From setup to monitoring. Suppose that when the chart setup project of Example 27.8 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?

Example 27.8:

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. Table 27.5 records x and s from samples of size n = 4 lots from the first 24 shifts as production begins.¹¹ An s 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.

Estimating _. We do not know the process mean µ and standard deviation σ  What shall we do? Sometimes we can easily adjust the center of a process by setting some control, such as the depth of a cutting tool in a machining operation or the temperature of a reactor vessel in a pharmaceutical plant. In such cases it is usual to simply take the process mean µ to be the target value, the depth or temperature that the design of the process specifies as correct. The  chart then helps us keep the process mean at this target value.