00352 Y81713c432e612628e0c1a55ba8c097

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Prairie & Zimmer

Let Ed be the number of defective units produced and submitted up to the time of detection, and assume that the inspected defective unit is not submitted. Then,

E_d=Q*E_p"¹

Assume that each unit to be sampled takes T units of time to determine whether it is defective or non-defective and that those T units are submitted. No units beyond the T units will be submitted until the results from the sample units are known. Then the expected number of defective units

submitted, Ed|Q*, during the period with defect ratę Q* that are defective

due to the modę associated with Q* is

E_d|Q.= E_d +Q*T(l-p)

= £z£ł(i _{+ p}TQ*), if Q*>0,p>0,N>——    [11]

P    PQ*

=0, if Q*=0

where N is the total number of units produced.

Figures 3 through 7 show contours of constant average numbers of submitted defective units, Ed|Q* as a function of sampling ratę p and test time T. Each figurę shows contours for a fixed value of incremental defect ratę

Q*. These figures show the impact of the sampling ratę for instantaneous test

time as well as the change in sampling ratę reąuired as test time increases. For

%

example, consider the results shown in Figurę 5 with Q = .2. With large values of Ed|Q*, the effect of T is negligible to about T = 40 and the reąuired sample ratę is less than .05. For smali values of Ed|Q*, the reąuired sample ratę is much higher and the effect of T is large. For example at Ed|Q* = 5, the sample ratę at T = 0 is about. 17 whereas for T = 40, it is about .50. The main use for these figures is to get some sense for the impact on number of accepted defective units as a function of sampling ratę and test time. The use of these figures for generating a plan involves some subjectivity.

Consider, for example, a plan that is to be developed for a component for which about 2000 units will be produced. Based on analysis of similar components and on engineering judgment, a new failure modę with a defect

increment of morę than Q* = .1 is seen as unlikely and, therefore, it is