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27

A Rule-Based Approach to Multiple Statistical Test Analysis

Coleman shows that the transformation makes each observation from the distribution in eąuation 8. Since the sum of independent chi-square variables are also chi-square distributed, a test statistic for a seąuence of failure observations can be developed. This statistic is shown as

£2xi/0    [10]

i=l

which is chi-square with 2k degrees of freedom. The test can be conducted for selected seąuence lengths of k, and measured against determined degrees of confldence.

Consider an example with seąuence length k = 4 and MTBF 0 = 20,000 observations. The time between failures, Xj, are Xj = 16,210, X2 = 21,050, x-j = 31,028, and x^ = 12,905. This provides for

4

£2xi/0 = 8.1203    [11]

i=l

with 8 degrees of freedom. The a = .99 two-tailed critical value is 1.344, therefore the process is determined to be in control.

Even though the GCC is a relatively easy and promising procedurę, it has been sparsely used and published.

EWMA

The Exponentially Weighted Moving Average (EWMA) was first investigated for control charting in 1959 (Roberts, [1959]). Early uses for the EWMA included economics, inventory control and forecasting. Although its contributions to the field of ąuality control are documented, the EWMA remains an underused tool. The EWMA is also known as the Geometrie Moving Average, Exponential Smoothing and a first order Integrated Moving Average (IMA (1,1)). It is also very similar to other methods, namely the Seąuential Moving Average and the Moving Average approaches. These approaches are intricately different, but have one common aspect-they all are based on a limited number of historie observations.

One key to understanding the differences between Shewhart, CUSUM, and EWMA control procedures relies on the methods each techniąue uses historical data. Shewhart charts compare observations to precalculated control limits. Even though past data was used to determine the control limits, all the evaluation weight is placed on the observed value. All past data has a weight