00110 j0536f1d3dde674795a26861d044a40

110

McWilliams

Table 2 are madę. In the case of sampling by attributes, I do modify the notation used by Lorenzen and Vance. Rather than expressing the control limit and the degree of shift induced by the assignable cause in standard deviation units, I find it morę natural to express the shift by directly specifying parameter values for in and out of control States (po and p\) and to express the control limit morę directly in terms of an acceptance number d.

A unique property of the Lorenzen-Vance model is the inclusion of a parameter (Co) to represent hourly ąuality costs due to the production of nonconforming items while the process is in control. Table 1 shows that the other models have no equivalent cost parameter. These models only consider the penalty incurred from production of additional nonconforming items when the process shifts to the out of control State. In situations where production continues during both searches and repairs (S\ =    = 1), the cost fiinction [1]

can be re-expressed as:

(Cl - Co) (-T+ nE + MARL2) + T\ + 72) ZŻARLI + W ^C_Co+    ECL    ⁺ ECL

\(a + bn)lh\\\IX- t+ nE + /?(ARL2) + T\ + T21 ⁺    ECL    ¹³¹

so the inclusion of Co has no effect on the choice of control chart parameters. Co is a "sunk cost" in the sense that, at a minimum, this hourly cost will be incurred regardless of how the process is controlled. As in the other models, the relevant penalty cost is the incremental cost incurred due to the shift, namely Ci - Co.

When the process is shut down for either searches or repairs (when 3\ and/or eąual zero), then the inclusion of Co in the model does affect the optimal solution, and the decision of whether to designate a non-zero value for this parameter depends upon one's philosophy regarding how ąuality costs should be measured. While the presentation of numerical results and sensitivity analyses is not the point of this article, a limited numerical study was performed to investigate the impact of increasing Co from zero with a corresponding increase in Ci to maintain a constant out of control penalty cost. This study did find input parameter combinations for which the optimal control chart parameter values are sensitive to the inclusion of a non-zero value for Co, so the issue of whether to include a value for Co may have practical significance.

As a finał comment on the model's input parameters, notę that when the process is shut down for either searches or repairs, the values assigned to parameters Y and/or W should reflect the cost of downtime (e.g., lost profit,