Develop a Count Chart

Amanda Christensen, BYU MBA Class of 2009

Professor: Dr. Tom Foster

What Will Be Covered• Communicate Number of Defects

– Collect Data– Graph Data

• Find Nonrandom Patterns– Calculate the Average– Determine Limits

• An Example and an Exercise

The Tool Defined• C Chart Graphs Number of Defects

– Clean Presentation

• Determines Whether a Process is in Control– Visual Determination

Brainstorming Exercise

How can this tool be used in your organization?

Communicate Number of Defects• Collect Data

– Number of Defects per Unit– Number of Defects per Inspection Lot

• Graph Data– X-Axis Represents Number of Inspected

Products– Y-Axis Represents Number of Defects

Find Nonrandom Patterns• Calculate the Average

– Find Average Number of Defects per Unit or Lot (C Bar)

– Add Line to Graph Representing C Bar. This is the Central Line.

Find Nonrandom Patterns• Determine Limits

– Find Standard Deviation of Data– Upper Control Limit

• UCL = c bar + 3*(√c bar)

– Lower Control Limit• LCL = c bar – 3 *(√c bar)

• Add Limit Lines to the Graph

Next Steps• Determine if Process is Random or

Nonrandom

• Evaluate Process if Necessary

Collide Shoes

A Real World Example

Collect Data

Record Date and Number of Defects per Shoe

11-Oct6

10-Oct1

9-Oct2

8-Oct4

7-Oct7

6-Oct6

5-Oct2

4-Oct2

3-Oct3

2-Oct5

1-Oct2

DateDefects

Graph Data

C Chart - Collide Shoes

012345678

10/1

/200

7

10/8

/200

7

10/1

5/20

07

10/2

2/20

07

10/2

9/20

07

11/5

/200

7

11/1

2/20

07

11/1

9/20

07

Date

Def

ects

Calculate the Average• Find C Bar• Add C Bar, Central Line, to Graph

C Chart - Collide Shoes

012345678

10/1/

2007

10/8/

2007

10/15

/2007

10/22

/2007

10/29

/2007

11/5/

2007

11/12

/2007

11/19

/2007

Date

Def

ects

Determine Limits• Find Standard Deviations, Then Use

Formulas:• UCL = c bar + 3*(√c bar)• LCL = c bar – 3 *(√c bar)

• Standard Deviation = 1.53• UCL = 7.53• LCL = -1.64

Find Nonrandom PatternsC Chart - Collide Shoes

012345678

10/1

/200

7

10/8

/200

7

10/1

5/20

07

10/2

2/20

07

10/2

9/20

07

11/5

/200

7

11/1

2/20

07

11/1

9/20

07

Date

Defe

cts

Gentry Bolts

An Exercise

Collect Data• Record Number

Inspected and Number Failed

10700

5450

10300

91000

4500

7800

6600

# Failed# Inspected

Graph the Data

Gentry GraphC Chart - Gentry Bolt

0

2

4

6

8

10

12

600 800 500 1000 300 450 700

# Failed

Next Steps• Calculate the Average• Find Standard Deviation• Calculate Upper and Lower Limits

• UCL = c bar + 3*(√c bar)• LCL = c bar – 3 *(√c bar)

Graph the Central Line and UCL and LCL

Find Nonrandom Patterns

C Chart - Gentry Bolt

0

2

4

6

8

10

12

14

16

600 800 500 1000 300 450 700

# Failed

Central Line

UCL

Summary• Communicate Number of Defects

– Collect Data– Graph Data

• Find Nonrandom Patterns– Calculate the Average– Determine Limits

Readings List• Calculating the (Almost) Exact Control

Limits for a C-Chart. By: Kittlitz Jr., Rudolf G.. Quality Engineering, Jul-Sep2006, Vol. 18 Issue 3, p 359-366, 8 p.

• Statistical Methods for SPC & TQM. By: Derek Bissell.

• Statistical Process Control and Quality Improvement. By: Gerald M. Smith