00353 [8365c31cc1dd1f95a44b8594b6530a

357

A Monitoring Plan for Detecting Product Degradation

sufficient to protect against such an increment. The value for Ed|Q* of the number of accepted defective units given a perturbation is important in

selecting a sampling plan. Since Q* = . 1 the curves in Figurę 4 can be used to evaluate Ed|Q* for various sampling rates and test times. If no morę than two accepted defective units are tolerable, then the minimum sampling ratę is p = .33 for T = 0, and up to p = .5 for T = 20. For a total production of 2000, two additional defective units represent an increase in unreliability of .001. Perhaps a morę realistic increase to detect would be .005 over the total production. An increase of .005 represents 10 additional defective units for a total production of 2000 units. For E<j|Q* = 10, the contour is not very steep until T » 50. Up to T = 20, a sampling ratę of p = . 1 is appropriate. It must be emphasized that with the effective inclusion of methods of statistical process control (SPC), the detection of a reliability perturbation would be ąuickened; this is one way to reduce the sampling ratę and yet not increase the risk of submitting a defective product.

Conclusion and Eiample

In summary, Figures 3 through 7 and Eąuation [11] can be useful in developing monitoring plans and assessing the risk associated with various sampling programs and allowable test times. This discussion has been centered on one process perturbation; additional perturbations would increase the number of accepted defective units proportionally. The exact plan depends strongly on the new failure modę probability that is to be protected against. It seems that one would want to carefully analyze past data, the development process, and failure modes and effects analysis in order to determine what new defect ratę is to be protected against with regard to the criterion on expected

number of defective units accepted. Unrealistically large values of Q would

lead to stringent values of p and/or T, whereas Iow values of Q would lead to values of p and/or T which would not give the desired protection.

Example A complex system is to be produced in a continuous manner and it is desired to subject the finał produced units to a sampling plan in order to monitor the finał system reliability. A total production of about 2000 units is expected. The reliability reąuirement for the system is .99. The ratę of production and test time are such that about 10 units are produced during the time that it takes to test one unit and designate it as a failed or non-failed unit. Based upon test costs and the protection required it is decided to use a plan