00351 ë9f2f4c540173aecfb5821ca7f62677

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A Monitoring Plan for Detecting Product Degradation

for N > ^1 + jc

Of most interest is the time it takes to discover a problem and the number of defective units shipped during periods of decreased reliability. For purposes of developing a formula that gives the expected number of defective units accepted, it will be assumed that the process is continuous and is producing products at an acceptable reliability, Q, expressed in terms of unreliability. At an unknown time, a process perturbation occurs and

introduces a new failure modÄ™ with defect ratÄ™ Q*. Thus, the new defect ratÄ™ is Q + Q . One way to assess a sampling plan is to compute the expected number of defective units submitted beyond those which would have been submitted with fraction defective Q. It will be assumed that if a defective unit

is sampled where defectiveness is due to the modÄ™ with ratÄ™ Q*, it will be correctly designated.

Let p be the sampling ratÄ™ and T the maximum allowable test time (if a sample test exceeds T units of production, submittal shall cease until the results of the test are known). NotÄ™ that T can be zero, which means that no units may be submitted beyond a sample test unit until the results of that test are known. This is the situation with conventional continuous sampling.

Because the number of defective units produced before detection is the Ä…uantity of interest, methods that use the algebra of life testing may be used. Parameters that will affect this number are the plan parameters, p and T, and

the process parameter, Q*.

Let E_s be the expected number of sample units reÄ…uired to detect a failure modÄ™, given that the defect ratÄ™ is Q*. Then,

Let Ep be the expected number of units produced up to detection of the modÄ™ with defect ratÄ™ Q given that the sampling is done at ratÄ™ p. Then,

p

E

KPJ

1

PQ*