Each day for two work weeks (10 days total), George weighs 4 bags from that day’s production. If the average of the means is 14 oz. and the average range is 0.4 oz., what is the lower control limit for an x-bar chart for this process?

The lower control limit for an x-bar chart for this process is 13.7084 oz.

Given that,

Based on the above information, the calculation is as follows

For the sample size of 4, the control limit factor (A2) = 0.729  i.e. obtained from the X-bar chart.

Now  

Lower control limit = X-bar-bar - (A2 × R-bar)

= 14 - (0.729 × 0.4)

= 14 - 0.2916

= 13.7084 oz

Therefore we can conclude that the lower control limit for an x-bar chart for this process is 13.7084 oz.

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13.7084

Explanation:

Given the following;

Average of means = 14 oz

Average range = 4 oz

Subgroup size = 4

The Lower Control Limit(LCL) of an x-bar chart is calculated using the relation:

LCL = average mean + (A2 × average range)

A2 is an x- bar constant which varies depending on the number of subgroups given.

A2 for a Subgroup of 4 for an x-bar chart is 0.729

LCL = 14 - (0.729 × 0.4)

LCL = 14 - 0.2916

LCL = 13.7084

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