00031 K394645726cad93868e1559957462ad

30

Molnau

0 ± k[a/(2-a)]^o50.    [15]

For the time-between-events (TBE) EWMA, the variable of interest is the median value. Since the median value is 69.3% of the mean for the exponential distribution, the necessaiy changes to equation 14 are simple. The k-sigma control limits for the TBE EWMA are now defined as

(0.6930) ± k[a/(2-a)]^O5(O.6930)    [16]

Using the new control limits, the procedurę can be conducted with no other changes necessary.

Since the EWMA chart is easy to plot, easy to interpret, and its control limits easy to obtain, it is an excellent choice for a charting scheme.

Test Performance Comparisons

Keats, Datę, and Kim (1989) studied the effectiveness of the CUSUM, SPRT, Gap, Runs, and Autocorrelation procedures for a rangę of process scenarios. The CUSUM was by far the most productive test for the continuous, step-shift, and sudden-shift situations. Other tests, including the Gap, Runs, and Autocorrelation tests all were successful in some special cases, but were limited to their rangę of applicability. Neither the EWMA or the GCC were included in the study.

Test Combinations

Of the literaturę reviewed, only Lucas (1982) and Rowlands et. al. (1982) deal with the multiple chart analysis of data. Lucas adds Shewhart-type control limits to the CUSUM chart, thus eliminating the complex calculations of the parabolic CUSUM. The limits don't have to be recalculated after every observation, as with the parabolic schemes. The CUSUM charts used in this report are all of the type presented by Lucas. Rowlands, Nix, Abdollahlan and Kemp discussed running multiple charts concurrently.

Although the CUSUM can be viewed as a SPRT run backwards (Johnson and Leone [1962]), and for the variables case the EWMA can be adjusted to match CUSUM performance (Lucas and Saccucci [1990]), in this study we have treated the CUSUM, SPRT and the EWMA as separate tests. For the attribute case it is not elear how these three tests interrelate, therefore our research treated them as providing separate sources of information.