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Instruction 18-12
the Manufacturer of Canned Food Constructed Control Charts

question 11

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Instruction 18-12
The manufacturer of canned food constructed control charts and analysed several quality characteristics. One characteristic of interest is the weight of the filled cans. The lower specification limit for weight is 2.95 kg. The table below provides the range and mean of the weights of five cans tested every 15 minutes during a day's production.
 Number  XBar  Range  Number  XBar  Range 13.050720.0215163.046460.07323.012280.087173.038680.069633.035580.0851183.033380.032943.010140.0674193.033220.045553.008580.0983203.050780.021563.027040.0527213.048080.039673.042680.0508223.053480.058183.010520.0791233.055160.068293.034640.0663243.034260.0325103.020340.0538253.05160.0641113.037640.0584263.055620.0809123.04090.0434273.044020.0374133.05190.0762283.064580.0284143.039940.0833293.05440.0738153.037880.0601\begin{array} { | l | l | l | l | l | l | } \hline \text { Number } & \text { XBar } & \text { Range } & \text { Number } & \text { XBar } & \text { Range } \\\hline 1 & 3.05072 & 0.0215 & 16 & 3.04646 & 0.073 \\\hline 2 & 3.01228 & 0.087 & 17 & 3.03868 & 0.0696 \\\hline 3 & 3.03558 & 0.0851 & 18 & 3.03338 & 0.0329 \\\hline 4 & 3.01014 & 0.0674 & 19 & 3.03322 & 0.0455 \\\hline 5 & 3.00858 & 0.0983 & 20 & 3.05078 & 0.0215 \\\hline 6 & 3.02704 & 0.0527 & 21 & 3.04808 & 0.0396 \\\hline 7 & 3.04268 & 0.0508 & 22 & 3.05348 & 0.0581 \\\hline 8 & 3.01052 & 0.0791 & 23 & 3.05516 & 0.0682 \\\hline 9 & 3.03464 & 0.0663 & 24 & 3.03426 & 0.0325 \\\hline 10 & 3.02034 & 0.0538 & 25 & 3.0516 & 0.0641 \\\hline 11 & 3.03764 & 0.0584 & 26 & 3.05562 & 0.0809 \\\hline 12 & 3.0409 & 0.0434 & 27 & 3.04402 & 0.0374 \\\hline 13 & 3.0519 & 0.0762 & 28 & 3.06458 & 0.0284 \\\hline 14 & 3.03994 & 0.0833 & 29 & 3.0544 & 0.0738 \\\hline 15 & 3.03788 & 0.0601 & & & \\\hline\end{array}
-Referring to Instruction 18-12,an R chart is to be constructed for the weight.The center line of this R chart is located at _______


Definitions:

Economies Of Scale

The cost advantage achieved by increasing production, which typically reduces the average costs per unit through improved efficiency.

High-Quality Products

Goods that meet or exceed customers' expectations in terms of performance, durability, and reliability.

Market Penetration

An assessment of how much a product or service is sold or used, in comparison to the full theoretical scope of the market for it.

Frozen Dessert Line

A category of cold, sweet products including ice cream, frozen yogurt, and sorbet, often part of a company's product offerings.

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