Question

The viscosity of a material is its resistance to flow when under stress. Viscosity is a critical characteristic of rubber and rubber‑like compounds called elastomers, which have many uses in consumer products. Viscosity is measured by placing specimens of the material above and below a slowly rotating roller, squeezing the assembly, and recording the drag on the roller. Measurements are in "Mooney units," named after the inventor of the instrument.

A specialty chemical company is beginning production of an elastomer that is supposed to have viscosity 45±5 Mooneys. Each lot of the elastomer is produced by "cooking" raw material with catalysts in a reactor vessel. The x¯ and s were recorded from samples of size ?=4 lots from the first 24 shifts as production begins. An ? chart therefore monitors variation among lots produced during the same shift. If the s chart is in control, an ?¯ chart looks for shift‑to‑shift variation.

Suppose that when this chart setup project is complete, the points remaining after removing special causes have ?¯¯=48.7 and ?¯=0.92. What are the center line and control limits for the ?¯ and ?s charts you would use to monitor the process going forward?

(Enter your answers rounded to three decimal places.)

LCL?¯ :

center?¯:

UCL?¯ :

LCL? :

center? :

UCL?¯ :

Answer 1