Is it reallyPoisson? Certain manufacturing environments, such as semiconductor manufacturing and biotechnology, require a low level of environmental pollutants (for example, dust, airborne microbes, and aerosol particles). For such industries, manufacturing occurs in ultraclean environments known as cleanrooms. There are federal and international classifications of cleanrooms that specify the maximum number of pollutants of a particular size allowed per volume of air. Consider a manufacturer of integrated circuits. One cubic meter of air is sampled at constant intervals of time, and the number of pollutants of size 0.3 microns or larger is recorded. Here are the count data for 25 consecutive samples: DATADATA DATADATADATA DATADATADATADATADATA DATADATADATADATADATA DATADATADATADATADATA DATADATADATADATADATA DATADATADATADATADATA DATADATADATADATADATA DATADATADATA DATADATADATADATADATA DATA FILE CLEANROOM 7 3 13 1 17 3 6 9 12 5 5 0 6 2 9 1 12 2 3 3 7 5 0 3 13

(a) Construct a c chart for the data. Does the process appear to be in control?

(b) Remove any out-of-control signals found in part (a), and reestimate the c chart limits. Does the process now appear to be in control?

(c) Remove all observations associated with out-of-control signals found in parts

(a) and (b). Reestimate the control limits and apply them to the remaining observations. Are there any more out-of-control signals? If so, identify them and remove them and reestimate limits. Continue this process until no out-of-control signals are present. Report the final control limits.

(d) A quality control manager took a look at the data and was suspicious of the numerous rounds of data point removal. Even the final control limits were bothersome to the manager because the variation within the limits seemed too large. The manager made the following statement, “I am not so sure the c chart is applicable here. I have a hunch that the process is not influenced by only Poisson-variation. I suggest we look at the estimated mean and variance of the data values.” Calculate the sample variance s2 of the original 25 values and compare this variance estimate with the mean estimate. Explain how such a comparison can suggest the possibility that a Poisson distribution may not fully describe the underlying process.