1. In a quality control test, 8 samples, each having four plates, were selected and the thickness of each plate in each sample was measured. The measurements in millimeters are given in the following Table. Calculate UCL and LCL for X-bar and R.

   sample	plate 1	plate 2	plate 3	plate 4
   number	thickness	thickness	thickness	thickness	Average	Maximum	Minimum	Range
   1	47	50	50	41
   2	38	47	43	43
   3	46	44	43	46
   4	48	42	47	47
   5	47	47	38	45
   6	48	40	47	48
   7	41	46	39	40
   8	46	37	45	43
   Total						Total

   Calculate the values in the last four columns and answer the questions.

   What is the total value of the average column (i.e. the sixth column in the table)

20 points

QUESTION 22

1. Refer to the Problem in question 21

   What is the value of the grand mean or the process mean or mean of means, denoted by X⁼ ?

   (Note: It is also called X-double bar)

10 points

QUESTION 23

1. Refer to the Problem in question 21

   What is the total value of the range column (the last column in the table) ?

18 points

QUESTION 24

1. Refer to the Problem in question 21

   What is the mean value of the range, R?

   (Note: It is also called R-bar)

10 points

QUESTION 25

1. What is the value of A₂ ? (Read the value from the Chart)

3 points

QUESTION 26

1. What is the value of D₄ ? (Read the value from the Chart)

3 points

QUESTION 27

1. Refer to the problem in question 21.

   What is the Upper Control Limit, UCL(X)?

4 points

QUESTION 28

1. Refer to the problem in question 21.

   What is the Lower Control Limit, LCL(X)?

4 points

QUESTION 29

1. Refer to the problem in question 21.

   What is the Upper Control Limit, UCL(R)?

4 points

QUESTION 30

1. Refer to the problem in question 21.

   What is the Lower Control Limit, LCL(R)? (Hint: First, you need to read the value of D₃ from the Chart)