Organic Grains LLC uses statistical process control to ensure that its health-co

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- and R-charts are UCL-=5.81, LCL,-5.39, UCLr." 0.909, LCLR = 0. Over the past few days, they have taken five random samples of four loaves each and have found the following: Net Weight Loaf # 3 6.5 5.6 5.0 5.5 Loaf # 4 6.4 5.3 5.3 5.3 Sample Loaf # 1 Loaf # 2 6.3 5.4 5.4 5.3 54-5.3-52-5. 6.4 5.3 5.4 5.7 4 5 Based on the x-chart, is one or more samples beyond the control limits? | Based on the R-chart, is one or more samples beyond the control limits? Click to select your answerts). Show All × QM 352 Grade Projec...xisx weingarten2.swf

Explanation / Answer

We calculate the X-bar and R for each of the samples :

X-bar is the average reading of the loaves in the sample and R is the maximum - minimum reading

We then check if all the readings are between the UCL and LCL limits.

UCLx = 5.81 and LCLx = 5.39

UCLR = 0.909 and LCLR = 0

Sample 1

X-bar = (6.3+6.4+6.5+6.4) / 4 = 6.4 : Outside Limit

R = 6.5 - 6.3 = 0.2 : Within Limits

Sample 2

X-bar = (5.4+5.3+5.6+5.3) / 4 = 5.4 : Within Limit

R = 5.6 - 5.3 = 0.3 : Within Limit

Sample 3

X-bar = (5.4+5.4+5.0+5.3) / 4 = 5.275 : Outside Limit

R = 5.4 - 5.0= 0.4 : Within Limit

Sample 4

X-bar = (5.3+5.7+5.5+5.3) / 4 = 5.45 : Within Limit

R = 5.7 - 5.3= 0.4 : Within Limit

Sample 5

X-bar = (5.4+5.3+5.2+5.1) / 4 = 5.25 : Outside Limit

R = 5.4 - 5.1= 0.3 : Within Limit

Based on above, we can conclude that

Based on x-bar chart, is one or more samples beyond the control limits : YES

Based on R chart, is one or more samples beyond the control limits : NO

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