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February 2, 2011
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July 20, 2010
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In this article, acceptance sampling plans are developed for the log-logistic distribution percentiles when the life test is truncated at a pre-specified time. The minimum sample size necessary to ensure the specified life percentile is obtained under a given customer's risk. The operating characteristic values (and curves) of the sampling plans as well as the producer's risk are presented. Two examples with real data sets are also given as illustration.
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October 18, 2010
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July 20, 2010
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This paper considers the analysis of reliability characteristics of an alpha distributed lifetime assuming that its parameters are subjected to random variations.
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July 20, 2010
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In this paper we establish certain recurrence relations for probabilities, raw moments and factorial moments of the three parameter binomial-Poisson distribution (BPD). The well-known extended Poisson distribution of order k is obtained as limiting case of BPD.
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September 8, 2010
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In this paper we evaluate the learnability of the virtual classroom Stochastikon Magister [International Journal of Emerging Technologies in Learning (iJET) 4: 52–57, 2009, International Journal of Emerging Technologies in Learning (iJET) 4: 44–50, 2009] by comparing the examination scores of teacher candidates who selected the Magister E-Learning system to learn Bernoulli stochastics with those who selected a regular course in statistics. The evaluation result shows that Stochastikon Magister may well replace traditional classroom teaching in statistics.
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November 15, 2010
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Sampling inspection is a product control technique and consists of rules or procedures for taking decisions on the disposition of lots of finished products based on the inspection of individual units in one or more random samples drawn from the lots. The basic assumption underlying the theory of such procedures by attributes is that the lot or process fraction nonconforming is a constant. Evidently, this assumption is not fulfilled, even if the production process is stable, i.e., if the nonconforming probability is a constant. However, in practice, the lots formed from a process will have different fractions nonconforming, which occur due to random fluctuations. In such cases, Bayesian acceptance sampling plans (BASP), which use prior information on the process variation for taking decisions about the submitted lots, can be employed as alternative to conventional plans. This paper presents a double sampling inspection plan by attributes with small acceptance numbers using the Bayesian methodology. The properties of its characteristic curves with reference to various parameters are highlighted. The design problem of selecting such sampling plans with reference to two prescribed points on the operating characteristic curve under the condition of gamma-Poisson distribution is addressed.
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November 18, 2010
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In this paper a system consisting of two subsystems A and B is analyzed. A has only one unit while B has two units, B 1 and B 2 , connected in such a manner that B 2 is in hot standby with B 1 . The system is modelled by a marked point process. There are two repairmen namely a supervisor and a novice. The supervisor is always present, while the novice might be in vacation. Two types of failure of the components of B are considered. The model is analyzed under “preemptive-repeat repair discipline”. By employing Laplace transformation and assuming the Gumbel–Hougaard copula, the state transition probabilities, reliability, availability and expected profit are obtained along with the steady state behaviour of the system. At the end some special cases of the system are investigated.
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November 18, 2010
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This paper is an extension of the paper “Optimal Replacement Policy Based on Number of Down Times” of the authors, which was published in EQC 25/1. While the former investigated a cold standby system consisting of two identical components, the present one considers the same situation, however, with two unequal components. The first component is very reliable while the second one is less reliable. Just as in the previous paper, a replacement policy based on the number of down times in a renewal cycle is determined that maximizes the long run expected reward per unit time. The explicit expression of the long run expected reward per unit time is derived and a numerical example is given for illustration.
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December 1, 2010
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Let the non-negative random variable X denote the life time of a unit, then the random variable X ( t ) = t – X for X ≤ t for a fixed t ∈ { x : F X ( x ) > 0}, is known as inactivity time or reversed residual life time. In this paper, we define a new non-parametric class of life distributions based on the median of the random variable X ( t ) and study its reliability properties. Some new results concerning the proposed class are given including some closure properties and characterizations. We also introduce and study a new stochastic ordering based on the median of X ( t ) and find its relationship with other well-known order relations. Finally, we provide the median inactivity time function of some well-known life time distributions.
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December 1, 2010
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Most of the software reliability models are based on reliability growth models which deal only with the fault detection process. In such models it is assumed that faults are corrected immediately after being detected or the time to correct a fault is not taken into account. This assumption may not be realistic in practice. In this paper we propose a software reliability model taking into account the fault correction time. The software failure times as well as correction times are assumed to be exponential. The model is formulated as an alternating renewal process. The properties of the reliability model are studied through the renewal process. The system parameters are estimated by means of the maximum likelihood estimators and the properties of the estimators are discussed. We also propose some large sample tests for the system parameters. Some numerical studies are made to evaluate the power of the tests.
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December 20, 2010
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A new test statistic for testing exponentiality against DMRL property of life distributions is introduced in this paper. Critical values are tabulated for small and moderate sample sizes based on Monte Carlo simulation. Two sets of real data are used as examples to elucidate the use of the proposed test procedure for practical reliability analysis. The performance of the proposed test statistic is compared with other established procedures described in the literature, and it is shown that the proposed test procedure has a similar performance.
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December 20, 2010
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Sampling plans by variables represent a well-known tool of acceptance sampling and often it is said that their sampling efficiency/economy is better than that of sampling plans by attributes. However, a comparison of the two types of sampling plans is questionable, because the underlying aims are different. The decision criterion in the case of sampling plans by variables is the quality of the production process, while the decision criterion of sampling plans by attributes is based on lot quality. Using sampling plans by variables is tantamount to consider the parameters of the process distribution as random variables. Based on the history of the production process, suitable prior distributions may be selected to the process parameters. In this paper, using the normal approximation for the process distribution, single sampling plans by variables are derived assuming conjugate priors for the process parameters. The performance of these plans is compared with conventional single sampling plans by variables and single sampling plans by attributes.
