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Register a new userA new approach of chain sampling inspection plan
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Added by
Mahendra Saha
Publication date
2019
fields
Mathematical Statistics
and research's language is
English
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To develop decision rules regarding acceptance or rejection of production lots based on sample data is the purpose of acceptance sampling inspection plan. Dependent sampling procedures cumulate results from several preceding production lots when testing is expensive or destructive. This chaining of past lots reduce the sizes of the required samples, essential for acceptance or rejection of production lots. In this article, a new approach for chaining the past lot(s) results proposed, named as modified chain group acceptance sampling inspection plan, requires a smaller sample size than the commonly used sampling inspection plan, such as group acceptance sampling inspection plan and single acceptance sampling inspection plan. A comparison study has been done between the proposed and group acceptance sampling inspection plan as well as single acceptance sampling inspection plan. A example has been given to illustrate the proposed plan in a good manner.
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We consider the problem of estimating the rate of defects (mean number of defects per item), given the counts of defects detected by two independent imperfect inspectors on one sample of items. In contrast with the setting for the well-known method of Capture-Recapture, we {it{do not}} have information regarding the number of defects jointly detected by {it{both}} inspectors. We solve this problem by constructing two types of estimators - a simple moment-type estimator, and a complicated maximum-likelihood estimator. The performance of these estimators is studied analytically and by means of simulations. It is shown that the maximum-likelihood estimator is superior to the moment-type estimator. A systematic comparison with the Capture-Recapture method is also made.
In this paper, we introduce single acceptance sampling inspection plan (SASIP) for transmuted Rayleigh (TR) distribution when the lifetime experiment is truncated at a prefixed time. Establish the proposed plan for different choices of confidence level, acceptance number and ratio of true mean lifetime to specified mean lifetime. Minimum sample size necessary to ensure a certain specified lifetime is obtained. Operating characteristic(OC) values and producers risk of proposed plan are presented. Two real life example has been presented to show the applicability of proposed SASIP.
Boson sampling is a promising candidate for quantum supremacy. It requires to sample from a complicated distribution, and is trusted to be intractable on classical computers. Among the various classical sampling methods, the Markov chain Monte Carlo method is an important approach to the simulation and validation of boson sampling. This method however suffers from the severe sample loss issue caused by the autocorrelation of the sample sequence. Addressing this, we propose the sample caching Markov chain Monte Carlo method that eliminates the correlations among the samples, and prevents the sample loss at the meantime, allowing more efficient simulation of boson sampling. Moreover, our method can be used as a general sampling framework that can benefit a wide range of sampling tasks, and is particularly suitable for applications where a large number of samples are taken.
In network modeling of complex systems one is often required to sample random realizations of networks that obey a given set of constraints, usually in form of graph measures. A much studied class of problems targets uniform sampling of simple graphs with given degree sequence or also with given degree correlations expressed in the form of a joint degree matrix. One approach is to use Markov chains based on edge switches (swaps) that preserve the constraints, are irreducible (ergodic) and fast mixing. In 1999, Kannan, Tetali and Vempala (KTV) proposed a simple swap Markov chain for sampling graphs with given degree sequence and conjectured that it mixes rapidly (in poly-time) for arbitrary degree sequences. While the conjecture is still open, it was proven for special degree sequences, in particular, for those of undirected and directed regular simple graphs, of half-regular bipartite graphs, and of graphs with certain bounded maximum degrees. Here we prove the fast mixing KTV conjecture for novel, exponentially large classes of irregular degree sequences. Our method is based on a canonical decomposition of degree sequences into split graph degree sequences, a structural theorem for the space of graph realizations and on a factorization theorem for Markov chains. After introducing bipartite splitted degree sequences, we also generalize the canonical split graph decomposition for bipartite and directed graphs.
In the past years we have witnessed the rise of new data sources for the potential production of official statistics, which, by and large, can be classified as survey, administrative, and digital data. Apart from the differences in their generation and collection, we claim that their lack of statistical metadata, their economic value, and their lack of ownership by data holders pose several entangled challenges lurking the incorporation of new data into the routinely production of official statistics. We argue that every challenge must be duly overcome in the international community to bring new statistical products based on these sources. These challenges can be naturally classified into different entangled issues regarding access to data, statistical methodology, quality, information technologies, and management. We identify the most relevant to be necessarily tackled before new data sources can be definitively considered fully incorporated into the production of official statistics.
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