Sampling Plans for Disk Defects Using Markov Chain Model

To minimize cost, sampling plans are extensively used in the disk manufacturing. For each disk, only a portion of the tracks is tested. Because of manufacturing constraints, the locations of the tracks are not random. Usually, every v(supth) track is tested. Most sampling plans assume that the tested tracks are random sample from a homogeneous population. However, adjacent tracks can be very correlated when the size of the defect is large compared to the size of the track on the disk. This paper described a two states Markov chain to model the disk defects. Two dimensional disk surface is simplified as a one dimensional line segment. Any point can be non-defective (state 0) or defective (state 1). The length of defect and nondefect are assumed to be exponential with rate lambda and mu are allowed to come from a mixture distribution. Parameters of the model can be estimated using the maximum likelihood method. The yield and escape rate can be calculated for any specified sampling rate. The manufacturer can then chose an optimum sampling rate to minimize escape rate and maximize the disk yield at low test cost.