
Concept explainers
a)
To determine: The value of
Introduction: Control charts used to determine whether the process is under control or not. Attributes and variables are the factors under the control charts.
a)

Answer to Problem 10P
The value of
Explanation of Solution
Given information:
The following information is given:
Determine
The standard deviation of the sample means denoted by
Here,
σ refers to process standard deviation
n refers to the sample size.
The given values are
The standard deviation of the sample means
b)
To determine: The control limits for the mean chart if the value of z is 3.
Introduction: Control charts used to determine whether the process is under control or not. Attributes and variables are the factors under the control charts.
b)

Answer to Problem 10P
The UCL value of
Explanation of Solution
Given information:
The following information is given:
Sample size is given as 5 and process standard deviation is given as 1.36.
Determine the control limits for the mean chart if the value of z is 3:
Formulae to calculate control limits:
Here,
The value of
the standard deviation of the mean
Calculate the average for each sample:
Working note:
Average for sample #1:
It is calculated by dividing the total of sample #1 and sample size.
Note: The same continues for all the samples.
Calculate the value of
It is calculated by dividing the sum of average of all the samples and the number of samples. Hence, the value of
Substitute the values in equation (1)to determine the value of UCL as follows:
Hence, the UCL value is 11.83.
Substitute the values in equation (2) to determine the value of LCL as follows:
Hence, the LCL value is 8.17.
c)
To determine: The control limits for the range chart.
Introduction: Control charts used to determine whether the process is under control or not. Attributes and variables are the factors under the control charts.
c)

Answer to Problem 10P
The UCL value of R-chart is 6.9795 and the LCL value is 0.
Explanation of Solution
Given information:
The following information is given:
Sample size is given as 5 and process standard deviation is given as 1.36.
Determine the control limits for the mean chart if the value of z is 3:
Formulae to calculate control limits:
Here,
Substitute the values in equation (3) to determine the value of UCL as follows:
Hence, the UCL value is 6.9795.
Substitute the values in equation (4) to determine the value of LCL as follows:
Hence, the LCL value is 0.
d)
To determine: Whether the process is in control.
Introduction: Control charts used to determine whether the process is under control or not. Attributes and variables are the factors under the control charts.
d)

Answer to Problem 10P
The process is in statistical control.
Explanation of Solution
Given information:
The following information is given:
Sample size is given as 5 and process standard deviation is given as 1.36.
Plot the sample mean values in the
Plot the sample mean values in theR-control chart where
The sample range values lie well within the upper control limit and lower control limits.
The process is in statistical control.
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Chapter 6 Solutions
EBK PRINCIPLES OF OPERATIONS MANAGEMENT
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