Question 1
For mean of all sample standard deviations=0.0094 and the sample size= 5, what will be the estimate of process standard deviation?
A. 100
B. 0.01
C. 0.0094
D. 94
View Answer
Answer: Option B
Explanation:
We know that estimate of the process standard deviation,\(\hat{\sigma} = \frac{\bar{s}}{c_4} \) Here for sample size=5, c4=0.94, and s = 0.0094, we get σ = 0.01.
Question 2
If the sample standard deviations for a process are 1.567, 1.429, 1.323, 1.525, 1.989, 1.457, what will be the mean standard deviation?
A. 1.548
B. 1.858
C. 1.327
D. 1.967
View Answer
Answer: Option A
Explanation:
The mean standard deviation of the sample standard deviations is given by,\(\bar{s} = \frac{1}{m} \sum_{i=1}^m s_i\) Where si denotes the standard deviation of ith sample. Calculating the mean using the above formaula gives, s=1.548.
Question 3
Process standard deviation is the mean of all sample standard deviations.
A. TRUE
B. FALSE
View Answer
Answer: Option B
Explanation:
It is not necessary that process standard deviation is the mean of all sample deviations. This is because there is some inherent and natural variability in the process. This may or may not appear in every sample.
Question 4
The center line of the s chart denotes ____
A. Standard deviation of the process
B. Mean of m number of standard deviations, where m is the number of samples
C. c4 s
D. B5 s
View Answer
Answer: Option B
Explanation:
The center line of the s chart denotes the mean of m number of standard deviations, where m is the number of samples. This is the desired value of the sample standard deviation for the process to be in control.
Question 5
The center line of the s chart with a standard value for σ given, denotes the value of _____
A. B6 σ
B. c4 σ
C. B5 σ
D. c5 σ
View Answer
Answer: Option B
Explanation:
The center line of the s chart with a standard value for σ given, denotes the value equal to,CL=B6 σ
Question 6
What does “s” denote in x bar and s charts?
A. Sample
B. Sample standard deviation
C. Process standard deviation
D. Statistics
View Answer
Answer: Option B
Explanation:
Process standard deviation in the x bar and s charts, is estimated directly instead of indirectly through the use of Range as in x bar and R charts. Here “s” denotes the sample standard deviation.
Question 7
What is an unbiased estimator of unknown variance of a probability distribution?
A. Sample mean
B. Sample standard deviation
C. Sample variance
D. Sample range
View Answer
Answer: Option C
Explanation:
If σ2 is the unknown variance of a probability distribution, then an unbiased estimator must be used to estimate σ2. In this case, sample variance is used as the required estimator.
Question 8
What is the estimator of standard deviation in the x bar and R charts?
A. Mean of one sample
B. Mean of whole process
C. Range
D. Process capability ratio
View Answer
Answer: Option C
Explanation:
In x bar and R charts, process standard deviation is estimated indirectly through the use of the range R. x bar is used as an estimator of mean.
Question 9
What is the value of LCL for the s chart when the standard value for σ is not given?
A. B5 s
B. B4 s
C. B6 s
D. B3 s
View Answer
Answer: Option D
Explanation:
The LCL of the s chart gives the value equal to, B3 s when the standard value for σ is not given. This is the lowest the value of s can be, for the process to be in-control.
Question 10
Which of these formulas gives the exact equation for the UCL of s chart with a std. value for σ given?
A. B6 σ
B. B5 σ
C. c4 σ
D. c3 σ
View Answer
Answer: Option A
Explanation:
The UCL parameter of the s chart with a std. value for σ given, is expressed byUCL=B6 σ.
Question 11
Which of these is a name of s control chart?
A. s2 Chart
B. Process standard deviation chart
C. σ Chart
D. σ2 Chart
View Answer
Answer: Option C
Explanation:
The s chart or sample standard deviation chart is also called σ chart by some practitioners. This is based on the control limits set by calculations using the sample standard deviations.
Question 12
Which of this is a situation when x bar and s charts should be utilized instead of x bar and R charts?
A. When sample size is constant
B. When sample standard deviation is less than 1
C. When sample range is more than 1
D. When sample size is variable
View Answer
Answer: Option D
Explanation:
It is favorable to use the x bar and s charts over x bar and R charts when the sample size is variable. This is because when sample size is variable, it leads to a changing center line of R chart, which is difficult to interpret.
Question 13
X bar and R charts are highly favorable when the sample size is high.
A. TRUE
B. FALSE
View Answer
Answer: Option B
Explanation:
X bar and R charts are not used for high sample sizes- say, n>10 or 12. This is because the range method for estimating σ loses its efficiency for moderate to large samples.
Question 14
X bar and S chart are more accurate in predicting out-of-control situations than the x bar and R charts, in the case of high sample size.
A. TRUE
B. FALSE
View Answer
Answer: Option A
Explanation:
X bar and R charts have a high level of β- risk when the sample size is high. This means they lose their efficiency at high or moderate sample sizes. So x bar and s charts are more accurate than the former ones.
Question 15
X bar chart should be interpreted before s chart if both are indicating out of control situations.
A. TRUE
B. FALSE
View Answer
Answer: Option B
Explanation:
The base rule of x bar and s chart is that if both charts indicate out-of-control situation then the s chart should be interpreted first as deleting assignable causes in the s chart will automatically delete assignable causes in x bar chart.