Complete Question
The UCL and LCL for an X-bar chart are 25 and 15 respectively. The central line is 20, and the process variability is considered to be in statistical control. The results of the next six sample means are 18, 23, 17, 21, 24, and 16. What should you do?
a. Explore the assignable causes because the second, fourth, and fifth samples are above the mean.
b. Explore the assignable causes because there is a trend.
c Nothing: the process is in control.
d Explore the assignable causes because there is a run
Answer:
The correct option is c
Step-by-step explanation:
From the question we are told that
The data for the next six means is 18, 23, 17, 21, 24, and 16.
The central line is k = 20
Generally the mean of the next six mean is mathematically represented as
[tex]c = \frac{18+ 23 + 17+ 21+ 24 + 16}{6}[/tex]
=> [tex]c = 19.8[/tex]
Generally given that the mean of the next six means is very close to the central line , it means that the distribution of the process is more centered (i.e it well within the limit of the central line ), and what this tell us is that the process is in control so we do nothing
