A Proctor and Gamble Factory Process Fills Boxes with Detergent

question 41

Essay

A Proctor and Gamble factory process fills boxes with detergent. Construct an appropriate set of control charts to monitor the process. Historical data for fill weight (in ounces) of eight samples is presented below. A sample size of eight was used. $$\begin{array} { | c | c | c | } \hline \text { Sample } & \text { Sample Mean } & \text { Sample Range } \\\hline 1 & 15.80 & 0.42 \\\hline 2 & 16.10 & 0.38 \\\hline 3 & 16.02 & 0.08 \\\hline 4 & 15.95 & 0.15 \\\hline 5 & 16.12 & 0.42 \\\hline 6 & 16.18 & 0.23 \\\hline 7 & 15.87 & 0.36 \\\hline 8 & 16.20 & 0.40 \\\hline\end{array}$$
a.Compute the limits for both an R-chart and x-bar chart. Compare the sample results to the limits of the charts.
b.Briefly explain what the quality control charts tell you. What actions, if any, would you take?

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Definitions:

Deuterostomes

Lineage of bilateral animals in which the second opening on the embryo surface develops into a mouth; for example, echinoderms and chordates.

Radial Symmetry

A symmetrical arrangement in which body parts radiate out from a central point, common in animals like jellyfish and starfish.

Embryonic Opening

The embryonic opening refers to the blastopore, an early stage in the development of an embryo that can develop into the mouth or anus in different animal groups.

Chelicerates

A subgroup of arthropods that includes spiders, scorpions, ticks, and mites, characterized by the presence of chelicerae, which are claw-like mouthparts.