The Perfect Circle Company manufactures bushings. Once each hour a sample of 125

Question

The Perfect Circle Company manufactures bushings. Once each hour a sample of 125 (n=125) finished bushings is drawn from the output; each bushing is examined by a technician. Those which fail are classified as defective; the rest are satisfactory. Here are data on ten consecutive samples taken in one week:

Sample no.

1

2

3

4

5

6

7

8

9

10

Defective

15

13

16

11

13

14

20

25

30

45

Calculate the UCL and LCL for a p chart based on the above data.

Sample no.

1

2

3

4

5

6

7

8

9

10

Defective

15

13

16

11

13

14

20

25

30

45

Explanation / Answer

Formulas for LCL and UCL for a p chart are –

UCL = p bar + 3 * (square root of (p bar (100 -p bar) /ni))

LCL = p bar - 3 * (square root of (p bar (100 -p bar) /ni))

CL = p bar = Summation of pi / summation of ni

= total number of defects / total amount of units in all the samples

Where pi is the number of non-conforming items and ni is the sample size

Hence CL = 100 (15+13+16+11+13+14+20+25+30+45) / 10 *125 = 16.16%

UCL = 16.16 + 3 * (square root of (16.16 (100 - 16.16)/ 125) = 16.16 + 3 * 3.29 = 26.03%

LCL = 16.16 - 3 * (square root of (16.16 (100 - 16.16)/ 125) = 16.16 - 3 * 3.29 = 6.29%

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