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-6.67, LCL6.25 UCLR 0.974, 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 # 4 6.6 Loaf # 2 Loaf # 3 Loaf # 1 7.0 6.3 6.1 Sample 6.9 6.1 6.3 6.1 5.9 6.8 6.4 6.4 6.1 6.5 5.7 5.7 6.0 Based on the x-chart, is one or more samples beyond the control limits? No Based on the R-chart, is one or more samples beyond the control limits? Yes

Explanation / Answer

The calculated values of Xbar and Range for 5 samples are correct.

Therefore ,

Mean values of Xbar = Xbar-bar = ( 6.83 + 6.23 + 6.23 + 6.28 + 5.83) / 5 = 6.28

Mean of Range values = Rbar = ( 0.40 + 0.30 + 0.30 + 0.40 + 0.30 )/5 = 0.34

Sample size = n = 4

Following are the relevant values of constants as derived from standard table for Xbar and Range chart :

A2 = 0.729

D4= 2.282

D3 = 0

Control limits for Xbar chart :

Upper Control Limit = UCLx = Xbar-bar + A2 x Rbar = 6.28 + 0.729 x 0.34 = 6.28+0.248=6.528

Lower Control Limit = LCLx = Xbar-bar – A2xRbar = 6.28 – 0.729x0.34 = 6.28 – 0.248=6.032

Control Limits for Range chart :

Upper Control Limit = UCLr = 2.282 xRbar = 2.282 x 0.34 = 0.775

Lower Control Limit = LCLr = 0

It is to be noted that Xbar of sample 1 i.e. 6.83 and Xbar of sample 5 i.e. 5.7 are outside control limits of Xbar chart which is 6.032 – 6.528

Therefore , one or more samples are beyond control limits.

BASED ON THE Xbar CHART, IS ONE OR MORE SAMPLES BEYOND CONTROL LIMITS : YES

It is to be noted that all values of Range are within the Rbar control limits of 0 – 0.775. Therefore , no samples are beyond control limits

BASED ON THE Rbar CHART, IS ONE OR MORE SAMPLES BEYOND CONTROL LIMITS : NO

BASED ON THE Xbar CHART, IS ONE OR MORE SAMPLES BEYOND CONTROL LIMITS : YES

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