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?

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

Step-by-step 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

solution:

→c= a b , that is product of a and b is possible only when when a is m × n matrix and b is n × p matrix.

that is, number of columns of a= number of rows of b.

so, size of matrix , c= a b is , if a = (m × n)matrix

b= (n × p)matrix

then a b = [ (m × n)matrix] ×[   (n × p)matrix ]

→→c= a b= [m × p ] matrix

→→size of product a b will be equal to = number of rows of a × number of columns of b