Iddq testing for CMOS VLSI

It is little more than 15-years since the idea of Iddq testing was first proposed. Many semiconductor companies now consider Iddq testing as an integral part of the overall testing for all IC's. This paper describes the present status of Iddq testing along with the essential items and necessary data related to Iddq testing. As part of the introduction, a historical background and discussion is given on why this test method has drawn attention. A section on physical defects with in-depth discussion and examples is used to illustrate why a test method outside the voltage environment is required. Data with additional information from case studies is used to explain the effectiveness of Iddq testing. In Section IV, design issues, design styles, Iddq test vector generation and simulation methods are discussed. The concern of whether Iddq testing will remain useful in deep submicron technologies is addressed (Section V). The use of Iddq testing for reliability screening is described (Section VI). The current measurement methods for Iddq testing are given (Section VII) followed by comments on the economics of Iddq testing (Section VIII). In Section IX pointers to some recent research are given and finally, concluding remarks are given in Section X     

A Shorter Truncated Sequential Test

This paper develops a truncated sequential test (TST) for production models that makes use of the preproduction testing and that allows unequal sample sizes from the production and the preproduction models. An example is given that compares the fixed time test (FTT) against the proposed truncated sequential test. In this example a significant reduction in testing required on the production model is achieved. Power tables for such tests are tabulated.     

A sequential procedure for multihypothesis testing

The sequential testing of more than two hypotheses has important applications in direct-sequence spread spectrum signal acquisition, multiple-resolution-element radar, and other areas. A useful sequential test which we term the MSPRT is studied in this paper. The test is shown to be a generalization of the sequential probability ratio test. Under Bayesian assumptions, it is argued that the MSPRT approximates the much more complicated optimal test when error probabilities are small and expected stopping times are large. Bounds on error probabilities are derived, and asymptotic expressions for the stopping time and error probabilities are given. A design procedure is presented for determining the parameters of the MSPRT. Two examples involving Gaussian densities are included, and comparisons are made between simulation results and asymptotic expressions. Comparisons with Bayesian fixed sample size tests are also made, and it is found that the MSPRT requires two to three times fewer samples on average     

Asymptotic efficiencies of truncated sequential tests

Truncation of a sequential test with constant boundaries is considered for the problem of testing a location hypothesis:f(x- theta_{0})versusf(x- theta_{1}). A test design procedure is developed by using bounds for the error probabilities under the hypothesis and alternative. By viewing the truncated sequential test as a mixture of a sequential probability ratio test and a fixed sample size test, its boundaries and truncation point can be obtained once the degree of mixture is specified. Asymptotically correct approximations for the operating characteristic function and the average sample number function of the resulting test are derived. Numerical results show that an appropriately designed truncated sequential test performs favorably as compared to both the fixed sample size test and the sequential probability ratio test with the same error probabilities. The average sample number function of the truncated test is uniformly smaller than that of the fixed sample size test, and the truncated test maintains average sample sizes under the hypothesis and the alternative that are close to those optimum values achieved by Wald's sequential probability ratio test. Moreover, the truncated test is more favorable than the sequential probability ratio test in the sense that is has smaller average sample size when the actual location parameter is betweentheta_{0}andtheta_{1}. This behavior becomes more pronounced as the error probabilities become smaller, implying that the truncated sequential test becomes more favorable as the error probabilities become smaller.     

序贯概率比检验法在导航精度试飞中的应用

以往导航精度试飞采用基于参数估计理论的误差统计法,须完成规定的试飞架次才能得出试飞结论。这里根据假设检验理论总结出序贯概率比检验法,在给定置信度和误差概率时,求出导航精度的拒绝域、接收域和观察域;当试验曲线收敛于接收域时即可提前结束试飞,达到节省架次的目的。通过应用表明该方法不但适用于导航系统,对其他系统也具参考价值。     

Authors' reply

For the original paper see ibid., vol. 42, no. 10, p. 1896-1903 (1994). Here the commenters aim to provide another reason in addition to those given in Section II of the aforementioned paper in response to the rhetorical question, “Which mode-matching equations are linearly independent?” When the mode-matching method is used to obtain the generalized scattering matrix of a discontinuity between two waveguides of different cross sections, it is essential to make an adequate choice of the eigenfunctions, which will be used to test the continuity equations of the tangential components of the electromagnetic field in the plane of the discontinuity. It is known that the testing eigenmodes are chosen as being those of the larger guide for enforcing the electric-field continuity and as those of the smaller guide for enforcing the magnetic-field continuity. This means that the electric-field test eigenmodes must be chosen from the smaller guide and the magnetic-field test eigenmodes must be chosen from the larger guide. In the original paper, the authors prove this, first qualitatively and then rigorously. Now the commenters would like to add their reason which lends further support to the point-of-view presented in the paper. In reply the authors disagree with the last sentence of the comments of Solano et al., i.e., that testing the continuity of the tangential magnetic field by the M modes of the larger guide would result in a wrong formulation if the testing cross section is the smaller one. In order to clarify the whole situation, the authors present a table of all possible testing equations     

Sequential detection of unknown frequency-hopped waveforms

The channelized receiver, which is optimal for the detection of unknown noncoherent frequency-hopped waveforms, bases its decisions on a fixed-length block of input data. A sequential method of interception is presented according to which whenever a new data element is collected, a decision is made as to the presence or nonpresence of a frequency-hopped waveform. If that decision is indeterminate, another data element is collected. An optimal sequential test is derived, under the assumption that the waveform signal-to-noise ratio (SNR) is known. It is shown that this sequential test requires less data, on average, than the fixed-length method to make a decision with the same reliability. A truncated sequential test is also derived where a decision is forced, if still indeterminate, after some fixed amount of data is collected. The truncated test is shown to improve the number of samples needed for a decision when the input SNR differs greatly from that assumed in the derivation of the test. Furthermore, it is shown that the truncated test yields a limited degree of robustness when the input SNR differs from that assumed.<>     

Reliability demonstration for safety-critical systems

This paper suggests a new model for reliability demonstration of safety-critical systems, based on the TRW Software Reliability Theory. The paper describes the model, the test equipment required, and test strategies based on the various constraints occurring during software development. The paper also compares a new testing method, single risk sequential testing (SRST), with the common probability ratio sequential testing method (PRST), and concludes that: (i) SRST provides higher chances of success than PRST; (ii) SRST takes less time to complete than PRST; and (iii) SRST satisfies the consumer-risk criterion, whereas PRST provides a much smaller consumer-risk than the requirement     

A lower bound to the distribution of computation for sequential decoding

In sequential decoding, the number of computations which the decoder must perform to decode the received digits is a random variable. In this paper, we derive a Paretian lower bound to the distribution of this random variable. We show thatP [C > L]L^{-rho}, whereCis the number of computations which the sequential decoder must perform to decode a block ofLambdatransmitted bits, and is a parameter which depends on the channel and the rate of the code. Our bound is valid for all sequential decoding schemes and all discrete memoryless channels. In Section II we give an example of a special channel for which a Paretian bound can be easily derived. In Sections III and IV we treat the general channel. In Section V we relate this bound to the memory buffer requirements of real-time sequential decoders. In Section VI, we show that this bound implies that certain moments of the distribution of the computation per digit are infinite, and we determine lower bounds to the rates above which these moments diverge. In most cases, our bounds coincide with previously known upper bounds to rates above which the moments converge. We conclude that the performance of systems using sequential decoding is limited by the computational and buffer capabilities of the decoder, not by the probability of making a decoding error. We further note that our bound applies only to sequential decoding, and that, in certain special cases (Section II), algebraic decoding methods prove superior.     

Iterative Antirandom Testing

Antirandom testing is a variation of pure random testing, which is the process of generating random patterns and applying it to a system under test (both software systems and hardware systems). However, research studies have shown that pure random testing is relatively less effective at fault detection than other testing techniques. Antirandom testing improves the fault-detection capability of random testing by employing the location information of previously executed test cases. In antirandom testing we select test case such that it is as different as possible from all the previous executed test cases. Unfortunately, this method essentially requires enumeration of the input space and computation of each input pattern when used on an arbitrary set of existing test data. This avoids scale-up to large test sets and (or) long input vectors. The objective of this paper is to find a more efficient method of the test generation which does not need any computation. The key idea of proposed approach is an iterative application of the short antirandom tests where the first test vector in each iteration is generated randomly. Moreover, we propose a new metric the Maximal Minimal Hamming Distance (MMHD) which allows us to define an optimal antirandom test with restricted number of patterns. Experimental results are given to evaluate the performance of the new approach.     

A generalized two-threshold detection procedure

A modified sequential procedure for testing binary hypotheses with different means, proposed by C.C. Lee and J.B. Thomas (ibid., vol.IT-30, no.1, p.16-23, Jan. 1984), is generalized for application to the case of multiple hypotheses with different means/variances of the Gaussian distribution. The method constitutes a two-threshold test for fixed-size packages of samples with a sequential procedure of discarding the package for which no decision is reached and subsequently testing a new package. The objective is to find an optimum package size N₀ which leads to the minimum overall average sample number (ASN) for a given overall error probability. An optimization algorithm is developed to extend the application of the Lee-Thomas procedure to the M-ary case. Performance characteristics of the generalized two-threshold (GTT) test procedure are compared with those of conventional sequential as well as fixed-sample-size (FSS) methods. It is shown for the M-ary different means/variances cases that for low error rates the number of samples required by the GTT test is, on the average, approximately half that needed by a FSS test. However, it is somewhat more than the ASN obtained with a conventional sequential test. With decreasing error probabilities the GTT test performance approaches that of conventional sequential methods     

斜缝法热像仪MTF参数测量的探讨和实践

结合红外热成像系统调制传递函数参数测试系统的研制,分析了斜缝法调制传递函数参数测试的理论,给出了其测量步骤和方法,以及相应的测试结果和分析对比数据。指出采取基于斜缝匹配的测量方法可以对探测器和光学系统分辨率等技术指标的要求适当降低。最后对影响测量结果的主要因素进行了分析。     

A Sequential Testing Procedure for a System's State Identification

The system and its components have only two states: complete success or complete failure. The components' states are random variables and the system's state depends deterministically on the states of its elements. This paper assumes the state of the system is unknown and presents a sequential testing procedure of the components in order to determine the system's state. The procedure minimizes the expected number of necessary tests for a wide class of systems. The procedure is needed when the system is entirely or partially consumed upon its use, e.g., the firing of a missile, and one wishes to know the system's state without actually operating the system.     

A system for the automatic recognition of moving patterns

A system for the automatic recognition of two-dimensional patterns is described; recognition taking place as images of the patterns move in a rapid nonstop manner across a stationary scanning unit which takes the form of a bank of photodiodes. Although emphasis is placed on the recognition of alphabetic and numeric characters, the principles developed are applicable to the recognition of more general types of two-dimensional patterns. The theoretical principles on which the system is based are developed in Section II and experimental and computer simulation results are given and discussed in Section III. In Section IV the difficulties involved in the manual design of the recognition "logic" are considered and reference is made to a machine algorithm for the automatic design and testing of a complete recognition system. Some results obtained when using the algorithm are presented.     

The Computer-Aided Approach to Susceptibility Testing

Susceptibility testing is generally performed using manual methods which result in the following disadvantages and limitations: tests are time consuming, frequency and amplitude accuracy may not be satisfactory, operator errors can easily occur, and test setup inaccuracies are seldom taken into account and compensated. A new and low-cost method of performing susceptibility testing automatically is presented in this paper. With the advent of test instrumentation operated under digital control and the availability of standardized interface systems, it is now possible to build test systems to carry out automated susceptibility tests which are particularly advantageous when digital equipment are to be tested. By driving power amplifiers from programmable sweep generators, the repeatability and accuracy of the testing will be considerably increased as a result of accurate frequency and amplitude controls using control loops (AFC and ALC). A computer can be used to control and to manage the execution oftests as well as the processing of off-line test results. Major advantages given by the automation of susceptibility testing are increased measurement accuracy, reduction of testing costs and EMC-problem prediction capabilities.     

Linear sequential pattern classification (Corresp.)

A nonparametric sequential pattern classifier called a linear sequential classifier (LSC) is presented. The pattern components are measured sequentially and the decisions either to measure the next component or to stop and classify the pattern are made using linear functions derived from sample patterns based on the least mean-square error criterion. The required linear functions are computed using an adaption of Greville's recursive algorithm for computing the generalized inverse of a matrix. A recursive algorithm for computing the least mean-square error is given and is used to determine the order in which the pattern components are measured. Under the assumption of two equiprobable classes that are normally distributed with equal covariance matrices, it is shown that the LSC is equivalent to Wald's sequential probability ratio test. Computer-simulated experiments indicate that the LSC is more effective than existing nonparametric sequential classifiers.     

On the sequential detection of emerging targets

Sequential analysis has been used in the literature for analyzing a radar search system. The procedure is to continually sample a given range "bin" until a yes-no decision concerning the presence of a target is made. The results, however, do not provide for the possibility of a target emerging into the bin during the sampling process. In this report we consider a likelihood-ratio test for detecting emerging targets by sequential sampling. It is shown that the decisioning threshold must be continually increased in order to maintain a fixed false alarm rate at each sample. An upper bound on the average number of samples required to detect an emerging target is computed, and the results are significant in that this bound may become quite large. A test using a fixed threshold in which the average false alarm rate is constrained is investigated and shown to be inferior to the variable threshold test. A suboptimum test using only a finite number of past samples is also considered. The results of this study are equally applicable to the converse problem, i.e., detecting when a known target exits from the bin, which is important in target tracking.     

Optimal Allocation of Effort to Improve System Reliability

The optimal allocation of development effort to improve reliability for systems of general, but fixed, structure is discussed from a deterministic standpoint and also when there is uncertainty in component reliabilities at various stages of development. A computational algorithm is given for implementing the optimal allocation, called the optimal policy, and the form of the solution is related to the special case of a series system when development effort functions are the same for all components. This methodology is a useful aid to decision-making about reliability improvements.     

TDRSS中的码同步技术

本文对ＴＤＲＳＳ中的码同步技术进行了理论研究。首重讨论了定长检测和序贯检测这两种捕获方法。基本理论分析和ＴＤＲＳＳ正返向链路同步性能的计算结果，序贯检测的捕获性能优于定长检测的性能。     

Design of Adaptive Procedures for Fault Detection and Isolation

An algorithm is presented for designing minimum-expected-cost test trees for detecting and isolating single faults in a system. A test is specified by the subset of components that must be good for the test to pass, and with each test is associated a fixed cost. Each component is assumed to have an a priori probability of failure. The test tree specifies an adaptive testing procedure that detects a failure and isolates the faulty component while minimizing the expected cost of testing.