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Control chart for Number of Defects (C-chart)

 Statistical quality control.:


Control  chart for Number of Defects (C-chart)

A C chart is a one type of chart in Statistical quality control (SQC)  to monitor the count or frequency of nonconforming items. it is particularly  used when dealing with discrete data or attribute data, where the outcomes are classified in to defective or non defectives or (conforming or nonconforming).

The Primary use of c chart is to monitor the number of defects or nonconforming items in a production or manufacturing process. it helps to identify the the trend of defectives in a process to take decision and action regarding the production process. this allows the continuous improvement in the production process. 

A C chart is also useful   for tracking and monitoring the occurrence of  defects over  a time. it allows to identify periods or specific factors that contributes to increasing number of  defects.

The C chart helps to evaluate the effectiveness of process optimise and guide to decision making in achieving the better quality outcome. 

Control chart for Number of Defects. (C- chart)

If we are interested in a number of defects in unit that makes the unit useless. The number of defects in items are in certain range, then item is acceptable, otherwise we rejecting the items. for this we used c-chart. In this chart the number of defect denotes as 'C'. 

For constructing the C-chart follow steps as

Step I:- firstly we finding the arithmetic mean of number of defects. And is calculated as 

         c̄ = ( Total number of defects) /(number of items are inspected)

Where the number of items are inspected is N.

Step II :- The control limits are 

Central line = c̄ 

Upper Central Line = c̄ +3 √ c̄ 

Lower Central Limit = c̄ -3√ c̄ 

Using this control limit we draw the control chart for number of defect. I.e.  C-chart

The C-chart is plotted as number of defect against sample number. 

we see the example on c chat to better understanding to construction of  C- chart. it is simple to construct a c chart for that first we find out the control limit that are central line, upper central line, lower central line. then plotting on graph paper. the number of defectives on x- axis and sample number on y- axis. then drawing the three line of control limit and then plotting point of number of defectives.  

Where C Chart is Used & Its Applications

 What is a C Chart?

·         A C chart (Count chart) is a type of control chart used to monitor the number of defects or nonconformities in a constant-size sample.

·         It is based on the Poisson distribution, which is suitable for count data (not measurements).

 

Where C Charts Are Used

C charts are used in any process where defects or nonconformities are counted, not measured.

 

 Applications of the C Chart

1. Manufacturing Industry

·         Tracking the number of defects on products such as scratches, cracks, or missing parts.

·         Example: Counting the number of surface defects on a batch of painted car doors.

 2. Packaging and Bottling

·         Monitoring the number of damaged or misprinted packages in a production run.

·         Example: Counting misaligned labels or broken seals in a batch of bottles.

 3. Quality Control Inspection

·         Counting nonconformities found during product inspections.

·          Example: Number of defective items in 100 inspected units.

 4. Printing Industry

·         Counting printing errors like smudges, misprints, or color mismatches.

·          Example: Number of misprints in a batch of 500 brochures.

 5. Healthcare

·         Monitoring the number of medical errors or hospital-acquired infections in a fixed number of patients or procedures.

·          Example: Number of post-surgery infections per 100 surgeries.

 6. Service Industry

·         Tracking errors in processes, such as the number of incorrect invoices, data entry errors, or complaints.

·         Example: Number of incorrect bills generated in a batch of 200 transactions.

 7. Automotive Industry

·         Counting assembly line defects in vehicles or parts.

·         Example: Number of missing bolts or welding defects in a batch of chassis.

 

C charts are used to monitor the count of defects in a fixed sample size and are applicable across industries where quality is tracked by counting errors or flaws.

 

Example 1. Construct control chart for following data. 

Sample no.

1

2

3

4

5

6

7

8

9

Number of defects

9

8

5

8

7

6

5

7

10

Solution :- in the table they gives the number of defects then for this type of data we used c-chart, for construction of C- chart firstly calculating the control limits for the 

     c̄    = ( Total number of defects) /(number of items are inspected)

    c̄    = 65 / 9 = 7.22

Central line =  c̄  = 7.22

Upper Central Line = c̄ +3 √ c̄  = 7.22 + 3 x √ 7.22 = 15.28

Lower Central Limit =  c̄ -3√ c̄ = 7.22 - 3 x √ 7.22 = -0.84 = 0

( the lower limit is consider as zero because the number of defect are always positive )

the control chart is C- chart

C-chart 


here all the point lies under the control limits the process is in control.

 The c chart is a valuable tool in a Quality control and process improvement efforts. it enables organizations to monitor the occurrence of defectives items, to take appropriate action to maintain the quality and the performance of process, using this chart it helps to organization to improve  the quality and reducing the defective items, to product meets to customer expectations. 

solve the following example. If you have any questions or doubts, feel free to ask

Expt. No. 8                                                                                      Date:    /    / 2025

Title: Application of c chart.

Q.1 A company manufactures LED bulbs. Each day, a randomly selected bulb is inspected for visible surface defects. The number of defects found each day over 20 days is recorded below

Day’s

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

No. of Defects

3

2

4

3

5

6

3

2

4

3

3

4

6

5

4

use a c-chart to check whether the manufacturing process is under control or not.

Q.2 A printing company inspects 1 printed sheet per day for printing defects. The number of defects per sheet over 20 days is recorded below.

Day’s

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

No. of Defects

1

3

0

4

2

5

1

2

6

3

2

4

1

2

5

use a c-chart to check whether the process is under control or not.

Q.3 A metal fabrication company checks 1 metal sheet per day for surface defects like scratches, dents, or holes. The inspection is done for 30 days, and the number of defects per sheet is recorded below,

Day’s

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

No. of Defects

4

5

6

4

3

5

6

3

4

5

2

4

6

3

5

Day’s

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

No. of Defects

2

4

5

3

7

8

6

7

5

6

4

9

6

3

5

use a c-chart to check whether the process is under control or not.

Q.4 A factory produces plastic bottles. Each day, one bottle is randomly selected and inspected for surface defects like bubbles, scratches, or deformities. The number of defects found each day is recorded over 24 days.

Day’s

1

2

3

4

5

6

7

8

9

10

11

12

No. of Defects

3

4

2

5

3

4

3

4

2

6

5

4

Day’s

13

14

15

16

17

18

19

20

21

22

23

24

No. of Defects

3

2

3

4

7

5

4

3

2

3

5

4

use a c-chart to check whether the process is under control or not.

 


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