Question

Compute & Co. uses a P-Chart to monitor the quality of their seat cushions. Each day they inspect 30 seat cushions. Below are the number of defective seats found over the last 10 days. With this information, what would be the LCL_p, and UCL_p of a P-Chart with Z=3?

Sample	Number of defective seats
1	1
2	3
3	4
4	1
5	5
6	2
7	5
8	2
9	3
10	4

Group of answer choices

0.1643: 0.3233

0.765; 0.9845

0; 0.2643

0.9826; 0.26433

2.233; 3.777

Answer 1

Solution:

Number of samples (N) = 10

Sample size (n) = 30

P-bar = Number of defective seats / Total Number of observations

P-bar = (1 + 3 + 4 + 1 + 5 + 2 + 5 + 2 + 3 + 4) / (10 x 30)

P-bar = 30 / 300

P-bar = 0.1

Standard deviation of P-bar (Sp) is calculated as,

Sp = SQRT [P-bar x (1 - P-bar)] / n

Sp = SQRT [0.1 x (1 - 0.1)] / 30

Sp = 0.05477

Lower Control Limit (LCLp) and Upper Control Limit (UCLp) of the P-chart are calculated as below:

LCLp = P-bar - (Z x Sp)

LCLp = 0.1 - (3 x 0.05477)

LCLp = -0.064 or 0 (Number of defective seats cannot be negative)

LCLp = 0

UCLp = P-bar + (Z x Sp)

UCLp = 0.1 + (3 x 0.05477)

UCLp = 0.2643

Answer: 0, 0.2643