Question

Q-4 Samples of size n 4 are selected from a production line. (a) What is the value of the A2 factor used to determine the upper and lower control limits for the mean? (b) What are the values of the D3 and D4 factors used to determine the upper and lower control limits for the range?

Q-5 Samples of size 5 are selected from a manufacturing process. The mean of the sample ranges is .50. What is the estimate of the standard deviation of the population?

Q-6 A new industrial oven has just been installed at the Piatt Bakery. To develop experience regarding the oven temperature, an inspector reads the temperature at four different places inside the oven each half hour. The first reading, taken at 8:00 A.M., was 340 degrees Fahrenheit. (Only the last two digits are given in the following table to make the computations easier.)

Sample piece and Time

Time

1

2

3

4

8:00 A.M

40

50

55

39

8:30 A.M

40

42

38

38

9:00 A.M

41

45

47

43

9:30 A.M

39

39

41

41

10:00 A.M

37

42

46

41

10:30 A.M

39

40

39

40

(a) Based on this initial experience, determine the control limits for the mean temperature. Determine the grand mean. Plot the experience on a chart. (b) Interpret the chart. Does there seem to be a time when the temperature is out of control?

Answer 1

Q-4 Samples of size n 4 are selected from a production line. (a) What is the value of the A2 factor used to determine the upper and lower control limits for the mean? (b) What are the values of the D3 and D4 factors used to determine the upper and lower control limits for the range?

For Sample size of 4

From below table given

A2 = 0.729

D3 = 0

D4 = 2.282

Q-5 Samples of size 5 are selected from a manufacturing process. The mean of the sample ranges is .50. What is the estimate of the standard deviation of the population?

where d₂ is a constant that depends on subgroup size.

d2 = 2.326

Sigma = R bar / d2 = 50 / 2.326 = 21.496

Q-6 A new industrial oven has just been installed at the Piatt Bakery. To develop experience regarding the oven temperature, an inspector reads the temperature at four different places inside the oven each half hour. The first reading, taken at 8:00 A.M., was 340 degrees Fahrenheit. (Only the last two digits are given in the following table to make the computations easier.)

X bar R chart calculation are given below

Sample	1	2	3	4	Sample Average X bar	Range ( max-min)	(x-xbar)^2	Sub group SD
8	40	50	55	39	46.00	16	18.0625	7.79
8.3	40	42	38	38	39.50	4	5.0625	1.91
9	41	45	47	43	44.00	6	5.0625	2.58
9.3	39	39	41	41	40.00	2	3.0625	1.15
10	37	42	46	41	41.50	9	0.0625	3.70
10.3	39	40	39	40	39.50	1	5.0625	0.58
		Total			250.50	38
		Average X bar			41.75
		R bar				6.33
		Σ(x-xbar)^2					36.375
		Σ(x-xbar)^2 / n-1					3.48
		SD			2.70
		Sample SD Average Sbar						2.95
		X bar USL	Xbar + A2*R	A2 =0.729	43.90
		Xbar LSL	Xbar - A2*R	A2 =0.729	39.60
		R bar USL	Rbar* D4	D4 = 2.282	14.45266667
		R bar LSL	Rbar* D3	D3=0	0
		S USL	S * B4	B4 = 2.089	6.17
		S LSL	S * B3	B3 = 0	0

X bar chart

R chart

Observations

Initally the mean ang range were outside the limits but later bought into control.

The mean temperature is shifting to the LSL whem time increases.

Corrective action to be taken to maintain the temperature level in oven.