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Optimization and Sensitiyity Analysis

procedures. With a single chart in use throughout the organization, training and the operational costs of ąuality should be reduced as well. The operational costs of statistical ąuality control include software installation, revision expenditures and the costs associated with shop-floor and managerial ąuality reporting schemes.

Sensitivity analyses were performed on inputs to the Lorenzen and Vance economic model using different scenarios, process shift levels, and control chart procedures. Our results indicate high consistencies for parameter significance regardless of input scenario, size of the shift, or control chart procedurę. Four inputs: ratę of shift, magnitude of shift, the cost while producing in-control and the cost while producing out-of-control have the most impact on the response, expected cost per time unit. We also determined the primary influences on the optimal cost control chart design yariables for each procedurę. These relations can be useful if sampling restrictions occur. The CUSUM control chart costs less to operate than the X chart for all sizes of process shift, making the economical choice simple for the decision-maker in industry.

The authors have discussed economic models of this type with industrial practitioners, representing a variety of manufactured product. They are enthusiastic about selecting a particular chart and the associated parameters on an economic basis. The drawback to implementation in their opinion is the ability to estimate the costs and times reąuired for use with the LV model. A possible altemative to estimating all 12 input yariables in the model would be (1) to eliminate terms in the model associated with factors shown to be insignificant and (2) to modify the economic eąuation using ratios involving factors in the remaining terms. The ratios may be identified based on practicality and ease of estimation. The number of terms reąuired in the model will drop significantly as a result. Our determinations of the primary influences on average cost will aid in both the selection of ratios and in the choices of yariables to eliminate, simplifying the model.

References

Baneijee, P. K. and Rahim, M. A., (1987) "The Economic Design of Control Charts: A Renewal Theory Approach," Engineehng Optimization, 12, 63-73.

Baneijee P. K. and Rahim, M. A., (1988) "Economic Design of X-Control Charts Under Weibull Shock Models," Technometrics, 30, 407-414.