D. S. Bai and J. S. Rustagi Communications in Statistics 3: (4) 361371 1974 
"Inference in a Waitingtime Distribution Derived from Dependent Bernoulli Trials " 
The problem of unbiased estimation of parameters and test of independence are studied for the probability distribution of the number of Markov dependent Bernoulli trials required so as to obtain a preassigned number of successes. It is shown that the maximum likelihood estimate of one parameter is minimumvariance unbiased while that of the other parameter tends to overestimate the true value. For this parameter an alternative estimate is given. A test procedure for the independence of trials is also proposed.

D. S. Bai The Annals of Statistics 3: (6) 13051317 1975 
"Efficient Estimation of Transition Probabilities in a Markov Chain " 
Let X1, ..., XN be N observation on an mstate Markov chain with stationary transition probability matrix P=(pij), pij>0, i, j=1,...,m, where N is a random variable. For any parametric function of P, the information inequality gives a lower bound on the variance of an unbiased estimator; attaining the lower bound depends on whether the sampling plan or stopping rule S, the estimator f=f(X1, ..., XN), and the function E(f)=g(P) are "efficient". All "efficient triples" (S, f, g) are characterized for the Markov chain in which pij and pi'j' (i'i¦ªi) are not related functionally. It is also shown that efficient triples do not exist if m>2 and g is a function of two or more rows of P. For the case m=2, efficient triples in which g's are functions of both rows are characterized.

D. S. Bai and S. I. Kim COMMUN. STATIST. THEOR. METH. 8: (6) 591599 1979 
"Estimation of Transition Probabilities in a Twostate Markov Chain " 
Small sample estimators for the transition probabilities of an irreducible Markov chain with tow ergodic states which have smallest possible biases are proposed. It is also shown that the conventional maximum likelihood estimator of the transition probability from a state to itself tends to underestimate the true value.

D. S. Bai and S. I. Kim COMMUN. STATIST.THEOR. METH. 9: (13) 14011410 1980 
"On Parameter Estimation in Bernoulli Trials with Dependence " 
A simple estimator is proposed for the dependence parameter for the Klotz model of Bernoulli trials with Markov dependence and it is compared with the ratio estimator given by Price and the approximate maximum likelihood estimator given by Klotz. The proposed estimator is shown to have considerably smaller bias than the other two estimators with comparable mean squared errors, and has all the large sample optimal properties that the other two estimators have.

D. S. Bai and D. W. Kim European Journal of Operational Research 8: (2) 159165 Oct. 1981 
"An adaptive algorithm for discretetime differential games " 
This paper presents an algorithm for a player to improve his performance by adapting optimally over his nonoptimally playing opponent in discretetime differential games. The algorithm first estimates the opponent's actual strategies and then constructs an adaptive strategy for the player. The adaptive strategy is periodically updated according to the opponent's behavior using the neighboring optimal closedloop solution technique. An example is given which demonstrates the superiority of this algorithm over the conventional one which assumes that the opponent plays optimally.

D. S. Bai and T. Y. Kwon Naval Research Logistics Quarterly 30: 347358 1983 
"Stochastic Duels with Multiple Hits and Limited Ammunition Supply " 
Ancker's stochastic duels with limited ammunition supply are extended to cases where a kill is obtained through repetitive multiple hits with two firing modes, singleshot firing and pattern firing. Examples with negative exponential firing time and geometric ammunition supply are given.

D. S. Bai and K. I. Choe Journal of Applied Probability 20: (4) 891896 1983 
"A Secretary Problem with Backward Solicitation and Uncertain Employment " 
A secretary problem which allows the applicant to refuse an offer of employment with a fixed probability and admits backward solicitations of previous interviewees with known probability of successful solicitation is considered. The optimal strategy that maximizes the probability of employing the best applicant is derived. Two types of probability of successful solicitation, constant and geometric, are discussed in detail.

D. S. Bai, J. S. Jang and Y. I. Kwon IEEE TRANSACTIONS ON RELIABILITY 32: (5) 512514 1983 
"Generalized Preventive Maintenance Policies for a System Subject to Deterioration " 
Preventive maintenance models are proposed for a system with two types of units operation sindependently and subject to deterioration. The system undergoes minimal repair on type1 unit failure and is replaced on type2 unit failure. Three policies which minimize average costs including the earning loss due to deteriorationare discussed; one is based on the cummulative operating time, a second on the number of minimal repairs performed, and the other on both.

D. S. Bai and M. C. Riew Journal of Quality Technology 16: (3) 136143 1984 
"An Economic Attributes Acceptance Sampling Plan with Three Decision Criteria " 
An economic acceptance sampling plan by attributes is developed for situations where sampling inspection is expensive and/or destructive. It is assumed that the sampling inspection is error free, but that screening inspection of rejected lots is subject to error. Three decision criteria are considered: acceptance, screening, or scrapping. A linear cost model is given and methods for finding optimal sampling plans are presented for both a beta binomial prior and a double binomial prior. Comparisons are made with plans using only two decisions.

D. S. Bai and J. S. Jang 
"Efficient Sequential Estimation in a Markov Branching Process with Immigration " 
Sequential estimation of parameters in a continuous time Markov breanching process with immigration with split rate N¥ä1, immigration rate N¥ä2, offspring distribution P1j, j>=0 and immigration distribution P2j, j>=1 is considered. A sequential version of the CramerRao type information inequality is derived which gives a lower bound on the variances of unbiased estimators for any function of these parameters. Attaining the lower bounds depends on whether the sampling plan or stopping rule S, the estimator f, and the parametric function g=E(f) are 'efficient'. All 'efficient' triples (S, f, g) are characterized; it is shown that for i=1,2, only linear combinations of N¥äiPij's or their ratios are 'efficiently' estimable. Applications to a Yule process, a linear birth and death process with immigration and an M/M/i¡û queue are also considered.

D. S. Bai and W. Y. Yun Reliability Engineering 16: 201206 1986 
"Optimal Numbers of Redundant Units for Parallel Systems with Common Mode Failures " 
This paper considers the problem of determining optimal numbers of redundant units in parallel systems with common mode failures. Cost models are obtained considering both the common mode failures and the components' random failures. The number of redundant units minimizing the expected cost rates is shown to be finite and unique.

D. S. Bai and W. Y. Yun IEEE TRANSACTIONS ON RELIABILITY 35: (4) 452454 1986 
"An Age Replacement Policy with Minimal Repair Cost Limit " 
A generalized replacement policy based both on the system age and the minimal repair cost limit is proposed. The system is replaced when it fails for the first time after age T. If it fails before age T, the repair cost is estimated and minimal repair is then undertaken if the estimated cost is less than a predetermined limit L; otherwise, the system is replaced. The mean cost rate is obtained, its behavior is examined, and ways of obtaining optimal T and L are explored.

D. S. Bai and S. I. Kim Statistics & Probability Letters 5: 225230 1987 
"On Unbiased Multinomial Estimation " 
The uniformly minimum variance unbiased estimate of a parametric function and its variance are derived under the inverse multinomial sampling plan of mth order (IMSP(m)), and it is shown that IMSP(m) can be used more advantageously than IMSP(j), j 
D. S. Bai and J. S. Jang IEEE TRANSACTIONS ON RELIABILITY 36: (2) 255258 1987 
"Efficient Sequential Estimation in Nonhomogeneous Poisson Process " 
Sequential estimation in a nonhomogeneous Poisson process with intensity function N¥äY(t) is considered where Y(t) is an observable process. A sequential version of the CramerRao type information inequality is derived which gives a lower bound on the variances of the unbiased estimators of parametric functions of N¥ä. All efficient estimators whose variances attain the lower bound are characterized together with the corresponding closed sampling plans.

D. S. Bai and W. Y. Yun Reliability Engineering 19: 99103 1987 
"Cost Limit Replacement Policy Under Imperfect Repair" " 
A repair cost limit policy is studied for a system whose repair cost can be estimated by inspection. When a system fails, the repair cost is estimated and repair is undertaken if the estimated cost is less than a predetermined limit L; otherwise, the system is replaced. After repair, the system is as good as new with (1p) or is minimally repaired with p. The sexpected cost rate is used as a criterion for optimization. The existence and uniqueness of optimum L are studied for the case of Weibull timetofailure distribution and negative exponential repair cost distribution.

D. S. Bai and W. Y. Yun IEEE TRANSACTIONS ON RELIABILITY 37: (1) 4144 1988 
"Optimum number of errors corrected before releasing a software system" " 
This paper considers software release problems based on JelinskiMoranda and decreasingfailurerate models. The following software release policy is considered: After a preassigned number, n, of errors are removed, the test is terminated and the software system is released to the operational phase. The average fin is used as a criterion; there exists a unique optimal value of n. Numerical examples indicate that software release policy based on the number of errors detected can be a good alternative to the existing policy.

D. S. Bai and W. Y. Yun Reliability Engineering and System Safety 23: 5964 1988 
"Repair cost limit replacement policy under imperfect inspection" " 
A replacement policy with minimal repair cost limit is discussed. When a system fails, the repair cost is estimated by inspection and minimal repair is then undertaken if the estimated cost is less than a predetermined limit L; otherwise, the system is replaced. It is assumed that repair cost can not be estimated exactly because of imperfect inspection. When the failure time follows a Weibull distribution and repair cost a normal distribution, the value of repair cost limit minimizing the expected cost rate is shown to be finite and unique.

D. S. Bai and J. S. Jang COOMMUN. STATIST.  THEORY METH. 17: (12) 43714388 1988 
"Efficient sequential estimation in multiplicative counting process" " 
The problem of efficient sequential estimation in counting processes with multiplicative intensity processes is considered. A sequential version of CramerRao type information inequality is obtained and all the 'efficient' triples (S,f,g) are characterized: the variance of an unbiased estimator f for g attains the lower bound under a sampling plan S. Applications to Poisson processes, Markov processes, birth and death processes and Markov branching processes with immigration are also considered.

D. S. Bai and S. W. Chung Reliability Engineering and System Safety 24: 223230 1989 
"An accelerated life test model with inverse power law" " 
Constant and progressive stress accelerated life test models based on the inverse power law and Weibull lifetime distributions are proposed in which the Weibull scale parameter at use condition has a gamma prior distribution and other parameters are unknown constants. Bayes and maximum likelihood methods are used to estimate the model parameters. Monte Carlo study is performed to investigate the behaviour of the estimators.

D. S. Bai, M. S. Kim and S. H. Lee IEEE TRANSACTIONS ON RELIABILITY 38: (5) 528532 1989 
"Optimum simple stepstress accelerated life tests with censoring" " 
This paper presents the optimum simple timestep and failurestep stress accelerated life tests for the case where a prespecified censoring time is involved. An exponential life distribution with a mean that is a loglinear function of stress, and a cumulative exposure model are assumed. We obtain the optimum test plans to minimize the asymptotic variance of the maximum likelihood estimator (MLE) of the mean life at a design stress. The optimum failurestep stress test plans are obtained in a closed for,. whereas for timestep stress nomographs are given for finding the optimum plans based on parameters that must be approximated from experience, similar data, or a preliminary test. For some selected values of the parameters, the effect of incorrect preestimates of the parameters in terms of the percentage of variance increase has been studies and is small.

D. S. Bai, M. S. Kim and W. Y. Yun IEEE TRANSACTIONS ON RELIABILITY 39: (2) 167170 1990 
"Optimum software release policy with random life cycle" " 
A software release problem based on 4 softwarereliability growth models(SRGMs) with random life cycle length is studied. Test of the software system is terminated after time T, and released (sold) to the user at a price. The price of the software system and three cost components are considered and average total profit is used as a criterion. The optimal values of release times are shown to be finite and unique. Hence, the optimal solutions can be obtained numerically by, for example, a bisection method. Numerical example indicates that the optimal release time increases as; 1) the error rate in each model decreases, and 2) the difference between the error fixing cost during test phase and that during operational phase increases. The case of unknown model parameters is considered only for JelinskiMoranda model because a Bayes model is not available for other SRGMs. the release decision depends on testing time; but other stopping rules, for example, based on number of corrected errors, can be considered.

D. S. Bai, S. B. Kim and M. C. Riew Metrika 37: 263280 1990 
"Economic screening procedures based on correlated variables" " 
Economic screening procedures for improving outgoing product quality based on screening variables are presented for the cases of one and twosided specification limits. It is assumed that the performance and screening variables are jointly normally distributed and that costs are incurred by screening inspection and misclassification errors. When all parameters are known, a closedform solution is obtained for the case of onesided specification limit and an approximate closedform solution is derived for the case of twosided specification limits. Methods for finding optimal solutions based on normal conditioned on tdistribution are presented for the cases of unknown parameters.

D. S. Bai and S. H. Hong Metrika 37: 905918 1990 
"Economic design of sampling plans with multidecision alternatives" " 
For situations where there are several markets with different profitcost structures, economic attributes sampling plans are developed for determining the market to ship the lot to. Two sampling plans are considered; the fixedsize sampling plan with several levels of acceptance numbers and the inverse sampling plan with several levels of sample sizes. Linear profit models are constructed which involve four profit/cost components; profit from a conforming item, inspection cost, replacement cost, and cost from an accepted nonconforming item. For fixed optimal sampling plans are presented and examples with betabinomial prior distributions are given.

D. S. Bai and S. B. Kim Naval Research Logistics 37: 919928 1990 
"Economic Screening Procedures in Logistic and Normal Models " 
Economic screening procedures based on a continuous screening variable X in place of a dichotomous performance variable T are presented. Optimal critical values on the screening variable minimizing the expected cost are obtained for two models; it is assumed that X given T is normally distributed in normal model and P[T=1X] is a logistic function of X in the logistic model, and that costs are incurred by screening inspection and misclassification errors. Cases where some parameters are unknown are also considered.

D. S. Bai and S. W. Chung Reliability Engineering and System Safety 42: 5764 1991 
"An Optimal Design of Accelerated Life Test for Exponential Distribution " 
This paper considers the optimal design of accelerated life tests in which two levels, high and low, of stress are constantly applied and the failed test items are replaced with new ones. For exponential distribution with mean life of a log linear function of stress, the maximum likilihood estimator of log mean life at design stress is to be used. The standardized low level of stress and initial sample proportion allocated to it which minimize the estimator's asymptotic variance are determined. Sensitivity analysis is given.

D. S. Bai, W. Y. Yun and S. W. Chung IEEE TRANSACTIONS ON RELIABILITY 40: (1) 5659 1991 
"Redundancy Optimization of koutofn Systems with CommonCause Failures " 
This paper considers the problem of determining the optimal number of redundant units in koutofn systems with commoncause failures (CCFs). The mean cost rate is obtained, its behavior is examined considering both CCFs and random failures of the units, and the number of redundant units minimizing the mean cost rate is shown to be finite and unique. For the problem of determining optimal number of redundant units and inspection period, the mean cost rate is obtained and a solution procedure is presented. Numerical studies indicate that CCFs tend to reduce the optimal number of redundant units.

D. S. Bai and Y. R. Chun IEEE TRANSACTIONS ON RELIABILITY 40: (5) 622627 1991 
"OPTIMUM SIMPLE STEPSTRESS ACCELERATED LIFETESTS WITH COMPETING CAUSES OF FAILURE " 
This paper presents optimum simple stepstress accelerated life tests (ALTs) for products with competing causes of failure. The life distribution of each failure cause, which is independent of the others, is assumed to be exponential with a mean that is a loglinear function of the stress, and a cumulative exposure model is assumed. Optimum plans for timestep and failurestep ALTs are obtained which minimize the sum over all failure causes of asymptotic variances of the maximum likelihood estimators of the log mean lives at design stress. The competing causes of failure affect the optimum test plan only through the product of two ratios  the ratio of the sums of the mean lives and the ratio of the sums of the failure rates over all failure causes at low and high stress levels. The effect of this product (of two ratios) is studied.

D. S. Bai and Y. W. Hong COMMUNICATIONS IN STATISTICSTHEORY AND METHODS 21: (1) 269282 1992 
"ESTIMATION OF PR(XLESSTHANY) IN THE EXPONENTIAL CASE WITH COMMON LOCATION PARAMETER " 
This paper considers the problem of estimating the probability P = Pr(X < Y) when X and Y are independent exponential random variables with unequal scale parameters and a common location parameter. Uniformly minimum variance unbiased estimator of P is obtained. The asymptotic distribution of the maximum likelihood estimator is obtained and then the asymptotic equivalence of the two estimators is established. Performance of the two estimators for moderate sample sizes is studied by Monte Carlo simulation. An approximate interval estimator is also obtained.

D. S. Bai and S. B. Kim Metrika 39 : 8593 1992 
"Economic Design of OneSided Screening Procedures Based on a Correlated Variable with All Parameters Unknown " 
Economic design of onesided screening procedures for improving outgoing product quality based on a screening variable is considered for the case with all parameters unknown. It is assumed that the performance and screening variables are jointly normally distributed and costs are incurred by screening inspection, acceptance of an imperfect item, and disposition of a rejected one. A method for finding optimal cutoff value based on the predictive distribution is presented.

D. S. Bai and S. H. Song NAVAL RESEARCH LOGISTICS 39: (4) 471485 1992 
"ECONOMIC SCREENING PROCEDURES USING A CORRELATED VARIABLE WITH MULTIDECISION ALTERNATIVES" 
Economic screening procedures using a correlated variable are developed for selecting markets in situations when there are several markets with different profit/cost structures. It is assumed that the performance variable and the screening variable are jointly normally distributed. Profit models are constructed which involve three profit/cost components: profit from a conforming item, cost from an accepted nonconforming item, and screening inspection cost. Methods of finding the optimal screening procedures are presented and numerical examples are given.

D. S. Bai and S. W. Chung IEEE TRANSACTIONS ON RELIABILITY 41: (3) 400406 1992 
"OPTIMALDESIGN OF PARTIALLY ACCELERATED LIFE TESTS FOR THE EXPONENTIALDISTRIBUTION UNDER TYPEI CENSORING" 
This paper considers optimal designs for two partially accelerated life tests (PALTs) in which items are run at both accelerated and use conditions until a predetermined time. The step PALT allows the test to be changed from use to accelerated condition at a specified time; the constant PALT runs each item at either use or accelerated condition only. For items having constant hazard (failure) rate, maximum likelihood estimators (MLEs) of the hazard rate at use condition and the acceleration factor, the ratio of the hazard rate at accelerated condition to that at use condition, are obtained. The changetime for the step PALT or the sampleproportion allocated to accelerated condition for the constant PALT is determined to minimize either the generalized asymptotic variance of MLEs of the acceleration factor and the hazard rate at use condition or the asymptotic variance of MLE of the acceleration factor.

D. S. Bai , M. S. Cha and S. W. Chung IEEE TRANSACTIONS ON RELIABILITY 41: (3) 407413 1992 
"OPTIMUM SIMPLE RAMPTESTS FOR THE WEIBULL DISTRIBUTION AND TYPEI CENSORING " 
This paper presents an optimum simple ramp test  accelerated life test with two different linearly increasing stresses  for the Weibull distribution under type I censoring. It is assumed that: 1) the inverse power law holds between the Weibull scale parameter and the constant stress, and 2) the cumulative exposure model for the effect of changing stress applies. The optimum plan  low stress rate and proportion of test units allocated to low stress mode  is found which minimizes the asymptotic variance of the maximum likelihood estimator of a stated quantile at design stress. For selected values of the design parameters, these optimum plans are tabulated, and the effect of the preestimates of these parameters are studied.

D. S. Bai and Y. I. Kwon ENGINEERING OPTIMIZATION 20: (3) 287302 1993 
"ECONOMIC DESIGN OF LIFE TEST SAMPLING PLANS FOR REPAIRABLE PRODUCTS " 
Economic designs of life test sampling plans are considered for repairable prodects which are sold under a general rebate warranty policy. It is assumed that the products in each lot have the same failure intensity function, but the parameters of the function vary from lot to lot according to a known prior distribution. Cost models are constructed which involve three cost components; test cost, accept cost, and reject cost. Method of finding optimal sampling plans which minimize the expected average cost per lot are presented. Numerical examples are given and sensitivity analyses for the prior distribution are performed.

D. S. Bai and M. K. Lee METRIKA 40: (2) 95113 1993 
"ECONOMIC DESIGNS OF SINGLE AND DOUBLE SCREENING PROCEDURES" 
Economic designs if single and double screening procedures for inproving outgoing product quality based on two screening variables ate presented for the case of onesided specification limit. Two screening variables are observed simultaneously in single screening procedure and are observed sequentially in double screening procedure. It is assumed that the performance variable and the two screening variables are jointly normally distributed. Three quality cost functions constant, linear, and quadratic are considered. Cost models are constructed which involve screening inspection cost. and costs of accepted and rejected item. Methods of finding the optimal cutoff values are presented and a numerical example is given.

D. S. Bai, S. W. Chung and Y. R. Chun RELIABILITY ENGINEERING & SYSTEM SAFETY 40: (1) 8592 1993 
"OPTIMALDESIGN OF PARTIALLY ACCELERATED LIFE TESTS FOR THE LOGNORMALDISTRIBUTION UNDER TYPEI CENSORING" 
This paper considers optimal designs of partially accelerated life tests in which test items are first run simultaneously at use condition for a specified time, and the surviving items are then run at accelerated condition until a predetermined censoring time. For items having lognormally distributed lives maximum likelihood estimators (MLEs) of the location and scale parameters of the lifetime distribution at use condition, and the acceleration factor which is the ratio of the mean life at use condition to that at accelerated condition are obtained. The change time is determined to minimize either the asymptotic variance of MLE of the acceleration factor or the generalized asymptotic variance of MLEs of the model parameters.

D. S. Bai and M. S. Kim NAVAL RESEARCH LOGISTICS 40: (2) 193210 1993 
"OPTIMUM SIMPLE STEPSTRESS ACCELERATED LIFE TESTS FOR WEIBULL DISTRIBUTION AND TYPEI CENSORING" 
This article presents an optimum simple stepstress accelerated life test for the Weibull distribution under Type I censoring. It is assumed that a loglinear relationship exists between the Weibull scale parameter and the (possibly transformed) stress and that a certain cumulative exposure model for the effect of changing stress holds. The optimum plantow stress and stress change timeis obtained, which minimizes the asymptotic variance of the maximum likelihood estimator of a stated percentile at design stress. For selected values of the design parameters, nomographs useful for finding the optimum plan are given, and the effects of errors in preestimates of the parameters are investigated. As an alternative to the simple stepstress test, a threelevel compromise plan is proposed, and its performance is studied and compared with that of the optimum simple stepstress test.

D. S. Bai, J. G. Kim and Y. R. Chun ENGINEERING OPTIMIZATION 21: (2) 197212 1993 
"DESIGN OF FAILURECENSORED ACCELERATED LIFETEST SAMPLING PLANS FOR LOGNORMAL AND WEIBULL DISTRIBUTION " 
This paper considers the design of lifetest sampling plans based on failurecensored accelerated life tests for products with lognormal and Weibull lifetime distributions. Two levels of stress higher than the use condition stress, high and low, are used. The sample size, sample proportion allocated to each stress level, and the lot acceptability constant which satisfy the producer's risk and consumer's risk and minimize the generalized asymptotic variance of the maximum likelihood estimators of the model parameters are obtained. The properties of the proposed sampling plans are investigated.

D. S. Bai and Y. R. Chun RELIABILITY ENGINEERING & SYSTEM SAFETY 41: (3) 217223 1993 
"NONPARAMETRIC INFERENCES FOR RAMP STRESS TESTS UNDER RANDOM CENSORING" 
This paper considers nonparametric estimation of lifetime distribution of a product under ramp stress accelerated life tests in which the stress on an item increases linearly with time and observations are randomly censored. Assuming that a cumulative exposure model holds, the lifetime distribution of an item under ramp stress is derived. Three nonparametric estimators of the lifetime distribution at use condition stress are obtained for the situation where the time transformation function relating stress to lifetime distributions of a test item is a version of the inverse power law. The proposed estimators are robust to underlying lifetime distribution and are computed in closed form. They are compared with maximum likelihood estimator for small samples under exponential lifetime distribution. The method is extended to the case of competing risks.

D. S. Bai and M. K. Lee INTERNATIONAL JOURNAL OF PRODUCTION ECONOMICS 32: (3) 327334 1993 
"OPTIMAL TARGET VALUES FOR A FILLING PROCESS WHEN INSPECTION IS BASED ON A CORRELATED VARIABLE" 
The problem of selecting optimal target values for the mean of the quantity Y of material in a container and the cutoff value on a correlated variable X is considered for a filling process in which a container is nonconforming if its Y value is less than the lower specification limit and inspection is based on X instead of Y. A profit model is constructed which involves selling price and filling, rework, inspection, and penalty costs. Assuming that X and Y are jointly normally distributed, a method of finding the optimal process mean and the cutoff value on X is presented. An example from the cement industry is presented.

D. S. Bai and S. H. Hong ENGINEERING OPTIMIZATION 22: (2) 153160 1994 
"ECONOMIC SCREENING PROCEDURES WITH MULTIDECISION ALTERNATIVES IN LOGISTIC AND NORMALMODELS " 
For situations where there are several markets with different profit/cost structures, economic screening procedures with dichotomous performance variable T and continuous screening variable X are proposed for determining the market to ship the products to. Logistic and normal models are considered. It is assumed that P[T = 1\X = x] is given by a logistic function in the logistic model and X given T is normally distributed in the normal model. Profit models are constructed which involve three profit/cost components: profit from a conforming item, cost from an accepted nonconforming item, and screening inspection cost. Methods of finding the optimal screening procedures are presented and a numerical example is given.

D. S. Bai and Y. I. Kwon NAVAL RESEARCH LOGISTICS 41: (4) 523535 1994 
"AN ECONOMIC SEQUENTIAL SCREENINGPROCEDURE FOR LIMITED FAILURE POPULATIONS" 
An economic sequential screening procedure is considered for limited failure populations in which defective items fail soon after they are put in operation and nondefective ones never fail during the technical life of the items. A cost model is constructed that involves screening test cost and external failure cost. A sequential scheme that minimizes the expected cost is derived from the solution of a dynamic programming formulation and the optimal decision at each stage is obtained in a closed form.

D. S. Bai and H. M. Kwon METRIKA 42: (1) 118 1995 
"ECONOMIC DESIGN OF A TWOSTAGE SCREENING PROCEDURE WITH A PRESCRIBED OUTGOING QUALITY " 
An economic twostage screening procedure based on screening and performance variables is proposed. A screening variable is used first to decide whether an item should be accepted, rejected, or undecided. The performance variable is then used to classify the undecided items. The two variables are assumed to have a bivariate normal distribution. A cost model is constructed which involves costs due to screening and performance inspections and misclassification errors. Optimal cutoff values on the screening variable minimizing the expected cost are obtained subject to the constraint that the outgoing quality exceeds a prespecified level. Methods of finding the optimal cutoff values are presented for both parametersknown and parametersunknown cases.

D. S. Bai and I. S. Choi JOURNAL OF QUALITY TECHNOLOGY 27: (2) 120131 1995 
"(X)OVERBARCONTROL AND RCONTROL CHARTS FOR SKEWED POPULATIONS" 
This paper proposes a heuristic method based on a weighted variance concept of setting up control limits of (X) over bar and R charts for skewed populations. It provides asymmetric control limits in accordance with the direction and degree of skewness estimated from the sample data, by using different variances in computing upper and lower control limits. For symmetric populations, however, these control limits are equivalent to those of Shewhart control charts. The new heuristic control charts are compared by Monte Carlo simulation with Shewhart charts and the geometric control charts of Ferrell. When the underlying population is Weibull or Burr's, the heuristic charts are found to perform better than Shewhart or geometric charts as the skewness increases.

D. S. Bai and Y. R. Chun RELIABILITY ENGINEERING & SYSTEM SAFETY 50: (1) 6168 1995 
"FAILURECENSORED ACCELERATED LIFE TEST SAMPLING PLANS FOR WEIBULL DISTRIBUTION UNDER EXPECTED TEST TIME CONSTRAINT" 
This paper considers the design of lifetest sampling plans based on failurecensored accelerated life tests. The lifetime distribution of products is assumed to be Weibull with a scale parameter that is a log linear function of a (possibly transformed) stress. Two levels of stress higher than the use condition stress, high and low, are used. Sampling plans with equal expected test times at high and low test stresses which satisfy the producer's and consumer's risk requirements and minimize the asymptotic variance of the test statistic used to decide lot acceptability are obtained. The properties of the proposed lifetest sampling plans are investigated. 
D. S. Bai and M. K. Lee INTERNATIONAL JOURNAL OF PRODUCTION ECONOMICS 39: (3) 255264 1995 
"MINIMUMCOST SINGLE AND DOUBLE SCREENING PROCEDURES WITH DICHOTOMOUS PERFORMANCE VARIABLE" 
Minimum cost single and double screening procedures are presented based on two screening variables (X(1),X(2)) as a substitute for one dichotomous performance variable T (conforming/nonconforming). It is assumed that X(1) and X(2) are highly correlated with T and relatively inexpensive to measure compared to T. It is also assumed that X(1) and X(2) given T are normally distributed. Two screening variables are observed simultaneously in the single screening procedure and sequentially in the double screening procedure. Cost model are constructed which involve the two screening inspection costs and costs of misclassification errors. Methods of finding the optimal cutoff values of the screening variables are presented. An illustrative example is given and numerical studies are performed to compare the proposed screening procedures based on two screening variables with the screening procedures based on one screening variable.

D. S. Bai , H. M. Kwon and M. K. Lee NAVAL RESEARCH LOGISTICS 42: (7) 10811097 1995 
"AN ECONOMIC 2STAGE SCREENINGPROCEDURE WITH A PRESCRIBED OUTGOING QUALITY IN LOGISTIC AND NORMALMODELS" 
An economic twostage screening procedure based on a dichotomous performance variable T and a continuous screening variable X is proposed. X is measured first to decide whether an item should be accepted, rejected, or additional observations should be taken. If no terminal decision is reached, T is then observed to classify the undecided items. Two models are considered; (i) the logistic model, where P(T = 1\X = x) is assumed to be a logistic function of x, and (ii) the normal model, where X given T is assumed to be normally distributed. A simple economic model based on inspection and misclassification costs is constructed. Optimal cutoff values on the screening variable are obtained by minimizing the expected costsubject to the constraint that the average outgoing quality attains a prespecified level. Solutions are provided for both knownparameter and unknownparameter cases.

D. S. Bai and M. K. Lee METRIKA 44: (1) 5369 1996 
"ECOMOMIC DESIGNS OF TWOSIDED SINGLE AND DOUBLE SCREENING PROCEDURES" 
Economic designs of single and double screening procedures for improving outgoing product quality based on two screening variables are presented for the case of twosided specification limits. Two screening variables are observed simultaneously in the single screening procedure. In the double screening procedure, one variable is used first to make one of three decisions  accept, reject, or undecided  and after the first screening, the second variable is employed to screen the undecided items; It is assumed that the performance and the two screening variables are jointly normally distributed, and the deviation of the performance variable from the 'ideal' value causes dissatisfication to the consumers. Two quality cost functions  constant and quadratic  are considered. Cost models are constructed which involve screening inspection cost, and costs of accepted and rejected item. Methods of finding the optimal cutoff values are presented and a numerical example is given.

D. S. Bai and H. J. Yun COMPUTERS & INDUSTRIAL ENGINEERING 30: (3) 387396 1996 
"OPTIMAL ALLOCATION OF INSPECTION EFFORT IN A SERIAL MULTISTAGE PRODUCTION SYSTEM" 
An economic design of inspection effort allocation is considered for a serial multistage production system in which a product consists of many identical components, only a limited number of automatic inspection machines are available, and the rate of production is constrained by the rate of inspection. A cost model is constructed and a method of finding optimal locations of inspection machines and inspection level  proportion of components inspected  is presented. For situations where the numbers of stages and inspection machines are large, a heuristic allocation algorithm using dynamic programming is proposed. A numerical example describing the solution procedure and a simulation study, evaluating performance of the proposed algorithm, are given.

D. S. Bai and N. Y. Lee RELIABILITY ENGINEERING & SYSTEM SAFETY 54: (1) 5358 1996 
"Nonparametric estimation for accelerated life tests under intermittent inspection" 
This paper considers nonparametric estimation of lifetime distribution based on grouped data from constant stress accelerated life tests under intermittent inspection in which test items are inspected only at specified points in time. A method of estimating the lifetime distribution at use condition stress is proposed for the case where the time transformation function relating stress to lifetime is a version of inverse power law. Numerical studies show that the proposed method is comparable to the maximum likelihood method for small sample size and is more accurate than existing nonparametric methods used for continuous inspection. The method performs better than the maximum likelihood method when the underlying lifetime distribution is incorrectly specified. (C) 1996 Elsevier Science Limited.

D. S. Bai and H. J. Yun IEEE TRANSACTIONS ON RELIABILITY 45: (4) 611618 1996 
"Accelerated life tests for products of unequal size" 
This paper considers 'estimation of the lifetime distribution' and 'optimal design of constantstress accelerated life test plans' for products of unequal size. The distribution is Weibull with a scale parameter that is a 'loglinear function of stress' and a 'power function of product size with a sizeeffect parameter'. Maximum likelihood estimators (MLE) of model parameters are obtained, and their properties are studied. Two stresslevel optimal test plans are obtained for products that come in two sizes, and a table useful for finding optimal test plans is given. The sum of asymptotic variances of MLE of a specified quantile of the distributions for products of both sizes is used as the optimality criterion. Optimum plans can be used when the ratio of two sizes is not too large. When the ratio is very large, the preestimate of size effect parameter should be carefully chosen.

D. S. Bai and H. M. Kwon EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 97: (1) 1721 1997 
"A NOTE ON THE DESIGN OF A TWOSEDED, TWOSTAGE SCREENING PROCEDURE WITH A PRESCRIBED OUTGOING QUALITY" 
Design of a twostage screening procedure is presented when both lower and upper specification limits are given on the performance variable. A variable correlated with the performance variable is first used for screening the items. The performance variable is then used to screen those items not accepted or rejected in the first stage. Optimal cutoff values on the correlated variable are determined so that the average outgoing quality exceeds a prespecified level and the expected total cost per item is minimized.

D. S. Bai, Y. R. Chun and M. S. Cha IEEE TRANSACTIONS ON RELIABILITY 46: (1) 99107 1997 
"Timecensored ramp tests with stress bound for Weibull life distribution" 
This paper considers ramp tests for Weibull life distribution when there are limitations on test stress and test time. The inverse power law and a cumulative exposure model are assumed. Maximum likelihood estimators of model parameters and their asymptotic covariance matrix are shown. The optimum ramp test plans are given which minimize the asymptotic variance of the ML estimator of a specified quantile of log(life) at design constant stress. The effects of the preestimates of design parameters are studied.

D. S. Bai and K. T. Lee INTERNATIONAL JOURNAL OF PRODUCTION ECONOMICS 54: (1) 5764 1998 
"AN ECONOMIC DESIGN OF VARIABLE SAMPLING INTERVAL (X)OVERBAR CONTROL CHARTS" 
This paper considers an economic design of variable sampling interval (X) over bar control charts in which the sampling interval between two successive sampling points is varied based on the value of the preceding sample mean. A cost model is constructed which involves the cost of false alarms, the cost of detecting and eliminating an assignable cause, the cost associated with production in outofcontrol state and the cost of sampling and testing. A method of finding optimal values of sample size, sampling interval lengths, control limits and threshold limits to select one of the sampling interval lengths is presented. Variable and fixed sampling interval (X) over bar control charts are compared with respect to the expected cost per unit time.

¹èµµ¼± ´ëÇÑ»ê¾÷°øÇÐÈ¸Áö 1: (1) 99103 JUNE 1975 
"Test of Independence in a Markov Dependent Waitingtime Distribution " 
A procedure for the test of independence of the observations and the null distribution are studied for a waitingtime distribution of the number of Bernoulli trials required to obtain a preassigned number of successes under Markov dependence. Selected critical values for the test statistic are tabulated.

¹èµµ¼± ±è¼ºÀÎ ´ëÇÑ»ê¾÷°øÇÐÈ¸Áö 3: (1) 6165 JUNE 1997 
"Unbiased Estimation of Transition Prababilities in a 2x2 Markov Chain " 
New estimators for the transition probabilities of an irreducible Markov chain with two ergodic states are proposed. These estimators are shown to have smallest possible biases. It is also shown that the conventional maximum likelihood estimator of the transition probability from a state to itself tends to underestimate the true value.

¹èµµ¼± ´ëÇÑ»ê¾÷°øÇÐÈ¸Áö 3: (2) 99106 DEC 1977 
"Double Sampling with Zero Acceptance Number for the First Sample " 
A double sampling procedure with zero acceptance number for the first sample whose operating characteristic closely matches that of a given single sampling plan and whose combined sample size does not exceed that of the given single sampling plan is proposed. The proposed double sampling plans corresponding to the MILSTD105D plans are tabulated and it is found that their ASN's are considerably smaller than those of corresponding MILSTD105D single or double sampling plans.

¹èµµ¼± Á¶¼º±¸ Åë°èÇÐ¿¬±¸ 7: (1) 2742 JUNE 1978 
"A Minimum Cost Sampling Inspection Plan for Destructive Testing " 
This paper deals with the problem of obtaining a minimum cost acceptance sampling plan for destructive testing. The cost model is constructed under the assumption that the sampling procedure takes the following form; 1) lots rejected on the first sample are screened with a nondestructive testing, 2) the screening is assumed to be imperfect, and therefore, after the screening, a second sample is taken to determine whether to accept the lot or to scrap it. The usual sampling procedures for destructive testing can be regarded as special cases of the above one. Utilizing Hald's Bayesian approach, procedures for finding the global optimal sampling plans are given. However, when the lot size is large, the global plan is very difficult to obtain even with the aid of an electronic computer. Therefore a method of finding suboptimal plan is suggested. An example with uniform prior is also given. 
¹èµµ¼± ±ÇÅÂ¿µ Åë°èÇÐ¿¬±¸ 7: (2) 121130 DEC 1978 
"Stochastic Duels with Random Detection " 
This paper presents a method of incorporating detection capability of weapon systems into the "fundamental" stochastic duels of Williams and Ancker when both detection and interfiring times are continuous random variables. An example with negative exponential detection and firing times is also given.

¹èµµ¼± ±è¼ºÀÎ Àü°æÇ¥ ´ëÇÑ»ê¾÷°øÇÐÈ¸Áö 5: (1) 717 JUNE 1979 
"Design of an Economic Double Sampling System " 
A procedure for constructing a double sampling plan with zero acceptance number for the first sample whose combined sample size does not exceed that of the given single or double sampling plan is studied. Using this procedure a double sampling system is proposed that can be used in place of MILSTD105D system when the quality history is good, and its composite quality characteristics are tabulated and compared with those of MILSTD105D system. The study reveals that composite ASN's of the proposed double sampling system are considerably smaller than those of corresponding MILSTD105D system with no appreciable changes in other composite quality characteristics. The procedure is also applied to K SA 3102 plans with similar results. A cost model that can be used in comparing a given single sampling plan with the proposed double sampling plan is also developed.

¹èµµ¼± À±¿ÏÃ¶ ´ëÇÑ»ê¾÷°øÇÐÈ¸Áö 5: (1) 5357 JUNE 1979 
"Continuous Sampling Plans with Prior Distribution " 
The concept of AOQL in designing Dodge's continuous sampling plans is modified to include probabilistic consideration reflecting the prior knowledge about the process average fraction defectives, and a new design criterion called AOQL 
¹èµµ¼± ±ÇÅÂ¿µ ´ëÇÑ»ê¾÷°øÇÐÈ¸Áö 5: (2) 17 DEC 1979 
"Stochastic Combats with Time Limitation " 
The fundamental stochastic duel of Williams and Ancker is combined with the probabilistic linear, square and mixed laws of Brown and Smith when the battle time is limited and interfiring times are continuous. The Probability of a given side's winnig or a draw is derived in a recursive equation with Laplace transforms. Examples with negative exponential firing times are given. In linear law and exact closed form solution is obtained, whereas for square and mixed laws only square (2x2) duels are considered.

¹èµµ¼± ±è´ë¿í ´ëÇÑ»ê¾÷°øÇÐÈ¸Áö 5: (2) 3743 DEC 1979 
"On the Equivalence of Stackelberg Strategy and Equilibrium Point in a Twoperson Nonzerosum Game " 
A sufficient condition for a Stackelberg strategy to coincide with an equilibrium point is presented. Information pattern of a Stackelberg strategy is essentially different from that of an equilibrium solution and therefore the two strategies need not be the same. However, under some restrictions on the cost functions the difference in information patterns between the two strategies can be disregarded so that the two strategies coincide. The result is extended to the case of discretetime dynamic games.

¹èµµ¼± ·ù¹®Âù ´ëÇÑ»ê¾÷°øÇÐÈ¸Áö 6: (2) 3747 DEC 1980 
"»ï´Ü°è »ùÇÃ¸µ °Ë»ç¹æ½Ä " 
A system of conditional sampling plans composed of three stages is developed. In the first stage, the decision to accept or reject the lot is based on the information obtained from the current lot. When a decision is not made in the first stage, a second stage is introduced and the information from the immediately preceding lot as well as the information from the current lot is used for the decision. When a decision is not made in the first stage, a second stage is introduced and the information from the immediately preceding lot as well as the information from the current lot is used for the decision. When a decision is not made in the second stage either, the decision is deferred until the information from the immediately following lot is obtained. Existing tables for constructing double sampling plans with n2=2n1 can be used to fine the parameters of these plans. These sampling plans can bring sizable savings in the amount of inspection when the process is relatively stable. The response delay to the change in process quality and the deferred events may be considered as shortcomings of these plans. However, these are not serious in practical applications, and the reduction in sample size may more than offset these shortcomings. 
¹èµµ¼± ÀåÁß¼ø ÇÑ±¹°æ¿µÇÐÈ¸Áö 6: (2) 5764 OCT 1981 
"Estimation of Parameters of a TwoState Markov Process by Interval Sampling " 
This paper develops a method of modifying the usual maximum likelihood estimators of the parameters of a two state Markov process when the trajectory of the process can only be observed at regular epochs. The method utilizes the limiting behaviors of the process and the properties of the state transition counts. An efficient adaptive strategy to be used together with the modified estimator is also proposed. The properties of the new estimators and the adaptive strategy are investigated using Monte Carlo simulation.

¹èµµ¼± ÀåÁß¼ø, ¾öÁÖÅÂ ´ëÇÑ»ê¾÷°øÇÐÈ¸Áö 8: (2) 2331 1982 
"¿¬¼Ó»ý»êÇü »ùÇÃ¸µ °Ë»ç¹æ½ÄÀÇ ¼±Á¤¿¡ °üÇÏ¿© " 
A method of selecting parameters of Dodgetype continuous sampling plans is proposed; a sampling plan is designed so that its AFI curve passes through two designated points. AOQL countour lines are also drawn which can be used as a reference in choosing these points.

¹èµµ¼± ±Ç¿µÀÏ ´ëÇÑ»ê¾÷°øÇÐÈ¸Áö 8: (2) 3336 1982 
"Preventive Maintenance Policies for a System with Two Types of Units Subject to Deterioration " 
This paper considers preventive maintenance policies for a system with two types of units which is subject to deterioration. Two generalized models are investigated; a preventive maintenance policy based on the cumulative operating time and a policy based on the number of minimal repairs performed. Optimal preventive maintenance policies which minimize the expected average cost per unit time including the earning loss due to the deterioration are discussed and some numerical examples are given.

¹èµµ¼± ½Åµ¿¿Ï Åë°èÇÐ¿¬±¸ 12: (1) 4656 JUNE 1983 
"Nonlinear Regression with Censored Data " 
An algorithm based on EM procedure which finds maximum likelihood estimators in a nonlinear regression with censored data is proposed, and asymptotic properties of the estimator are investigated in detail. Some numerical examples are also given.

¹èµµ¼±, ±èÁø¿í ´ëÇÑ»ê¾÷°øÇÐÈ¸Áö; 10: (2) 5165 DEC 1984 
"ÄÄÇ»ÅÍ¸¦ ÀÌ¿ëÇÑ °øÁ¤Ç°Áú°ü¸® ½Ã½ºÅÛ" 
A process quality control system is designed which incorporates run tests, normality test, process capability studies, etc., into control chart scheme, and a software package for microcomputers is developed. The system is interactive and has data base management capabilities. All programs are written is BASIC language.

¹èµµ¼±, À±¿ø¿µ ´ëÇÑ»ê¾÷°øÇÐÈ¸Áö; 11: (1) 310 JUNE 1985 
"Periodic replacement policies with minimal repair cost limit" 
Periodic replacement polices are proposed for a system whose repair cost, when it fails, can be estimated by inspection. The system is replaced when it reaches age T (Policy A), or when it fails for the first time after age T (Policy B). If it fails before reaching age T, the repair cost is estimated and minimal repair is then undertaken if the estimated cost is less than a predetermined limit L; otherwise, the system is replaced. The expected cost rate functions are obtained, their behaviors are examined, and ways of obtaining optimal T and L are explored.

¹èµµ¼±, ·ù¹®Âù Åë°èÇÐ¿¬±¸; 14: (1) 1828 JUNE 1985 
"Optimal screening procedures for improving outgoing quality based on correlated normal variables" 
Optimal screening procedures for improving outgoing product quality based on correlated normal variables are presented. The performance variable and the screening variables are assumed to be jointly normally distributed. These procedures do not require specialized tables, and closedform solutions are obtained for the case of onesided specification. Methods for finding optimal solutions for the case of twosided specifications are also considered.

¹èµµ¼±, ±è»óºÎ ´ëÇÑ»ê¾÷°øÇÐÈ¸Áö; 11: (2) 1927 DEC 1985 
"Optimal numbers of repeat inspections with decreasing detection probability " 
Optimal numbers of repeat inspections are obtained for a single inspector who has a fixed probability of detecting a nonconforming item on each inspection and will continue to inspect until further inspection is not warranted when comparing the expected increase of total gain with the inspection cost. It is assumed that the detection probability decreases as the number of repeat inspections increases, and that the lot to be inspected contains an unknown but Poisson distributed number of nonconforming items.

¹èµµ¼±, ÀåÁß¼ø, ±è»óºÎ ´ëÇÑ»ê¾÷°øÇÐÈ¸Áö; 12: (2) 101108 DEC 1986 
"ºñ¸ð¼öÀû Åë°è ÇÁ·Î±×·¥ÀÇ °³¹ß " 
Computer programs for IBM PC/XT/AT or compatibles, are presented for running 9 nonparametric tests. They include sign test, Wilcoxon signed rank test, MannWhitneyWilcoxon test, KruskalWallis test, KolmogorovSmirnov one sample and two sample tests, Kendall and Spearman rank correlation coefficient tests, and Chi square test for contingency table. Each program is written with BASIC language and is combined into a statistical package, NONPARA. It is easily accessible through the menu programs. The algorithms on which each test is based, are also explained and 3 examples are given.

¹èµµ¼±, ±è¸í¼ö, ÀåÁß¼ø Åë°èÇÐ¿¬±¸; 15: (2) 8796 DEC 1986 
"Efficient sequential estimation in a compound Poisson process" 
Sequential estimation of parameters in a Poisson process whose jump sizes are oneparameter exponential class random variables is discussed. CramerRao type information inequality is used as an efficiency criterion. Unbiased estimators for certain parametric function whose variances attain the lower bound are all characterized with the corresponding sampling plans.

¹èµµ¼±, ±è»óºÎ, ¾È»ó½Ä ´ëÇÑ»ê¾÷°øÇÐÈ¸Áö; 14: (1) 8390 JUNE 1988 
"ÀÌÄ¡Çü ¼º´Éº¯¼ö ´ë½Å ¿¬¼ÓÇü º¯¼ö¸¦ ÀÌ¿ëÇÑ ÃÖÀû ¼±º° °Ë»ç¹æ½Ä" 
Optimal screening procedures with dichotomous performance variable T and continuous screening variable X are presented for assuring with a specified degree of confidence that at least l out of m items found acceptable in screening inspection are conforming. It is assumed that T is a Bernoulli random variable and that the conditional distribution of X given T=t is normal. When m is also to be determined, optimal m and cutoff value of X minimizing the total expected cost are obtained. Cases of known and unknown parameters are considered and for unknown parameter cases, Bayesian approaches are used to find the optimal screening procedures.

¹èµµ¼±, Àü¼ö¸í ´ëÇÑ»ê¾÷°øÇÐÈ¸Áö; 14: (2) 8190 DEC 1988 
"µÎ°¡Áö °íÀå ÇüÅÂ¸¦ °¡Áø Á¦Ç°¿¡ ´ëÇÑ º¸Áõºñ¿ë ¸ðÇü" 
This paper is concerned with warranty cost models for a product with two types of failure ; type 1 failures corrected by minimal repair and type 2 failures removed only by replacement. Two warranty policies involving an initial free service period followed by a prorata period are considered ; the difference is whether the warranty is renewed or not when type 2 failure occurs during its free service period. Expected warranty costs under the two policies are obtained, and their behaviors are examined for the case where type 1 and 2 failure distributions are Weibull and exponential, respectively.

¹èµµ¼±,À±¿ø¿µ, ÀÌ¿µºÀ ´ëÇÑ»ê¾÷°øÇÐÈ¸Áö; 15: (1) 5164 JUNE 1989 
"Áõ°¡ÇÏ´Â ¿À·ù¼öÁ¤ºñ¿ëÇÏ¿¡¼ÀÇ ÃÖÀû ¼ÒÇÁÆ®¿þ¾î ¹æÃâÁ¤Ã¥" 
This paper considers software release problems based on GoelOkumoto and Sshaped reliability growth models. Test of the software system is terminated after a preassigned time T, and it is released to the operational phase. It is assumed that correction cost of an error is increasing with test or operation time. Optimum software release time is obtained using total expected cost on the software life time as a criterion for optimization. In addition. optimal software release policies under the constraint of a software reliability requirement are discussed.

¹èµµ¼±,±è¸í¼ö, ÀÌ»óÇõ Åë°èÇÐ¿¬±¸; 18: (2) 125134 DEC 1989 
"Optimal simple stepstress accelerated life tests under periodic observation" 
This paper presents optimum simple stepstress accelerated life test plans for the case where the test process is observed periodically at intervals of the same length. Two types of failure data, periodically observed complete data and periodically observed censored data, are considered. An exponential life distribution with a mean that is a loglinear function of stress, and a cumulative exposure model for the effect of chaning stress are assumed. For each type of data, the optimum test plan which minimizes the asymptotic variance of the maximum likelihood estimator of the mean life at a design stress is obtained and its behaviors are studies.

¹èµµ¼±,È«¼ºÈÆ, ¼Õ¹Ì¾Ö ´ëÇÑ»ê¾÷°øÇÐÈ¸Áö; 16: (1) 116 JUNE 1990 
"°è·®Á¶Á¤Çü »ùÇÃ¸µ °Ë»ç¿¡ °üÇÑ ¿¬±¸" 
An AQL type variables sampling system with switching rules is proposed. Comparative studies of existing variables sampling standards  MILSTD414,ANSI Z 1.9,ISO 3951,and BS 6002  are made, and simulation studies on switching procedures are conducted. Based on comparative and simulation studies, a variables sampling standard for Korean industry is proposed. The master sampling tables of the proposed standard are taken from the variables standard ANSI Z 1. 9 and the switching rules are matched to the attributes standard KS A 3109 to enable us to move between the proposed variables standard and KS A 3109. Composite OC and ASN curves of the proposed standard are calculated for selected combinations of lot sizes and AQLs and they are compared with those of ANSI Z l. 9.

¹èµµ¼±,È«¼ºÈÆ ´ëÇÑ»ê¾÷°øÇÐÈ¸Áö; 17: (1) 18 JUNE 1991 
"´Ù°áÁ¤ ´ë¾ÈÀ» °®´Â °æÁ¦Àû °è·®Çü »ùÇÃ¸µ°Ë»ç¹æ½Ä" 
For situations where there are several markets for a product with different profit/cost structures, an economic variables sampling plan is developed for determining the market to ship the lots to. It is assumed that the quality characteristic X is normally distributed with known variability and unknown mean having a normal prior distribution. Profit models are constructed which involve four profit/cost components ; profit from a conforming item, inspection cost, replacement cost, and cost from an accepted nonconforming item. Methods of finding optimal sampling plan are presented and a numerical example is given.

¹èµµ¼±,ÀÌ¹Î±¸ ´ëÇÑ»ê¾÷°øÇÐÁö; 20: (1) 314 MARCH 1994 
"Æò±ÕÀÌ º¯ÇÏ´Â ÃæÀü°øÁ¤ÀÇ ÃÖÀû ¸ñÇ¥Ä¡ÀÇ °áÁ¤" 
The problem of selecting the optimal target values in a canning process is considered for situations where there is a linear shift in the mean of the content of a can which is assumed to be normally distributed with known variance. The target values are initial process mean,length of resetting cycle and controllable upper limit. Profit models are constructed which involve giveaway, rework, and resetting costs. Methods of finding the optimal target values are presented and a numerical example is given.

"°íÀå¿øÀÎÀÌ ¿©·µÀÎ Á¦Ç°ÀÇ »ç¿ëÇöÀå µ¥ÀÌÅÍ ºÐ¼®" 
»ç¿ëÇöÀå¿¡¼ÀÇ °íÀåµ¥ÀÌÅ¸´Â ¹Ì¸®Á¤ÇØÁø º¸Áõ±â°£µ¿¾È °íÀåÀÌ ¹ß»ýÇÑ Á¦Ç°À¸·ÎºÎÅÍ ¾ò¾îÁö´Â °íÀå½Ã°£, °íÀå¿øÀÎ, ¼³¸íº¯¼ö°ª°ú º¸Áõ±â°£µ¿¾È °íÀå³ªÁö ¾Ê´Â Á¦Ç° Áß ÀÏÁ¤ºñÀ²À» ÃßÀûÁ¶»çÇÏ¿© ¾òÀº ¼³¸íº¯¼ö °ªµé·Î ±¸¼ºµÈ´Ù. »ç¿ëÇöÀå¿¡¼ ¾ò¾îÁö´Â ÀÌ¿Í°°Àº µ¥ÀÌÅÍ¸¦ ÀÌ¿ëÇÏ¿© Á¦Ç°¼ö¸íºÐÆ÷ÀÇ ¸ð¼ö°¡ ¼³¸íº¯¼ö¿Í ´ë¼ö¼±Çü°ü°èÀÏ ¶§, ¼ö¸íºÐÆ÷ÀÇ ¸ð¼ö¿¡ ´ëÇÑ ÀÇ»ç(pseudo) ÃÖ¿ìÃßÁ¤·®À» ±¸ÇÏ°í ±× Á¡±Ù¼ºÁúÀ» ±Ô¸íÇÏ¿´À¸¸ç, °íÀå¿øÀÎº° Á¦Ç°¼ö¸íÀÌ ´Þ·Â½Ã°£ÀÌ°í Á¦Ç°ÀÇ °íÀåÀÌ ¿î¿µ½Ã°£¿¡ ÀÇÁ¸ÇÏ´Â °æ¿ì¿Í Á¦Ç°ÀÇ º¸ÁõÀÌ ´Þ·Â½Ã°£°ú ¿î¿µ½Ã°£ÀÇ È¥ÇÕÀÎ °æ¿ìÀÇ ºÐ¼®¹æ¹ýµµ Á¦½ÃÇÏ¿´´Ù. ¶ÇÇÑ ¸ðÀÇ½ÇÇèÀ» ÅëÇÏ¿© ÃßÀûÁ¶»çºñÀ²¿¡ µû¸¥ È¿°ú¸¦ ¾Ë¾Æº¸¾Ò´Ù.

¹èµµ¼±, À±ÇüÁ¦, ÃÖÀÎ¼ö ÀÀ¿ëÅë°è¿¬±¸; 8: (2) 133145 SEP 1995 
"¼ö¸®°¡´ÉÇÑ Á¦Ç°ÀÇ »ç¿ëÇöÀå µ¥ÀÌÅÍ ºÐ¼®" 
°íÀå¿øÀÎÀÌ ¿©·µÀÎ ¼ö¸®ºÒ°¡´ÉÇÑ Á¦Ç°¿¡ ´ëÇÏ¿© »ç¿ëÈ¯°æ¿¡¼ ¾ò¾îÁø °íÀåµ¥ÀÌÅ¸¿Í ÃßÀûÁ¶»ç¿¡ ÀÇÇØ ¾ò¾îÁø ¼³¸íº¯¼ö¿¡ °üÇÑ µ¥ÀÌÅÍ¸¦ ÀÌ¿ëÇÏ¿© Á¦Ç°ÀÇ °íÀå¿øÀÎº° ¼ö¸íºÐÆ÷¸¦ ÃßÁ¤ÇÑ ¹èµµ¼± µî(1995)ÀÇ ¿¬±¸¸¦ ¼ö¸®°¡´ÉÇÑ Á¦Ç°ÀÇ °æ¿ì·Î È®ÀåÇÏ¿´´Ù. ¼ö¸íºÐÆ÷ÀÇ ¸ð¼ö¿Í ¼³¸íº¯¼ö°¡ ´ë¼ö¼±Çü °ü°èÀÏ ¶§ ºñµ¿Áú¼º Æ÷¾Æ¼Û°úÁ¤À» ÀÌ¿ëÇÏ¿© ÀÇ»ç¿ìµµÇÔ¼ö¸¦ À¯µµÇÏ°í, °íÀå¿øÀÎº° ¼ö¸íÀÌ ¿ÍÀÌºí ºÐÆ÷¸¦ µû¸¦ ¶§ÀÇ ÀÇ»ç ÃÖ¿ìÃßÁ¤·®°ú Á¡±ÙºÐ»êÀ» ±¸ÇÏ¿´´Ù. ÃßÀûÁ¶»ç ¹æ¹ýÀ¸·Î´Â º¸Áõ±â°£ µ¿¾È °íÀåÀÌ ¹ß»ýÇÏÁö ¾ÊÀº Á¦Ç°ÀÇ ÀÏÁ¤ºñÀ²À» ÃßÀûÁ¶»çÇÏ´Â °æ¿ì¿Í ÃÑ ½ÃÇèÁ¦Ç°ÀÇ ÀÏÁ¤ºñÀ²À» ·£´ýÇÏ°Ô ¼±ÅÃÇÏ°í ÀÌµé Áß¿¡¼ º¸Áõ±â°£ µ¿¾È ÇÑ¹øµµ °íÀåÀÌ ¹ß»ýÇÏÁö ¾ÊÀº Á¦Ç°¿¡ ´ëÇØ¼¸¸ ÃßÀûÁ¶»çÇÏ´Â °æ¿ì¸¦ °í·ÁÇÏ¿´´Ù.

¹èµµ¼±,±ÇÇõ¹« ´ëÇÑ»ê¾÷°øÇÐÈ¸Áö; 22: (1) 1736 MARCH 1996 
"Economic Design of a TwoSided TwoStage Screening Procedure with a Prescribed Outgoing, Quality " 
An economic twostage screening procedure is presented when both lower and upper specification limits are given on the performance variable. A screening variable which is highly correlated with the performance variable is used first to decide whether an item should be accepted, rejected, or undecided. The performance variable is then used to classify the undecided items. The two variables are assumed to be jointly normally distributed. A cost model is constructed on the basis of six cost components; inspection costs of screening and performance variables and costs caused by type 1 and type 11 misclassification errors related with lower and upper specification limits. Optimal cutoff values on the screening variable are determined so that the average outgoing quality exceeds a prespecified level. Solution methods are provided for both knownparameter and unknownparameter cases.

¹èµµ¼±, ±è¸í¼ö, Àü¿µ·Ï ÀÀ¿ëÅë°è¿¬±¸; 9: (1) 5373 MARCH 1996 
"ÀÏÁ¤Çü °¡¼Ó¼ö¸í½ÃÇè°ú °è´ÜÇü °¡¼Ó¼ö¸í½ÃÇèÀÇ ºñ±³ : ÃÖÀû¼³°è¸¦ Áß½ÉÀ¸·Î" 
ÀÏÁ¤Çü ¹× °è´ÜÇü °¡¼Ó¼ö¸í½ÃÇèÀÇ ½ÃÇè¼³°è¿¡ ´ëÇÑ ÀÏ¹ÝÀûÀÎ ¸ðÇü°ú ÃÖÀû¼³°è¿¡ ´ëÇÑ ÃÖ±ÙÀÇ ¿¬±¸°á°ú¸¦ ¼Ò°³ÇÏ°í, ¼ö¸íºÐÆ÷°¡ ¿ÍÀÌºíÀÎ °æ¿ì¿¡ ´ëÇÏ¿© µÎ°¡Áö ½ÃÇè¹æ¹ý¿¡ ´ëÇÑ ÃÖÀû¼³°è¸¦ Á¡±ÙºÐ»êÀÇ ÇüÅÂ, ¼³°èº¯¼öÀÇ È¿°ú, ÃÖÀû½ÃÇèÁ¶°Ç¿¡¼ ½ÃÇèÁ¾°á ½ÃÁ¡±îÁöÀÇ ±â´ë°íÀå°³¼ö ¹× ±â´ë½ÃÇèÁ¾°á½Ã°£, Á¡±ÙºÐ»êÀÇ »ó´ëÀûÈ¿À²°ú ¼³°èº¯¼öÀÇ »çÀüÃßÁ¤Ä¡¿¡ ´ëÇÑ µÐ°¨¼ºÀÇ Ãø¸é¿¡¼ ºñ±³¡¤ºÐ¼®ÇÏ¿´´Ù.

¹èµµ¼±, Àü¿µ·Ï, Â÷¸í¼ö ´ëÇÑ»ê¾÷°øÇÐÈ¸Áö; 22: (3) 459472 SEP 1996 
"½ºÆ®·¹½º ÇÑ°è°¡ ÀÖ´Â ·¥ÇÁ½ÃÇèÀÇ ÃÖÀû¼³°è : Áö¼ö¼ö¸íºÐÆ÷ÀÇ °æ¿ì" 
This paper considers ramp tests for exponential lifetime distribution when there are limitations on test stress and test time. The inverse power law and a cumulative exposure model are assumed. Maximum likelihood (ML) estimators of model parameters and their asymptotic covariance matrix are obtained. The optimum ramp test plans are also found which minimize the asymptotic variance of the ML estimator of the log mean life at design constant stress. For selected values of the design parameters, tables useful for finding optimal test plans are given. The effect of the preestimates of design parameters is studied.

¹èµµ¼±, ÀÌ°æÅÃ, ÃÖÀÎ¼ö ´ëÇÑ»ê¾÷°øÇÐÈ¸Áö; 23: (4) 793802 DEC 1996 
"´ë¿ëÇ°ÁúÆ¯¼ºÄ¡¸¦ ÀÌ¿ëÇÑ °è¼ö¼±º°Çü »ùÇÃ¸µ °Ë»ç¹æ½ÄÀÇ °æÁ¦Àû ¼³°è" 
A sampling plan is presented for situations where sampling inspection is based on the quality characterstic of interest and items in rejected lots are screened based on a correlated variable. A cost model is constructed which involves the costs of misclassification errors, sampling and screening inspections. A method of finding optimal values of sample size, acceptance number and cutoff value on the correlated variable is presented, and numerical studies are given.

¹èµµ¼±, ÀÌ°æÅÃ ´ëÇÑ»ê¾÷°øÇÐÈ¸Áö; 24: (3) 333344 SEP 1998 
"°¡º¯ ½ºÆ®¸² ¹× Ç¥º»Å©±â ±×·ì°ü¸®µµ" 
This paper proposes variable stream and sample size(VSSS) group control charts in which both the number of streams selected for sampling and sample size from each of the selected streams are allowed to vary based on the values of the preceding sample statistics. The proposed charts select a small portion of streams and take samples of size n=1 if both the largest and smallest of sample means fall between the lower and upper threshold limits, and select a large portion of streams and take samples of size n>1 otherwise. A Markov chain approach is used to derive the formulas for evaluating the performances of the proposed charts. Numerical comparisons are made between the VSSS and fixed stream and sample size(FSSS) group control charts.
