This chapter is about different types of control charts for the discrete variable.


C-Chart

C-chart works with discrete variables and sample sizes of same size. So the data needed to plot in excel our graph are those in table1. In this case, we are working on the total number of defects on ten samples of size 100. The total number means you can have more than one defect, for example, and you count all.

# Sample12345678910
Defects (C)109812111099813
Sample Size100100100100100100100100100100
Averege (C bar)9,9 9,9 9,9 9,9 9,9 9,9 9,9 9,9 9,9 9,9
UCL19,3 19,3 19,3 19,3 19,3 19,3 19,3 19,3 19,3 19,3
LCL0,5 0,5 0,5 0,5 0,5 0,5 0,5 0,5 0,5 0,5
Table1 – Data

We calculated the UCL, CentralLine, and LCL with the formula in image1. Note that C is just the number of defects in a sample. C Bar is the arithmetic average on all the pieces.

image1 - C-Chart formula
image1 – C-Chart formula

The C-Chart plotted in excel is the one in image2.

Image2 - C-Chart
Image2 – C-Chart

U-Chart

U-chart works with discrete variables and sample sizes of different sizes. So the data needed to plot in excel our graph are those in table2. In this case, we are working on the total number of defects on ten samples of different sizes. The total number means you can have more than one defect, for example, and you count all.

# Sample12345678910
Defects (U)21335511225133221118
Sample Size10012011013012511811713110195
Fraction (U/size)0,210,280,50,080,180,430,280,170,110,19
Averege (U)0,2 0,2 0,2 0,2 0,2 0,2 0,2 0,2 0,2 0,2
UCL0,4 0,4 0,4 0,4 0,4 0,4 0,4 0,4 0,4 0,4
LCL0,1 0,1 0,1 0,1 0,1 0,1 0,1 0,1 0,1 0,1
Average size of sample114,7
Table2 – Data

We calculated the UCL, CentralLine, and LCL with the formula in image3. Note that now we doesn’t work with the number of defect, but with the fraction of deffects in the sample size.

 image4 - U-Chart formula
image3 – U-Chart formula

The U-Chart plotted in excel is the one in image4.

Image4 - U-Chart
Image4 – U-Chart

NP-Chart

NP-chart works with discrete variables and sample sizes of same size. So the data needed to plot in excel our graph are those in table3. In this case, we are working to classify that something has been defected and not the defect number.

# Sample12345678910
Defects (np)21335511225133221118
Sample Size500 500 500 500 500 500 500 500 500 500
Averege24,8 24,8 24,8 24,8 24,8 24,8 24,8 24,8 24,8 24,8
UCL39,4 39,4 39,4 39,4 39,4 39,4 39,4 39,4 39,4 39,4
LCL10,2 10,2 10,2 10,2 10,2 10,2 10,2 10,2 10,2 10,2
Table3 – Data

 We calculated the UCL, CentralLine, and LCL with the formula in the image5. Note that NP, in this case, is the number of objects classified as defects, and we also used the sample size even if it is fixed.

Image5 - Np-chart formua
Image5 – NP-chart formula

In image6 we have the NP-Chart plotted in excel.

Image6 - NP-Chart
Image6 – NP-Chart

We calculated the UCL, CentralLine, and LCL with the formula in the image7

P-Chart

P-chart works with discrete variables and sample sizes of different sizes. So the data needed to plot in excel our graph are those in table4. In this case, we are working to classify that something has been defected and not the defect number.

# Sample12345678910
Defects (P)21333911223833221118
Sample Size10012011013012511811713110195
Fraction (P/size)0,210,280,350,080,180,320,280,170,110,19
Averege (P)0,2 0,2 0,2 0,2 0,2 0,2 0,2 0,2 0,2 0,2
UCL0,3 0,3 0,3 0,3 0,3 0,3 0,3 0,3 0,3 0,3
LCL0,1 0,1 0,1 0,1 0,1 0,1 0,1 0,1 0,1 0,1
Average size of sample114,7
Table4 – Data

In image7 we can look at the formula.

Image7 - P-Chart formula
Image7 – P-Chart formula

In image8, we have the plot of it on excel.

Image8 - P-Chart
Image8 – P-Chart

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