run chart - balanced scorecard institute

38
Basic Tools for Process Improvement RUN CHART 1 Module 9 RUN CHART

Upload: others

Post on 12-Feb-2022

2 views

Category:

Documents


0 download

TRANSCRIPT

Basic Tools for Process Improvement

RUN CHART 1

Module 9

RUN CHART

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