00145 bd64c30a9510b5eb82a95c582420bd

146

Simpson & Keats

nonlinear optimization techniąue is a good candidate approach sińce it has been successful (see, for example, Saniga 1989 and Del Castillo et al. 1994) in solving problems of this type. A morę detailed description of tłiis techniąue can be found in Luenberger (1989) or Reklaitis et al. (1983).

Similar to the economic statistical designs, the trade-off approach was developed to address the concems mentioned in the introduction about economic designs. By focusing on designs with improved in-control and out-of-control run length performance, false alarm rates can be reduced and the ability to ąuickly detect shifts can be increased. lmproved statistical performance with focus on achieving the largest improvement in the region of minimum cost is also consistent with Deming's philosophy of tight process Controls. The charts presented in the examples enable designers to ąuickly understand the financial impacts of ARL improvements.

The trade-off approach provides the analyst or engineer with a view of a portion of the cost surface that may not be available under the constrained statistical economic approach. The constrained approach is certainly valid if the constraints are reąuired for a specific reason. It is possible though, that in many instances the control chart designer may not be able to define firm statistical constraints needed to successfiilly monitor and detect process assignable causes. The primary advantage of the trade-off approach over other economical statistical approaches is that it focuses the attention on the design altematives in the immediate vicinity of the minimum cost. It takes some of the guess work out of constraint formulation. Instead of arriving at a single best constrained design, the analyst can prepare several options with slightly different benefits, so that the decision maker can select the best choice for the organization.

Shewhart Chart vs. CUSUM in the LV Model

Statistical process control experts do not generally regard the X and CUSUM charts as competitors, but rather as complementary techniąues for solving a rangę of problems. The X detects larger shifts in the process mean versus the CUSUM which handles smaller shifts better. Rather than comparing these two charts on the basis of statistical performance, we propose a comparison in terms of cost of implementation. Statistical or ARL comparisons are often used to indicate the strengths of certain procedures under different process shift scenarios. Table 10 compares ARL values for the X and CUSUM charts with sample sizes of 1, 3 and 5.