Question

Problem 13-7 Ten samples of 15 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 n NUMBER OF DEFECTIVE ITEMS IN THE SAMPLE

1 15 1

2 15 0

3 15 0

4 15 0

5 15 2

6 15 0

7 15 3

8 15 1

9 15 0

10 15 3

a. Determine the p− , Sp, UCL and LCL for a p-chart of 95 percent confidence (1.96 standard deviations). (Leave no cells blank - be certain to enter "0" wherever required. Round your answers to 3 decimal places.)

b. What comments can you make about the process? Process is in statistical control Process is out of statistical control

Answer 1

Solution:

Number of samples (N) = 10

Sample size (n) = 15

(a) P-bar = Number of defects / Total Number of observations

P-bar = 10 / (10 x 15)

P-bar = 10 / 150

P-bar = 0.067

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

Sp = SQRT [0.067 x (1 - 0.067)] / 15

Sp = 0.065

UCL = P-bar + (Z x Sp)

UCL = 0.067 + (1.96 x 0.065)

UCL = 0.194

LCL = P-bar - (Z x Sp)

LCL = 0.067 - (1.96 x 0.065)

LCL = -0.060 or 0 (Number of defects cannot be negative)

LCL = 0

(b) For each of the given defects, defect rate is calculated as,

Number of defects = 1, P-bar = 1/15 = 0.067

Number of defects = 2, P-bar = 2/15 = 0.133

Number of defects = 3, P-bar = 3/15 = 0.200

Process is out of statistical control, since for number of defects = 3, the defective rate P-bar (0.200) lies outside the calculated values of UCL (0.194) and LCL (0).