Question

Organic Grains LLC uses statistical process control to ensure that its health-conscious, low-fat, multigrain sandwich loaves have the proper weight.

Based on a previously stable and in-control process, the control limits of the

x overbarx -

and R-charts are:

UCL Subscript x overbarUCLx

=

5.48

LCL Subscript x overbarLCLx

=

5.12

UCL Subscript Upper RUCLR

=

0.923

LCL Subscript Upper RLCLR

=

0

Over the past few days, they have taken five random samples of four loaves each and have found the following:

  

	Net Weight
Sample	Loaf # 1	Loaf # 2	Loaf # 3	Loaf # 4
1	5.3	5.6	5.6	5.5
2	5.1	5.3	5.2	5.2
3	4.6	4.7	4.6	4.9
4	5.2	5.0	5.2	5.4
5	5.0	4.9	5.0	4.7

Based on the

x overbarx -chart,

is one or more samples beyond the control limits?

No

yes

.

Based on the R-chart, is one or more samples beyond the control limits?

Yes

No

.

Answer 1

The following problem can be solved using simple calculations in Excel.

UCL of Xbar chart = 5.48

LCL of Xbar chart = 5.12

UCL of R chart = 0.923

LCL of R chart = 0

To calculate the Xbar(average value of the sample) and the range of the samples, the formulation of the table is as follows

Formulas used

Ans a)

Based on the Xbar values in the above spreadsheets, we can see that there are multiple samples that are beyond the control limits. Samples 1, 3, and 5 are beyond the control limits. Hence YES.

Ans b)

Based on the Range values in the above spreadsheets, we can see that all the samples lie within the control limits. Hence NO.