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Pignatiello & Ramberg
the process is in-control or is normal and they are not calculated using the subgroup sample statistics. That is, they are calculated using all of the data collected and without regard for whether points were out-of-control. The process performance indices make use of the sample standard deviation S sińce
it includes both common and special cause variation. Here, S = , where
S2 is calculated by dividing the sum of the squares of each individual observation about the grand overal! average by n - 1. That is, they use procedurÄ™ 2 (given below), but use all of the unedited data.
Process performance indices do assume that the data has been collected over a representative period. Thus, process performance indices provide a morę realistic assessment of what is being produced. We are unable, however, to represent their uncertainty, sińce we cannot calculate a standard error or give confidence intervals.
Process Modeling
A process model is useful for understanding and assessing the capability of a process. In the simplest situation, we could entertain the model:
Observation = Mean + Noise [ 1 ]
Which assumes independent noise elements. In this primitive model the noise represents the variability due to all sources, including measurement equipment, machines, raw materials and people. In this situation, control charts for the individual measurements are useful for controlling the process and as a data collection scheme.
There are two obvious procedures for estimating the process characteristics from a process capability study. We interpret the draft of the forthcoming standard to view both procedures as acceptable. The first step of both procedures is to delete data corresponding to ‘but-of-control†situations before summarizing the data. Typically, control charts for individual observations and moving ranges are used in this situation. In this setting, the two procedures are:
•Procedurę 1: Estimate the process mean, p, by X . Estimate the process standard deviation, a, by MR/d2 .
•Procedurę 2: Estimate the process mean, p, by X . Estimate the process standard deviation, a, by the sample standard deviation of the (edited) data.
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