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Such a phenomenon occurs with some probability. If the number of defective devices x detected in a sample of n devices does not exceed c, the entire lot is considered to have passed R inspection. IX through IX, the Pascal and Gamma distributions are the discrete and continuous probability distributions for the same probability model. Therefore, the MTBF for a truncated portion of the life of the equipment up to the time T0 is estimated using the following expression: Each test result is independent from one another.
A.1 AQL Sampling Table
In this case as well, the failures of individual devices are taken to be mutually independent. We deal with this issue in B.
Let us assume that a x lot of semiconductor devices are storage tested at temperature T. This is analogous to the fact that the remaining life of an adult is not necessarily equal to the expected lifetime of a new born child minus the adult’s actual age.
This is explained as follows. As time t passes, the failure rate of these semiconductor devices changes.
JIS Z – Test methods for flat pallets (FOREIGN STANDARD)
A mask defect can be detected at the same level of expectation at the inspection area t and at the number of inspection cycles x figure 0620. If the operating time between subsequent failures of a device throughout its life until discarded is given by t1, t2, Use first sampling plan below arrow.
The reliability function R t for this system is given by the Poisson partial sum. The area of the wafer surface S is divided into many portions. Let us assume that floating dust causes an average of jix mask defects on the surfaces of silicon wafers of a given lot.
The probability of defective items produced in the iis process is p. The jiz rate K using this model is given by the following expression: To serve as an example, consider the life L in equation IX This model consists of m units connected in series, which i-th unit has ni devices connected in parallel. In general, once a semiconductor device has failed, it cannot be repaired and used again. The number of samples is determined according to the limits of the binomial distribution indexes.
If the sampled device is not returned non-replacementwe will have a hypergeometric distribution. This is referred to as upper 20 percent point. This is because the denominator of js defining expression equation IX component hours does not refer to any particular device.
A.1 AQL Sampling Table
The AQL plan measures the lot whose fraction defective is p1 as having the lowest acceptable quality level. For studying the change, in this model, probabilities of individual devices failing by the time t are uniformly p tand the probability that at least one of the n devices will fail is F t.
This is consistent with the fact that the geometric and exponential distributions are discrete and continuous distributions, respectively IX In this case, the failure probability density function becomes equation IX for the Gamma distribution. As long as there is no great variation in the quality of this lot, the distribution of the life L as caused by the stress placed on the devices by the temperature T is expressed as a logarithmic normal distribution and should be analyzed jiz such.
When equipment can be repaired by renewing a failed device, the mean value of the interval that operation is possible between occurrences of failures is know as the MTBF Mean S Between Failures. The Weibull chart is useful for analysis of failure mode since observed data are graphed on the Weibull chart in the shape of an linear expression.
In such a case, stress is applied locally to the device and the life or zz withstanding limit of the device depends on its weak point. Wear-outfailures which almost suddenly outbreak after a certain period approximate the normal distribution. By inspecting n randomly sampled devices, x defective devices are detected with the probability fH – geo N, R, n, x.
Noting the relation expressed by Eqs.
This approximates AQL values. Displacement mm [single amplitude] v: Chapter 5 – Basic Concepts of Probability. The Poisson distribution approximates the binomial probability distribution a the population is large a the phenomenon occurs with a low probability. By considering the probability of detecting the first failure at time t, the relation of exponential and geometric distributions can be identified. The average probability of finding a mask defect within the area C approaches the probability that a mask defect exists on a point jiis the surface of the wafer.
The lot is acccepted when failures are grater than Ac but less then Re. This process is explained in detail as follows. MTBF known after the life of equipment is of no practical use. Regular versus Military Time.
The double exponential distribution is suitable for analysis of such kinds of phenomena. Since the location of the dust particles on the wafer surface is unpredictable, we can assume that mask defects occur completely at r random.
For ease of understanding we have chosen “failure” and “no failure” for results 1 and 2respectively. Will not be passed. The cumulative failure rate FWbl t determined from observed data is described by the Weibull distribution. From one end of the wafer, each portion is inspected with a microscope.