Question

Whole Grains Inc. uses statistical process control to ensure that its health-conscious, low-fat, multigrain sandwich loaves have the proper weight. Based on periodic process sampling, the following observed weights (in ounces) were recorded:

	Sample 1	Sample 2	Sample 3	Sample 4	Sample 5	Sample 6
Loaf # 1	5.94	6.18	5.94	6.18	6.18	4.74
Loaf # 2	7.02	5.58	5.94	7.02	5.58	5.40
Loaf # 3	6.00	6.12	6.48	6.60	5.64	6.60
Loaf # 4	6.90	5.40	6.30	4.80	4.50	7.20

  
  
Provide the following values:
  
X-double bar =                  R-bar =  
  

You are asked to compute 3σ control limits for X-bar and Range charts. Provide the following values:
  
A2 =                     D3 =                     D4 =                    
  
  
For X-bar Chart,           LCL =      UCL =                              
  
For R-Chart,                 LCL =     UCL =  
  
  
Is the process under control? (Enter YES or NO):
  
NOTE: All values should be rounded to the nearest hundredth (two decimal after dot, for example 9.99)
  Whole Grains Inc. uses statistical process control to ensure that its health-conscious, low-fat, multigrain sandwich loaves have the proper weight. Based on periodic process sampling, the following observed weights (in ounces) were recorded:

	Sample 1	Sample 2	Sample 3	Sample 4	Sample 5	Sample 6
Loaf # 1	5.94	6.18	5.94	6.18	6.18	4.74
Loaf # 2	7.02	5.58	5.94	7.02	5.58	5.40
Loaf # 3	6.00	6.12	6.48	6.60	5.64	6.60
Loaf # 4	6.90	5.40	6.30	4.80	4.50	7.20

  
  
Provide the following values:
  
X-double bar =                  R-bar =  
  

You are asked to compute 3σ control limits for X-bar and Range charts. Provide the following values:
  
A2 =                     D3 =                     D4 =                    
  
  
For X-bar Chart,           LCL =      UCL =                              
  
For R-Chart,                 LCL =     UCL =  
  
  
Is the process under control? (Enter YES or NO):
  
NOTE: All values should be rounded to the nearest hundredth (two decimal after dot, for example 9.99)
  

Answer 1

The Sample Data is:

	Sample 1	Sample 2	Sample 3	Sample 4	Sample 5	Sample 6
Loaf #1	5.94	6.18	5.94	6.18	6.18	4.74
Loaf #2	7.02	5.58	5.94	7.02	5.58	5.4
Loaf #3	6	6.12	6.48	6.6	5.64	6.6
Loaf #4	6.9	5.4	6.3	4.8	4.5	7.2
x-bar	6.465	5.82	6.165	6.15	5.475	5.985
Range	1.08	0.78	0.54	2.22	1.68	2.46

Range is the difference between the maximum and minimum for a sample.

X- double-bar = average of all x-bar = (6.465 + 5.82 + 6.165 + 6.15 + 5.475 + 5.985)/6 = 6.01

Range-bar = average of all range = (1.08 + 0.78 + 0.54 + 2.22 + 1.68 + 2.46)/6 = 1.46

Number of observations = 4

The Control Chart Constants:

Hence,

A2 = 0.729

D3 = 0

D4 = 2.282

X-double-bar = 6.01

R-bar = 1.46

For X-bar chart:

We know that,

UCL(x) = X-double-bar + A2*R-bar

= 6.01 + 0.729*1.46

= 6.01 + 1.06434

= 7.07434

LCL(x) = X-double-bar – A2*R-bar

= 6.01 – 0.729*1.46

= 6.01 – 1.06434

= 4.94566

UCL(x) = 7.07434

LCL(x) = 4.94566

For R Chart:

UCL(R) = R-bar*D4 = 1.46*2.282 = 3.33172

LCL(R) = R-bar*D3 = 1.46*0 = 0

UCL(R) = 3.33172

LCL(R) = 0

Is the process under control?

Answer is: YES. All the Sample mean are in between UCL(x) and LCL(x). All the Sample range are between UCL(R) and LCL(R). So the process is under control.

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