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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.
Quality control studies for Leaky Jet Computer Printers show the lifetime of the printer follows a normal distribution with a mean of 4.5 years and a standard deviation of 0.85 years.
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