A formulation to optimize stress testing

Although hard-defects may be detectable in factory tests, weak products may exhibit failures or degrade only under certain stress conditions. Without stress testing, these weak products may often be shipped to customers causing early failures in the field. A candidate product for stress testing needs to get more business benefits to more than pay off the cost of stress testing. A business measure of the success of the stress testing program is the net benefit, which is the total benefit minus the total cost of the program. The optimum stress testing program maximizes this net benefit. A given unit of a product has a probability of encountering a maximum stress X during its product life. It also has a probability of possessing a product yield strength Y, which is the maximum stress the unit can survive without failure. While the strength distribution depends on the design and manufacture processes, the distribution of the maximum stress is determined by the customers´ environment. A convenient picture is to construct the contour map of the joint probability distribution of X and Y. In this contour map, a unit falling in the Y<X region will fail during its product life, whereas one falling in the Y>X region will not result in field failure. The effects of stress testing at a given maximum stress level, X^ST, are shown by a dividing line on the product strength into stress test failure and stress test pass. The units in the contour map are then divided into four regions by the Y=X line and the X^ST line. The cost and benefits may now be evaluated for each region. Now the value of X^ST is a free parameter that determines the relative size of each region. The second free parameter is the fraction of units going through stress testing. These two parameters may be adjusted to maximize the net benefit of the stress testing program