, a run stops and a new one starts.
When your Run Chart shows nine or more consecutive data points
on 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 special
cause. A cycle must be interpreted in the context of the process that
produced it. In the example in Viewgraph 8, a housing office charted data on
personnel moving out of base housing during a four-year period and
determined that there was an annual cycle. Looking at the 1992-1993 data,
it's evident that there were peaks during the summer months and valleys
during the winter months. Clearly, understanding the underlying reasons why
a cycle occurred in your process enables you to predict process results more
accurately.
A cycle must recur at least eight times before it can be interpreted
as a signal of a special cause of variation.
When interpreting a cycle, remember that trends or runs might also be
present, signaling other special causes of variation.
NOTE: The absence of signals of special causes does not necessarily mean that a
process is stable. Dr. Walter Shewhart suggested that a minimum of 100 observations without a signal is required before you can say that a process is in statistical
control. Refer to the Control Chart module for more information on this subject.
8
RUN CHART
Basic Tools for Process Improvement
Run Example
DUPLICATE MESSAGES
Number of Messages
40
30
20
Centerline
= 15
10
0
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
March 1994 - Weekdays only plotted
Signal of special cause variation:
9 or more consecutive data points
on the same side of the centerline
Data taken from manual daily count
of incoming messages, entered on
checksheet by L. Zinke, NAVEUR
Fleet Quality Office.
RUN CHART
VIEWGRAPH 7
Cycle Example
HOUSING MOVE-OUTS
Number of Units
40
30
20
Centerline
= 10
10
0
J
F
M
A
M
J
J
A
S
O
N
D
J
F
M
A
M
J
J
A
S
O
N
D
1992-1993
Signal of special cause variation:
Repeating patterns
RUN CHART
RUN CHART
Data from Housing Office records
for 1992-93. Compiled and charted
on 1 FEB 94 by Gail Wylie.
VIEWGRAPH 8
9
Basic Tools for Process Improvement
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 customers
because of valve overhaul backlogs which kept some aircraft grounded.
To overcome the complaints and satisfy their customers, they realized
they needed to reduce valve overhaul time without lessening reliability.
EXERCISE 1 - PART A: They collected data from their process for 14 days, placing
their measurements in a table (Viewgraph 9). The table told them that it took them
between 170 and 200 minutes to complete one valve overhaul. Although the
workload assignment for the 14-day period was 20 overhauls, their process allowed
them to complete only 1 per day. This meant that they were adding 6 valves to the
backlog every 2 weeks.
They decided to display their data in a Run Chart which they could analyze for
signals of special cause variation. To do this, they put their data in numerical order
and calculated the centerline as follows:
1
200
2
191
3
190
4
190
5
187
6
185
7
184
Centerline (184 + 183) / 2 = 183.5
8
183
9
175
10
175
11
175
12
174
13
173
14
170
Draw a Run Chart of the overhaul time for the 14 valves shown in Viewgraph 9.
Viewgraph 10 is an answer key.
10
RUN CHART
Basic Tools for Process Improvement
EXERCISE 1A DATA
Overhaul Times
First 14 Valves
VALVE
1st
2nd
3rd
4th
5th
6th
7th
TIME
174
190
185
170
191
187
183
DAY
1
2
3
4
5
6
7
VALVE
8th
9th
10th 11th 12th 13th 14th
TIME
DAY
175
8
200
9
175
10
RUN CHART
RUN CHART
173
11
184
12
190
13
175
14
VIEWGRAPH 9
11
Basic Tools for Process Improvement
EXERCISE 1A RUN CHART
First 14 Valves
210
Minutes
200
190
Centerline
= 183.5
180
170
160
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Days
Valve 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th 11th 12th 13th 14th
Time
Day
RUN CHART
12
174 190 185 170 191 187 183 175 200 175
1
2
3
4
5
6
7
8
9
10
173 184 190
11
12
13
175
14
VIEWGRAPH 10
RUN CHART
Basic Tools for Process Improvement
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, it
appears that the process is not meeting customers’ expectations in terms of the
number of valves that can be repaired within a given period of time.
The helicopter maintenance team realized that they needed to decrease the time
required to overhaul each valve so that they could increase the number of overhauled
valves produced. Using tools such as Flowcharts, Pareto Charts, and Cause-andEffect Diagrams, they analyzed their process and made some changes.
RUN CHART
13
Basic Tools for Process Improvement
EXERCISE 1 - PART B: The team collected data from the overhaul of the next 14
valves and placed them in a table (Viewgraph 11). The table told them that the new
range of the overhaul process was 95 to 165 minutes.
Perform the centerline calculation for the two sets of data. Viewgraph 12 is
an 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 these
questions:
What can we tell about the performance of this process?
What has occurred?
How do we know?
14
RUN CHART
Basic Tools for Process Improvement
EXERCISE 1B DATA
Overhaul Times
Second 14 Valves
VALVE 15th 16th 17th 18th 19th 20th
TIME
165 140 125 110 108 105
DAY
15
16
17
18
19
20
21st
100
21
VALVE 22nd 23rd 24th 25th 26th 27th 28th
TIME
95
108 115 120 105 100
95
DAY
RUN CHART
RUN CHART
22
23
24
25
26
27
28
VIEWGRAPH 11
15
Basic Tools for Process Improvement
EXERCISE 1B
Centerline Calculations
Old Process
Starts
1
200
Ends
2
191
3
190
4
190
5
187
6
185
7
184
8
183
9
175
10
175
11
175
12
174
13
173
14
170
}
Centerline (184 + 183)/2 = 183.5
New Process
Starts
15
165
Ends
16
140
17
125
18
120
19
115
20
110
21
108
22
108
23
105
24
105
25
100
27
95
26
100
28
95
}
Centerline (108 + 108)/2 = 108
RUN CHART
VIEWGRAPH 12
EXERCISE 1B RUN CHART
All 28 Valves
240
220
200
Centerline = 183.5
Minutes
180
160
140
120
Centerline
= 108
100
80
60
0
1
2
3
4
5
6
7
8
2nd
190
2
3rd
185
3
RUN CHART
16
4th
170
4
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
Days
TREND
Valve 1st
Time 174
1
Day
9
5th
191
5
6th
187
6
7th
183
7
8th
175
8
9th
200
9
10th 11th 12th 13th 14th 15th 16th 17th 18th 19th 20th 21st 22nd 23rd 24th 25th 26th 27th 28th
95 108 115 120 105 100
95
175 173 184 190 175 165 140 125 110 108 105 100
10
11
12 13
14
15
16
17
18
19
20 21
22
23
24
25
26
27
28
VIEWGRAPH 13
RUN CHART
Basic Tools for Process Improvement
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 shows
that the new process has significantly improved the throughput by reducing the valve
overhaul time.
RUN CHART
17
Basic Tools for Process Improvement
EXERCISE 2: A team was tasked with reducing the time required to launch the
ship's motor whaleboat during man-overboard drills. Their analysis identified starting
the motor as the factor having the greatest affect on time to launch. The team
collected data on the time, measured in minutes, required to start the motor during 10
drills using the current process. The data table they prepared is shown in Viewgraph
14.
The team then brainstormed factors that might contribute to the amount of time it took
the engine to start. Fuel injector fouling was cited numerous times. The team
investigated and learned that the engine started promptly on four earlier occasions
when the injectors were removed and cleaned or completely replaced. They then
used 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 this
method of inquiry produced. To deal with the fouling problem, they (1) initiated a
schedule for cleaning or replacing the fuel injectors, (2) made long-term plans to
replace the worn piston rings, and (3) reviewed the maintenance schedule to ensure
that the rings would be replaced routinely at particular maintenance intervals. After
these changes in the process were instituted, the team collected data on the next 10
drills. 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 the
centerline 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?
18
RUN CHART
Basic Tools for Process Improvement
EXERCISE 2 DATA
Minutes 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 14
EXERCISE 2 DATA
Minutes 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
RUN CHART
RUN CHART
VIEWGRAPH 15
19
Basic Tools for Process Improvement
EXERCISE 2 RUN CHART
Minutes to Start Engine
TREND
20
Minutes
15
Centerline = 14.3
10
5
0
Centerline
= 4.2
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Drill
Drill
1
Time
15 .3
RUN CHART
20
2
3
12 .1 14 .4
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
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
VIEWGRAPH 16
RUN CHART
Basic Tools for Process Improvement
When you interpret the Run Chart in Viewgraph 16, you’ll see that there is indeed a
signal of a special cause of variation—a trend. This trend charts the dramatic
reduction in the number of minutes required to start the engine during the second ten
drills. The efforts of the team described in Exercise 2 were rewarded with an
improvement in the process.
RUN CHART
21
Basic Tools for Process Improvement
REFERENCES:
1. Brassard, M. (1988). The Memory Jogger, A Pocket Guide of Tools for
Continuous Improvement, pp. 30 - 35. Methuen, MA: GOAL/QPC.
2. Department of the Navy (November 1992). Fundamentals of Total Quality
Leadership (Instructor Guide), pp. 6-52 - 6-56. San Diego, CA: Navy Personnel
Research and Development Center.
3. Department of the Navy (September 1993). Systems Approach to Process
Improvement (Instructor Guide), pp. 7-13 - 7-43. San Diego, CA: OUSN Total
Quality Leadership Office and Navy Personnel Research and Development
Center.
4. U.S. Air Force (Undated). Process Improvement Guide - Total Quality Tools for
Teams and Individuals, pp. 52 - 53. Air Force Electronic Systems Center, Air
Force Materiel Command.
22
RUN CHART
What is a Run Chart?
A line graph of data points plotted in
VIEWGRAPH 1
chronological order that helps detect
special causes of variation.
RUN CHART
RUN CHART
Why Use Run Charts?
• Understand process variation
• Analyze data for patterns
• Monitor process performance
• Communicate process
performance
VIEWGRAPH 2
2
4
0.360
0.350
0.340
0.330
0.320
0.310
0.300
0.290
0
2
1
3
2
3
5
6
6
7
7
8
9
9
10
11
12
13
14
15
16
17
18
19
20
21
23
1
5
October 15, 1994
Durham Bulls’
Team Batting
Avg. recorded on
Mon. of every
week during the
1994 season by
Rob Jackson,
team statistician
Centerline = .3325
24
6
315 310 318
7
VIEWGRAPH 3
7 DATA TABLE
305 298 306 310
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Weeks of the Season
8
TEAM BATTING AVERAGE (1994)
4
3
5
22
Parts of a Run Chart
4
5 CENTERLINE
325 318
3 X-AXIS
6 LEGEND
350 344 333
1 TITLE
4 DATA POINT
300 333 325 332 340 345 350 340 341 345 349 354
2 Y-AXIS
RUN CHART
AVG
WEEK 1
Batting Average
6
5
4
3
2
1
RANK
.315
.310
.310
.306
.305
.300
.298
AVG
16
15
14
13
12
11
10
9
RANK
.340
.340
.333
.333
.332
.325
.325
.318
AVG
= .3325
(.332 + .333) / 2
MEDIAN:
24
23
22
21
20
19
18
17
RANK
.354
.350
.350
.349
.345
.345
.344
.341
AVG
How to Construct a Run Chart
Step 2 - Order data & determine range
Step 3 - Calculate the median
7
.318
RANGE: .354 - .298 = 0.56
VIEWGRAPH 4
8
RUN CHART
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
VIEWGRAPH 5
Step 8 - Provide a title and a legend
RUN CHART
RUN CHART
40
36
32
28
24
20
16
12
8
4
0
J
Trend Example
J
A S O N D J
J
A S O N D
Centerline
= 23
VIEWGRAPH 6
Data taken from OSHA Reports and
CA-1 forms by Bob Kopiske. Compiled
and charted on 15 January 1994.
F M A M J
Stretch & Flex Started: January 1993
MONTHLY REPORTED BACK INJURIES
F M A M J
1992 - 1993
Signal of special cause variation:
7 or more consecutive ascending
or descending points
Number of Injuries
40
30
20
10
0
0
RUN CHART
1
2
3
4
5
6
7
8
Run Example
DUPLICATE MESSAGES
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Centerline
= 15
VIEWGRAPH 7
Data taken from manual daily count
of incoming messages, entered on
checksheet by L. Zinke, NAVEUR
Fleet Quality Office.
March 1994 - Weekdays only plotted
Signal of special cause variation:
9 or more consecutive data points
on the same side of the centerline
Number of Messages
40
30
20
10
0
RUN CHART
J
F
M
A
M
J
S
O
N
D
J
F
M
A
M
J
HOUSING MOVE-OUTS
A
A
S
O
N
D
Centerline
= 10
VIEWGRAPH 8
Data from Housing Office records
for 1992-93. Compiled and charted
on 1 FEB 94 by Gail Wylie.
J
Cycle Example
J
1992-1993
Signal of special cause variation:
Repeating patterns
Number of Units
EXERCISE 1A DATA
1st
2nd
3rd
4th
5th
187
6
6th
183
7
7th
Overhaul Times
First 14 Valves
VALVE
191
5
VIEWGRAPH 9
14
170
4
13
185
3
12
190
2
11
174
1
10
TIME
DAY
9
9th 10th 11th 12th 13th 14th
200 175 173 184 190 175
8
VALVE 8th
TIME
175
DAY
RUN CHART
210
200
190
180
170
160
RUN CHART
Minutes
0
2
3
5
6
7
8
9
10
11
First 14 Valves
4
12
13
14
EXERCISE 1A RUN CHART
1
Days
Valve 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th 11th 12th 13th 14th
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Time 174 190 185 170 191 187 183 175 200 175 173 184 190 175
Day
Centerline
= 183.5
VIEWGRAPH 10
EXERCISE 1B DATA
Overhaul Times
Second 14 Valves
VALVE 15th 16th 17th 18th 19th 20th 21st
TIME
165 140 125 110 108 105 100
DAY
15
16
17
18
19
20
21
VIEWGRAPH 11
VALVE 22nd 23rd 24th 25th 26th 27th 28th
TIME
95 108 115 120 105 100 95
DAY
22
23
24
25
26
27
28
RUN CHART
2
191
18
120
EXERCISE 1B
5
187
6
185
20
110
7
184
21
108
8
183
22
108
9
175
23
105
10
175
24
105
}
Centerline (108 + 108)/2 = 108
19
115
Centerline (184 + 183)/2 = 183.5
}
17
125
4
190
25
100
11
175
26
100
12
174
Centerline Calculations
3
190
Old Process
Starts
1
200
16
140
New Process
Starts
15
165
RUN CHART
13
173
27
95
Ends
14
170
Ends
28
95
VIEWGRAPH 12
240
220
200
180
160
140
120
100
80
60
0
2nd 3rd
190 185
2
3
RUN CHART
Valve 1st
Time 174
Day
1
1
2
4th
170
4
TREND
Minutes
6th
187
6
4
5
7th
183
7
6
8th
175
8
7
9
11
12
13
14
15
Days
16
17
18
20
21
22
23
24
25
Centerline = 183.5
19
27
28
Centerline
= 108
10th 11th 12th 13th 14th 15th 16th 17th 18th 19th 20th 21st 22nd 23rd 24th 25th 26th 27th 28th
175 173 184 190 175 165 140 125 110 108 105 100
95 108 115 120 105 100
95
10
11
12 13
14
15
16
17
18
19
20 21
22
23
24
25
26
27
28
10
All 28 Valves
8
9th
200
9
26
EXERCISE 1B RUN CHART
3
5th
191
5
VIEWGRAPH 13
EXERCISE 2 DATA
TIME
DRILL
6th
15.3
1st
14.2
7th
12.1
2nd
12.0
8th
14.4
3rd
11.3
9th
16.8
4th
13.9
10th
17.3
5th
Minutes to Start Engine
First 10 Drills
DRILL
16.6
VIEWGRAPH 14
TIME
RUN CHART
EXERCISE 2 DATA
TIME
DRILL
16th
8.1
11th
2.6
17th
7.6
12th
2.2
18th
7.2
13th
4.5
19th
5.1
14th
5.3
20th
4.4
15th
Minutes to Start Engine
Second 10 Drills
DRILL
4.0
VIEWGRAPH 15
TIME
RUN CHART
20
15
10
5
1
1
0
Drill
15 .3
RUN CHART
Time
Minutes
2
2
5
7.6
17
18
4 .4
14
5 .1
13
16
7.2
12
15
Centerline = 14.3
14
12
13
11
11
10
10
9
9
13 .9
8
8
11.3
7
7
12 .0
6
6
14.2
Drill
5
16 .6
8 .1
17.3
19
15
4.0
17
2.2
4.5
18
5.3
19
Centerline
= 4.2
2.6
16
20
TREND
EXERCISE 2 RUN CHART
4
16 .8
4
Minutes to Start Engine
3
3
12 .1 14 .4
20
VIEWGRAPH 16