Fuzzy Parameters Based Sampling Strategy Using ZIPD

Effectiveness of sampling plans by attributes based on mixture distributions characterising microbial clustering in food

ABSTRACTAn acceptance sampling plan (ASP) is a commonly used tool in quality assurance that allows business partners to make decisions about lot disposition. To enhance the efficiency and applicability of inspection, various ASPs have been constructed to meet different circumstances in practical applications. One of these ASPs is the skip‐lot sampling plan (SkSP), which reduces inspection time and cost for a series of product lots from a supplier with excellent quality records. Based on the structure of the SkSP, we propose an improved variables SkSP that uses a repetitive group sampling (RGS) plan based on the most commonly used capability index Cpk as the reference plan, designated as Cpk‐based SkSP‐RGS. This plan is optimized using a model that ensures the operating characteristic function meets a two‐point condition and minimizes the average sample number (ASN). Additionally, two main performance measures of sampling plans, ASN and discriminatory power, are investigated. The results reveal the superiority of the proposed plan over conventional Cpk‐based sampling plans. Lastly, a case study from the liquid crystal module industry is demonstrated using the proposed plan to show its applicability and practicality.

The control chart based on a Poisson distribution has often been used to monitor the number of defects in sampling units. However, many false alarms could be observed due to extra zero counts, especially for high-quality processes. Therefore, some alternatives have been developed to alleviate this problem, one of which is the control chart based on the zero-inflated Poisson distribution. This distribution takes into account the extra zeros present in the data, and yield more accurate results than the Poisson distribution. However, implementing a control chart is often based on the assumption that the parameters are either known or an accurate estimate is available. For a high quality process, an accurate estimate may require a very large sample size, which is seldom available. In this paper the effect of estimation error is investigated. An analytical approximation is derived to compute shift detection probability and run length distribution. The study shows that the false alarm rates are higher than the desirable level for smaller values of the sample size. This is further supported by smaller average run length. In general, the quantitative results from this paper can be utilized to select a minimum size of the initial sample for estimating the control limits so that certain average run length requirements are met.

In this dissertation an on-line interactive system for generating and analyzing various acceptance sampling plans is presented. This real-time sampling plan system utilizes a series of algorithms to perform the necessary functions for generating information pertinent to single, double, and multiple sampling plans. These algorithms along with other special programming considerations allow for fast generation of the following information relative to single, double, and multiple sampling plans: (1) the operating characteristic (OC) curve, (2) the average outgoing quality (AOQ) curve, (3) the average sample number (ASN) curve, (4) the average total inspection (ATI) curve, (5) multiple plots per graph, (6) the sample size(s), (7) the acceptance number(s), (8) the rejection number(s), (9) the average outgoing quality number (AOQL), (10) the lot size, (11) the lot quality (p' 95' p' 50' p' 10), and (12) the alpha and bet&adot value&sdot for a specified AQL and LPTD. This information for single, double, and multiple sampling plans can be generated by using either the Poisson, binomial, or hypergeometric distribution. Two procedures are available to the user for generating information pertinent to a particular sampling plan. The first procedure enables the user to generate single, double, and multiple sampling plans given the acceptance quality level (AQL) and the lot tolerance percent defective (LTPD). This procedure allows for the generation of two types of sampling plans: one plan minimizes consumers' risk and the other plan minimizes producers' risk. The second procedure permits the user to specify the sample size(s), the acceptance number(s), the rejection numbers (in case of multiple sampling plans), the lot size, and the percent defective used to scale the x-axis. The system is designed for use by a person with various backgrounds in programming or statistical quality control. Several examples of its use are given to illustrate one or more important points. The sampling plan system was found to be an acceptable means of generating and analyzing various sampling plans on a real-time basis.

Acceptance sampling is one of the imperative methods used in statistical quality control through judgement a lot concerning its quality of 100% inspection and no inspection. Acceptance sampling plan is able to minimise the inspection cost and sampling error. It is a technique that deals with accepting or not the lot to be found on sampling inspection that delivers the quality of products manufactured by industries. This paper portrays designing procedure and development of skip-lot sampling plan of type SkSP-T with special type double sampling plan (STDSP) as reference plan which is designated as SkSTDSP-T. Operating characteristics and performance measures are derived, evaluated and tables involving incoming and outgoing quality levels are constructed for SkSTDSP-T plan. Tables are simulated by changing various parametric values of SkSP-T and STDSP plan. Table values are calculated, operating characteristic curve is drawn by using R (programming) language. Additionally, the efficiency of the proposed plan is discussed.

Bayesian signal detection methods, including the multiitem gamma Poisson shrinker (MGPS), assume a Poisson distribution for the number of reports. However, the database of the adverse event reporting system often has a large number of zero-count cells. A zero-inflated Poisson (ZIP) distribution can be more appropriate in this situation than a Poisson distribution. Few studies have considered ZIP-based models for Bayesian signal detection. In addition, most studies on Bayesian signal detection methods include simulation studies conducted assuming a gamma distribution for the prior. Herein, we extend the MGPS method using the ZIP model and apply various prior distributions. We evaluated the extended methods through an extensive simulation using more varied settings for the model and prior than existing methods. We varied the total number of reports, the number of true signals, the relative reporting rate, and the probability of observing a true zero. The results show that as the probability of observing a zero count increased, methods based on the ZIP model outperformed the Poisson model in most cases. We also found that using the mixture log-normal prior resulted in more conservative detection than other priors when the relative reporting rate is high. Conversely, more signals were found when using the mixture truncated normal distributions. We applied the Bayesian signal detection methods to data from the Korea Adverse Event Reporting System from 2012 to 2016.

The percentage of zero observations necessitating zero-inflated distributions in count data modelling has been a major issue. The challenge in such a situation is determining when to shift from parent distributions to their zero-inflated versions. In most studies, the performances of parent distributions are assessed with those of their zero-inflated forms. This study conducts simulation studies for the Poisson and the negative binomial distributions and their respective zero-inflated forms. Count data [0, 4] with different percentages of zero counts are simulated using different sample sizes. Both negative log-likelihood and Bayesian information criterion (which considers the number of estimated parameters) are used to assess performance. Results show that the zero-inflated Poisson distribution best suits modelling all forms of data when the negative log-likelihood value is used to assess performance. When the BIC is used, the Poisson distribution gives the best performance for both 10% and 20% zeros, while the ZIP distribution is the best for both 50% and 90% zeros. The NB distribution outperforms the ZINB distribution in all situations. Also, in all cases, the negative binomial performs better than the zero-inflated negative binomial distributions. To further assess the distributions, four count data sets with varying percentages of zero are examined. Both the ZIP and the NB distributions perform better than others.

Coronavirus disease 2019 (COVID-19) has spread rapidly throughout the world and has caused millions of deaths. However, the number of daily COVID-19 deaths in Thailand has been low with most daily records showing zero deaths, thereby making them fit a Zero-Inflated Poisson (ZIP) distribution. Herein, confidence intervals for the Coefficient Of Variation (CV) of a ZIP distribution are derived using four methods: the standard bootstrap (SB), percentile bootstrap (PB), Markov Chain Monte Carlo (MCMC), and the Bayesian-based highest posterior density (HPD), for which using the variance of the CV is unnecessary. We applied the methods to both simulated data and data on the number of daily COVID-19 deaths in Thailand. Both sets of results show that the SB, MCMC, and HPD methods performed better than PB for most cases in terms of coverage probability and average length. Overall, the HPD method is recommended for constructing the confidence interval for the CV of a ZIP distribution. Doi: 10.28991/esj-2021-SPER-05 Full Text: PDF

The objective of this article is to propose a comprehensive solution for analyzing multidimensional non-life claim count data that exhibits time and cross-dependence, as well as zero inflation. To achieve this, we introduce a multivariate INAR(1) model, with the innovation term characterized by either a multivariate zero-inflated Poisson distribution or a multivariate zero-inflated hurdle Poisson distribution. Additionally, our modeling framework accounts for the impact of individual and coverage-specific covariates on the mean parameters of each model, thereby facilitating the computation of customized insurance premiums based on varying risk profiles. To estimate the model parameters, we employ a novel expectation-maximization (EM) algorithm. Our model demonstrates satisfactory performance in the analysis of European motor third-party liability claim count data.

The odds ratio estimation when observed frequencies are very small usually causes difficulty in calculation. In this paper, we proposed the estimator of odds ratio for small count using Empirical Bayes (EB) in Zero-inflated Poisson distribution, where the hyper-parameters can be estimated via the posterior marginal distribution function. We compare the proposed estimator of odds ratio based on EB in Zero-inflated Poisson distribution with moments method estimator (MME) and modified maximum likelihood estimator (MMLE) using the Estimated Relative Error (ERE) as criterion of comparison. The result of a simulated study indicates that the EB estimator is more efficient than MME and MMLE. For application, the EB odds ratio estimation is implemented in AIDS-related data which the response was the self-reported number of times that respondents having a risky sexual partners, classified by gender. The estimation based EB also yields consistent result as those in simulation, resulting in smallest ERE when compared to MME and MMLE.

Recently, although advances were made on modeling multivariate count data, existing models really has several limitations: (i) The multivariate Poisson log-normal model (Aitchison and Ho, 1989) cannot be used to fit multivariate count data with excess zero-vectors; (ii) The multivariate zero-inflated Poisson (ZIP) distribution (Li etal., 1999) cannot be used to model zero-truncated/deflated count data and it is difficult to apply to high-dimensional cases; (iii) The Type I multivariate zero-adjusted Poisson (ZAP) distribution (Tian etal., 2017) could only model multivariate count data with a special correlation structure for random components that are all positive or negative. In this paper, we first introduce a new multivariate ZAP distribution, based on a multivariate Poisson distribution, which allows the correlations between components with a more flexible dependency structure, that is some of the correlation coefficients could be positive while others could be negative. We then develop its important distributional properties, and provide efficient statistical inference methods for multivariate ZAP model with or without covariates. Two real data examples in biomedicine are used to illustrate the proposed methods.

The concept of acceptance sampling plans ensures the quality of products and materials used in highway construction. These acceptance sampling plans require the testing of each and every individual lot of products for the highway construction and materials. This approach of sampling is applicable and appropriate if the supplier or contractor is unreliable. If the contractor is consistent and reliable, then instead of inspecting each and every lot of products, skip-lot sampling system can be utilized where only a fraction of the lots are inspected after assuring the quality and after a certain number of conforming lots is obtained. Skip-lot sampling plan can be used for reducing the amount of inspection on product that has an excellent quality history. Thus, skip-lot sampling plans are designed to reduce inspection costs. Moreover, skip-lot concept is sound and useful and it is economically advantageous in the design of sampling plans. Hence, this paper presents an improved system of skip-lot sampling plans designated as SkSP-V plan for the application of highway construction and materials. Advantages of this plan over the existing skip-lot plan and AASHTO’s lot-by-lot sampling plan are also discussed. The efficiency of this new plan is also investigated.

From quality and reliability perspectives, acceptance sampling plans play a significant role in manufacturing and industries in order to minimize the defect in the process. It is essential that the final product received by the customers, either external or internal, to be defect-free. In this regard, this paper presents the special case of acceptance sampling plan referred to as quick switching sampling (QSS) plan in the context of failure censoring reliability tests by considering the information from lifetime performance index (LPI). Unlike the common process capability indexes, LPI is usually appropriate for processes with non-negative quality characteristics. It is assumed that the lifetime of items follows Weibull distribution. Derivations of the operating characteristic curves are developed and a mathematical model is presented which determines the optimal parameters of the QSS plan. In order to see the effectiveness of proposed QSS, a real example is presented. In addition, different sensitivity analyses are conducted which the results indicate that proposed QSS plan can significantly decrease the costs of the life testing and sampling in comparison with a single sampling plan.

Investigating confidence intervals generated by zero-inflated count models: Implications for fisheries management

Massively Parallel Signature Sequencing (MPSS) is a high-throughput, counting-based technology available for gene expression profiling. It produces output that is similar to Serial Analysis of Gene Expression and is ideal for building complex relational databases for gene expression. Our goal is to compare the in vivo global gene expression profiles of tissues infected with different strains of Salmonella obtained using the MPSS technology. In this article, we develop an exact ANOVA type model for this count data using a zero-inflated Poisson distribution, different from existing methods that assume continuous densities. We adopt two Bayesian hierarchical models—one parametric and the other semiparametric with a Dirichlet process prior that has the ability to “borrow strength” across related signatures, where a signature is a specific arrangement of the nucleotides, usually 16–21 base pairs long. We utilize the discreteness of Dirichlet process prior to cluster signatures that exhibit similar differential expression profiles. Tests for differential expression are carried out using nonparametric approaches, while controlling the false discovery rate. We identify several differentially expressed genes that have important biological significance and conclude with a summary of the biological discoveries. This article has supplementary materials online.