Question

Five samples of size 4 were taken from a process. A range chart was developed that had LCLR​ = 0 and UCLR​ = 2.50.​ Similarly, an average chart was developed with the average range from the five​ samples, with LCL ​= 15.0 and UCL ​ = 22.0. The ranges for each of the five samples were​ 1.75, 2.22,​ 2.35, 2.04, and​ 2.30, respectively. The values of the sample average for each sample were​ 19.5, 22.3,​ 17.4, 20.1, and​ 18.9, respectively. What can you tell management from this​ analysis?

Answer 1

Answer: The process variability is in​ control, but the process average is out of control.

Explanation:

The control limits for the process variability (range) are '0' and '2.50'. From the question, we can reduce that the range values of (1.75, 2.22,​ 2.35, 2.04, and​ 2.30) lie within the control limits. Therefore, the process variability is in control.

But the average of the samples are 19.5, 22.3,​ 17.4, 20.1, and​ 18.9, and the average sample 2 lie beyond the upper control limits (22.3>UCL) since UCL is 22.0. This implies that the process average is out of control