Question

Tom is the quality control manager for the company XYZ. XYZ recently received some complaints about its product D's quality and the general manager Steve requested Tom to investigate it. To gain a better understanding of the production process, Tom decided to use p-chart to monitor and identify the assignable cause variations. For the next 10 working days, Tom collected 10 samples (each of the size 300 units) and found the following number of defects, 4, 6, 0, 1, 3, 5, 10, 3, 2, 3.

a. What is the defect rate for sample 2? Ignore the percentage sign, and round your answer to the nearest integer. For example, if your answer is 12.34%, input 12.
Your answer is Blank 1.
b. What is p-bar? Ignore the percentage sign, and round your answer to two decimals. For example, if your answer is 12.34%, input 12.34. (Note that this is different from question a.)
Your answer is Blank 2.
c. What is sigma? Ignore the percentage sign, and round your answer to two decimals. For example, if your answer is 12.34%, input 12.34.
Your answer is Blank 3.
d. What is upper control limit UCL for this p-chart? Ignore the percentage sign, and round your answer to two decimals. For example, if your answer is 12.34%, input 12.34.
Your answer is Blank 4.
e. What is lower control limit LCL? (If LCL is negative, input 0) Ignore the percentage sign, and round your answer to two decimals.
f. How many outlier(s) is(are) identified? Round your answer to the nearest whole number. For example, if the answer is 3.12, input 3.

Answer 1

Total number of items = 300 units per sample x 10 samples = 3000 units

Total number of defects = 4 + 6 + 0+1+3+5 + 10 + 3 + 2+ 3 = 37

a) Defect rate for sample 2 = 6/300 x 100= 2%

b) Pbar = Total number of defects / Total number of items = 37/3000 x 100 = 0.0123 x 100 = 1.23%

c) Sigma = Square root ( Pbar in fraction term x ( 1 – Pbar in fraction term)/ n)

= Square root ( 0.0123 x ( 1 – 0.0123)/300)

= Square root ( 0.0123 x 0.9877/300)

= 0.00636

= 0.636 % ( or 0.64% rounded to 2 decimal places)

d) Upper control limit ( in % terms)

= pbar + 3 x sigma

= 1.23 + 3 x 0.64

= 1.23 + 1.92

= 3.15%

e) Lower control limit ( in terms of percentage)

=higher of ( 0, Pbar – 3 x Sigma)

= higher of ( 0, 1.23 – 1.92 )

= Higher of ( 0, - 0.69)

= 0

f) Outliers will be those sample defectives which will be outside control limit range of 0 to 3.15%

Percentage defectives in 10 samples as follows :

Number of defects

Percentage defects in sample of 300

4

1.33

6

2

0

0

1

0.33

3

1

5

1.66

10

3.33

3

1

2

0.66

3

1

The outlier is the sample with 10 defects and there is only 1 outlier

Step-by-step explanation: