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A Quality Manager has compiled data for the last 115 production lots manufactured. Each value represents a single Rear Zone Temperature (RZT) reading obtained randomly during the period of time that the particular lot was being processed. Summary statistics were calculated to check for Normality. The distribution of values for the RZT variable in this furnace does not pass the skewness test for normality (p-value < 0.05). This means that the data follow another type of distribution, so we will try to fit a Gamma distribution. With an appropriate statistical test and the help of a plot we can check whether the calculated natural limits of a Gamma distribution make sense, and we can see that this is the case.
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I-MR Chart with Gamma Distribution for the individuals. We see that the process is in a state of statistical control. This condition being met, we can afterwards proceed with the assessment of capability measures to determine process risk. See page 2.
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Capability and Performance Indices: We would ideally expect Cp, Cpk and Cpm at a minimum of 1, long-term. When Cp, Cpk and Cpm equal 1, you have a maximum predicted to be 0.27% out of specification (or nonconforming parts). The values for Cp, Cpk and Cpm show that this process is not capable as all indices are < 1. The potential of the process to be capable, if properly targeted, based upon the spread or dispersion, is reflected in the index called Cp. The capability of the process to conform to specifications is the Cpk index. Finally, the capability of the process to conform to target is the Cpm index. This process is clearly off-center.
statistic eq n value
1 Cp = 0.6018636
2 Cpk = 0.6183494
3 Cpm = 0.5967405
4 Pp = 0.5961479
5 Ppk = 0.5862514
6 Ppm = 0.5958853
7 Obs. n / PPM (lower) = 2 17391.0000000
8 Obs. n / PPM (upper) = 7 60870.0000000
9 Obs. n / PPM (total) = 7 60870.0000000
10 Pot. PPM (lower) = 31795.0000000
11 Pot. PPM (upper) = 39275.0000000
12 Pot. PPM (total) = 71070.0000000