A major customer for a vendor of plastic containers requires that its containers have a volume of 10,000 cubic inches with a tolerance of 50 cubic inches.Forty subgroups of five containers each were selected periodically from the production process.The average of the means across all subgroups was found to be 10,012 cubic inches and the average range was 48 cubic inches.The lower and upper control limits for the X-bar chart are ________________________ .
A)0 and 111.65 cubic inches
B)9984.30 and 10,039.70 cubic inches
C)9910.53 and 10,113.47 cubic inches
D)0 and 101.47 cubic inches
E)9950 and 10,050 cubic inches

Question

Quizplus · Accepted Answer

The lower and upper control limits for the X-bar chart can be calculated using the formula: LCL = $ \bar{X} - A_2 \times R $ and UCL = $ \bar{X} + A_2 \times R $, where $ \bar{X} $ is the average of subgroup means, R is the average range, and $ A_2 $ is a factor from a control chart constants table based on the subgroup size (n=5). For n=5, $ A_2 $ is typically around 0.577. Using the given values, $ \bar{X} = 10,012 $ and $ R = 48 $, the calculations would yield LCL and UCL values that fit the range provided in option B, considering the typical application of the formula and the values provided.

A Major Customer for a Vendor of Plastic Containers Requires