Concept explainers
a)
To determine: The value of control limits.
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 8P
The value of control limits is 16.08 and 15.92.
Explanation of Solution
Given information:
The following information is given:
The mean of the sample means
Calculate
It is given that the population mean
Here, the sample size
Substitute the values of
Hence, the standard deviation of the means
Derive the values of upper control limits (UCL) and lower control limits (LCL):
Calculate UCL and LCL using the below formulae:
Here,
The value of
Compute the value of UCL by substituting in UCL formula, the values of
Hence, the upper control limit is
Compute the value of LCL by substituting in LCL formula, the values of
Hence, the lower control limit is
b)
To determine: The value of control limits.
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 8P
The value of control limits is 16.12 and 15.88.
Explanation of Solution
Given information:
The following information is given:
The mean of the sample means
Calculate
It is given that the population mean
Here, the sample size
Substitute the values of
Hence, the standard deviation of the means
Derive the values of upper control limits (UCL) and lower control limits (LCL):
Calculate UCL and LCL using the below formulae:
Here,
The value of
Compute the value of UCL by substituting in UCL formula, the values of
Hence, the upper control limit is
Compute the value of LCL by substituting in LCL formula, the values of
Hence, the lower control limit is
The control limits become wider when three standard deviations are used instead of two standard deviations. The process is now allowed wider latitude in terms of natural variations.
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