00024 ´b995e2ba34fa28ca2a7269f112a0d5

23

A Rule-Based Approach to Multiple Statistical Test Analysis

research framework is based on combining the strengths of some tests to offset the weaknesses of other tests. Following are brief discussions on four on-line attribute analysis methods and their applicability. Ali four methods are useful for the fuli rangÄ™ of probable defect rates.

TBE CUSUM

The Cumulative Sum (CUSUM) procedurÄ™, first introduced by Page (1954), provides for tighter process control than regular Shewhart charts. The CUSUM stresses the importance of aiming for target values, as opposed to allowing values to vary within prescribed limits. The CUSUM accumulates deviations from the target, therefore any variance is noted. Instead of waiting for nonconforming items to be produced, the CUSUM can predict when action needs to be taken to avoid producing bad items. In operations where PPM or DPM criteria are used, the shift detection capability could be very useful. The additional sensitivity would allow for slight shift detections to be madÄ™ much sooner than if an out-of-control signal from another method was waited for.

While most applications of the CUSUM procedurÄ™ have been for continuous variables, procedures have been developed for attribute variables as well. Lucas (1985) describes the use of the Time-Between-Events (TBE) CUSUM using counted data. This procedurÄ™ allows for the detection of increasing or decreasing defect count levels.

The CUSUM procedurÄ™ accumulates the differences between observed values and reference values. The accumulated test statistic is then measured against a decision interval. If the value exceeds or is equal to the decision interval, the process is determined to be out-of-control.

The TBE CUSUM test statistic to detect a decrease in time between

events is

Sj = max [0, K_b-Yj + S_(M)]    [1]

where

Sj = the fth CUSUM statistic value Yj = the observed value of units between defects = the reference value for the CUSUM

The increasing ratÄ™ TBE test statistic is defined as Sj = max [0, Yj-Kjj + S^.^]

The reference value, K^, is computed as:

[2]