Question

PLEASE SHOW HOW TO CALCULATE EACH STEP IN EXCEL.

Siders Breakfast Foods Inc., produces a popular brand of raisin bran cereal. The package indicates it contains 25.0 ounces of cereal. To ensure that the firm makes good in its marketing promo claim regarding box weight content, the Siders inspection department makes hourly check on the production process. As part of the hourly check, four boxes are selected and their contents weighed. The results for 25 samples are reported below.

Sample Number	Weight-1	Weight-2	Weight-3	Weight-4
1	25.1	24.4	25.6	23.2
2	23.2	23.9	25.1	24.8
3	25.6	24.5	25.7	25.1
4	22.5	23.8	24.1	25
5	23.2	24.2	22.3	25.7
6	22.6	24.1	20	24
7	23	26	24.9	25.3
8	24.5	25.1	23.9	24.7
9	24.1	25	23.5	24.9
10	25.8	25.7	24.3	26
11	24.5	23	23.7	24
12	25.1	24.4	25.6	23.2
13	23.2	24.2	23	25.7
14	23.1	23.3	24.4	24.7
15	24.6	25.1	24	25.3
16	24.4	24.4	22.8	23.4
17	25.1	24.1	23.9	26.2
18	24.5	24.5	26	26.2
19	25.3	24.5	24.3	25.5
20	24.6	25.3	25.5	24.3
21	24.9	24.4	25.4	24.8
22	23.2	24.2	22.3	25.7
23	24.8	24.3	25	25.2
24	23.2	24.2	23	25.7
25	24.8	24.3	25	25.2

1. Develop the appropriate control charts to evaluate and monitor the boxing process (10 pts)
2. What do the control charts tell you about the process during the 25-hour inspection period (i.e. Do a thorough interpretation and analysis of the charts.)? (10 pts)

3. An FDA regulation controlling the contents of packaged food items states that no more than 5 percent of the items produced and sold can contain less than 95 percent of the stated/labeled weight. Assuming that the standard deviation of the process, when in control or is operating as expected, is 0.90, determine if Siders Breakfast Foods, Inc., is in compliance or not in compliance with the FDA regulation given these parameters, i.e. process mean of 25 ounces and standard deviation of 0.90. Explain and show evidence supporting your conclusion. (10 pts). What should Siders Breakfast do if they discover their process to be in violation of the Federal regulation? (5 pts)

   (Assume that the content weight follows the normal distribution).

Answer 1

a. Develop the appropriate control charts to evaluate and monitor the boxing process (10 pts)

Load the data into Excel.

Go to Data>Megastat.

Select the option Quality Control Process Charts and go to Variables(X bar and R).

Select the Input Range as the data set.

Click OK.

The output obtained will be as follows:

	Sample size	4
	Number of samples	25
		Mean	Range
	Upper Control Limit, UCL	25.867	4.500
	Center	24.429	1.972
	Lower Control Limit, LCL	22.991	0.000

b. What do the control charts tell you about the process during the 25-hour inspection period (i.e. Do a thorough interpretation and analysis of the charts.)? (10 pts)

The control chart for the mean tells us that the process during the 25-hour inspection period is out of control while the control chart for the range tells us that the process during the 25-hour inspection period is in control.

c. An FDA regulation controlling the contents of packaged food items states that no more than 5 percent of the items produced and sold can contain less than 95 percent of the stated/labeled weight. Assuming that the standard deviation of the process, when in control or is operating as expected, is 0.90, determine if Siders Breakfast Foods, Inc., is in compliance or not in compliance with the FDA regulation given these parameters, i.e. process mean of 25 ounces and standard deviation of 0.90. Explain and show evidence supporting your conclusion. (10 pts). What should Siders Breakfast do if they discover their process to be in violation of the Federal regulation? (5 pts)

(Assume that the content weight follows the normal distribution).

Considering Mean = 25 and Standard Deviation = 0.90, we have x bar table as:

		A2	0.729
		D3	0
		D4	2.282
		R bar	1.972
Mean Weights	Mean	CL	UCL	LCL
24.575	25	25	26.44	23.56
24.25	25	25	26.44	23.56
25.225	25	25	26.44	23.56
23.85	25	25	26.44	23.56
23.85	25	25	26.44	23.56
22.675	25	25	26.44	23.56
24.8	25	25	26.44	23.56
24.55	25	25	26.44	23.56
24.375	25	25	26.44	23.56
25.45	25	25	26.44	23.56
23.8	25	25	26.44	23.56
24.575	25	25	26.44	23.56
24.025	25	25	26.44	23.56
23.875	25	25	26.44	23.56
24.75	25	25	26.44	23.56
23.75	25	25	26.44	23.56
24.825	25	25	26.44	23.56
25.3	25	25	26.44	23.56
24.9	25	25	26.44	23.56
24.925	25	25	26.44	23.56
24.875	25	25	26.44	23.56
23.85	25	25	26.44	23.56
24.825	25	25	26.44	23.56
24.025	25	25	26.44	23.56
24.825	25	25	26.44	23.56

The control chart is:

Since the process is out of control, Siders Breakfast Foods, Inc., is not in compliance with the FDA regulation given these parameters, i.e. process mean of 25 ounces and a standard deviation of 0.90.

Siders Breakfast should input some restrictions on the production process to get the process in control.