Question

Question 1. How many statements are true?

(A) 0   (B) 1   (C) 2   (D) 3   (E) 4

Statement 1. The P and C charts are for attributes and the M and R charts are for variables.

Statement 2. The upper control limit is three standard deviations of the mean above the center line and the lower control limit is three standard deviations of the mean below the mean of the quality characteristic.

Statement 3. The sample size for the experiment that determines the estimates of the parameters can be different than the sample size used to construct the M-chart, the R-chart, the P-chart, and the C-chart.

Statement 4. The P chart monitors the proportion of an attribute quality characteristic which the C chart monitors the count of an attribute quality characteristic.

Questions 2-3

The following experiment was carefully designed and performed on a process under control. A random sample of 80 is drawn for each sample and the number of attributes is recorded.

Sample #:	1	2	3	4	5	6
Attributes:	4	3	5	3	4	5

Question 2. What is the upper control limit, center line, and lower control limit for a P-chart with n=96? (A) ( 0.000 , 0.050 , 0.140 ) (B) ( -0.040 , 0.050 , 0.140 ) (C) ( 0.020 , 0.050 , 0.080 ) (D) ( -0.023 , 0.050 , 0.123 ) (E) None of the above Question 3. What is the upper control limit, center line, and lower control limit for a C-chart with n=176? (A) ( 0.000 , 1.000 , 2.000 ) (B) ( -2.000 , 4.000 , 4.073 ) (C) ( 0.000 , 1.000 , 4.000 ) (D) ( -2.000 , 1.000 , 4.000 ) (E) None of the above

Questions 4-5

Destructive sampling was performed measuring the life of six batteries in hours.

		Sample A	Sample B	Sample C
	Measurement #1	171	173	187
	Measurement#2	185	187	201

Question 4. What is the upper control limit, center line, and lower control limit for an M-chart? (A) ( 153.920 , 184 , 214.080 ) (B) ( 157.680 , 184 , 210.320 ) (C) ( 169.678 , 184 , 198.322 ) (D) ( 173.794 , 184 , 194.206 ) (E) None of the above Question 5. What is the upper control limit, center line, and lower control limit for an R-chart? (A) ( 0 , 14 , 36.050 ) (B) ( 0 , 14 , 31.948 ) (C) ( 0 , 16 , 52.272 ) (D) ( 0 , 14 , 45.738 ) (E) None of the above

Answer 1

Q1. (C) 2

Following two statements are true:

Statement 2. The upper control limit is three standard deviations of the mean above the center line and the lower control limit is three standard deviations of the mean below the mean of the quality characteristic.

Statement 3. The sample size for the experiment that determines the estimates of the parameters can be different than the sample size used to construct the M-chart, the R-chart, the P-chart, and the C-chart.

Q2.

(D) (

-0.023

,

0.050

,

0.123

)

Total number of defects = 4+3+5+3+4+5 = 24

Total number of observations = 80*6 = 480

Average Proportion defective, p? = 24/480 = 0.050

Standard deviation, s = SQRT(p? (1-p?)/n) =  SQRT(0.05*(1-0.05)/80) = 0.0244

Lower Control Limit = p? - 3*s =0.050 - 3*0.0244 = -0.023

Upper Control Limit = p? + 3*s =0.050 + 3*0.0244 = 0.123

Q3. Control limits of c-chart are following