Question

> Use the following to answer questions 20-25: A company makes plastic cups. Four samples of 15 cups 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 Defectives 1 15 2 2 15 0 3 15 3 4 15 5 What is the proportion defective for Sample 1? 0 0.667 O 0.133 O 0.200 O 0.167 O 0.333

Answer 1

Sample	n	Number of defectives	Fraction Defective
1	15	2	0.1333
2	15	0	0
3	15	3	0.2
4	15	5	0.3333

(Q 20). Proportion defective for sample 1 = 0.133

(Q 21).

Total number of defects (p) = 2+0+3+5 = 10

Number of samples (m) = 4

Sample size = 15

р p= n.Xm

$\bar{p}=\frac{10}{15X4}$

$\bar{p}=0.1667$

Therefore, average proportion defective = 0.167

(Q 22).

Let Standard deviation = $\sigma$

$\sigma=\sqrt{\frac{\bar{p}(1-\bar{p})}{n}}$

$\sigma=\sqrt{\frac{0.167(1-0.167)}{15}}$

$\sigma=0.0963$

Standard deviation = 0.0963

(Q 23).

Given vale of alpha risk = 3%

Confidence level = 100% - 3% = 97%

Value of Z corresponding to confidence level of 97% is 2.17

Therefore, value of Z = 2.17

(Q 24).

$UCL = \bar{p}+Z.\sigma$

UCL = 0.167 + (2.17 × 0.0963)

UCL = 0.3760

$LCL = \bar{p}-Z.\sigma$

LCL = 0.167 - (2.17 × 0.0936)

LCL = -0.036

Since LCL can't be negative, therefore LCL = 0

LCL = 0 ; UCL = 0.3760

(Q 25.)

ANSWER: SAMPLE 4

Given UCL = 0.30

LCL = 0

It can be seen that fraction defective for sample 4 is 0.333 which is outside the control limit range given. Therefore, sample 4 is out of control.