solution

Ten samples of 20 parts each were taken from an ongoing process to establish a p-chart for control. The samples and the number of defectives in each are shown in the following table:

Sample Number of defective Proportion Defective

items in the sample

1 5

2 2

3 0

4 0

5 0

6 3

7 0

8 4

9 2

10 0

16

Develop a p-chart for a standard deviation of 1.96 (Z=1.96)

What are the upper control limit (UCL) & lower control limit (LCL) and what points are “out of control”?

FORMULAS

Proportion of defectives = Number of defective items in the sample .
Sample Size (that is the number of parts in each sample)

p bar = total defectives .
total overall number of observations

Sp = Square Root [(p bar) (1 – p bar) / n]

UCL = p bar + Z (Sp)

LCL = p bar – Z (Sp)

Multiple Choice

• UCL = 0.9

  LCL = 0.01

  Everything is “out of control” for being above the UCL

• UCL = 0.1

  LCL = 0.03

  Samples 1 and 2 are out of control since they are below the LCL

• UCL = 0.19

  LCL = -0.039

  Samples 1 and 8 are “out of control” since they are above the UCL

• UCL = 0.08

  LCL = 0.06

  Everything is under control

• A different answer (not included in the options)

• UCL = 1.1

  LCL = 0.1

  Samples 3 and 4 are out of control for being above the UCL and below the LCL respectively

• UCL = 0.9

  LCL = 0.01

  Everything is “out of control” for being below the LCL