A Parameter-Tuned Genetic Algorithm for Economic-Statistical Design of Variable Sampling Interval X-Bar Control Charts for Non-Normal Correlated Samples

Among innovations and improvements that occurred in the past two decades on the techniques and tools used for statistical process control (SPC), adaptive control charts have shown to substantially improve the statistical and/or economical performances. Variable sampling intervals (VSI) control charts are one of the most applied types of the adaptive control charts and have shown to be faster than traditional Shewhart control charts in identifying small changes of concerned quality characteristics. While in the designing procedure of the VSI control charts the data or measurements are assumed independent normal observations, in real situations the validity of these assumptions is under question in many processes. This article develops an economic-statistical design of a VSI X-bar control chart under non-normality and correlation. Since the proposed design consists of a complex nonlinear cost model that cannot be solved using a classical optimization method, a genetic algorithm (GA) is employed to solve it. Moreover, to improve the performances, response surface methodology (RSM) is employed to calibrate GA parameters. The solution procedure, efficiency, and sensitivity analysis of the proposed design are demonstrated through a numerical illustration at the end.     

A Non-Typical Least-Squares Solution to an Engineering Problem

In preposterior analysis, Bayesians use an Expected-Net-Gain chart to identify the optimal sample size. This kind of chart, it turns out, is also an excellent educational vehicle for illustrating many of the reasons given for preferring sampling from a population over taking a census, preferring one type of sampling over another (e.g., stratified sampling rather than simple random sampling), or allocating part of a fixed budget to reduce systematic error rather than using it all to reduce sampling errors. The use of such a chart in a basic statistics course is described.     

Short-run characteristics of samples drawn by random walks

An alternative to using acceptance-rejection methods to generate a sample of points distributed uniformly over a region is to employ a random walk over that region. The sequence of points generated by a random walk has been shown, under certain easily satisfied conditions, to be a realization of a vector-valued discrete parameter Markov process, and to have the uniform distribution as its limiting distribution. The purpose of this paper is to point out that even if the marginal distribution of each point is actually uniform, rather than merely being asymptotically uniform, small samples may exhibit nonuniform characteristics due to serial autocorrelation within the sample.     

Multiple dependent state repetitive sampling plans with or without auxiliary variable

In this article, a new variable acceptance sampling plan has been developed using the multiple dependent state repetitive sampling scheme for the normal distribution. The plan parameters have been determined so as to minimize the average sample number while satisfying the producer's and the consumer's risks under the operating characteristic function. The multiple dependent state repetitive sampling scheme has also been extended to the case of utilizing an auxiliary variable. The proposed sampling plans are compared with the existing sampling plans.     

Robust Bayesian analysis of generalized inverted family of distributions

ABSTRACT

In the current study we develop the robust Bayesian inference for the generalized inverted family of distributions (GIFD) under an ε-contamination class of prior distributions for the shape parameter α, with different possibilities of known and unknown scale parameter. We used Type II censoring and Bartholomew sampling scheme (1963) for the following derivations under the squared-error loss function (SELF) and linear exponential (LINEX) loss function : ML-II Bayes estimators of the i) parameters; ii) Reliability function and; iii) Hazard function. We also present simulation study and analysis of a real data set.     

Solution Structure of Some Inverse Combinatorial Optimization Problems

In this paper we consider some inverse combinatorial optimization problems, that is, for a given set of feasible solutions of an optimization problem, we wish to know: under what weight vectors (or capacity vectors) will these feasible solutions become optimal solutions? We analysed shortest path problem, minimum cut problem, minimum spanning tree problem and maximum-weight matching problem, and found that in each of these cases, the solution set of the inverse problem is charaterized by solving another combinatorial optimization problem. The main tool in our approach is Fulkerson's theory of blocking and anti-blocking polyhedra with some necessary revisions.     

The new unified representation of multivariate skewed distributions

There are so many proposals in construction skewed distributions, and it is worth finding an overall class which covers all of these proposals. We introduce a new unified representation of multivariate skewed distributions. We will show that this new unified multivariate form of skewed distributions includes all of the continuous multivariate skewed distributions in the literature. This new unified representation is based on the multivariate probability integral transformation and can be decomposed into one factor that is original multivariate symmetric probability density function (pdf) f on ? ^k and skewed factor defined by a pdf p on [0, 1] ^k . This decomposition leads us to prove some useful properties of this new unified form. Stochastic representations and basic properties of this new form are also investigated in this article. Our work is motivated by considering the different skewing mechanisms which lead to different skewed distributions and show that all of these common-used distributions can be viewed as a new unified form.     

A cost model for deferred state life test plans with replacement

This paper presents a cost model for the deferred state life test plan, which is one of the lot-by-lot acceptance sampling plans by attributes. In most sampling plans, the decision to accept or reject a submitted lot depends only on the sampling test results of the lot concerned; other information will not be considered. Deferred state life test plan is a sampling plan which uses information about subsequent lots for making decisions to accept or reject the current lot. The objective of this paper is to evaluate the total test cost of using the deferred state life test plan to see whether the use of this life test plan can reduce the total cost of the sampling test. In order to calculate the expected total test cost of the deferred state life test plan, a cost model is developed for the deferred state life test plan with replacement. Also, a cost comparison is made between a deferred state life test plan and a comparable military standard sampling plan which offers the same level of producer's and consumer's protection. The results show that the deferred state life test plan consistently reduces the overall cost of sampling tests over a variety of test conditions.     

On optimality of a two-stage sawpling method for binomial populations

We consider a family of two-stage sampling methods for a binomial parameter that guarantee a certain precision. It is shown that, among all such methods, one due to Birnbaum and Healy minimizes the average expected second stage sample size with respect to a certain density on the parameter space. It does not, however, minimize the average expected second stage sample size with respect to the uniform density.     

Nonparametric recovery of duration distrbutions from cross-sectional sample surveys

When lifetimes consist of two phases, and information about a population must be based on a cross-sectional sample, it is sometimes possible to estimate nonparametrically the phase duration distributions, even though the phase durations themselves are not observed. The key requirements are that the process sampled must be stationary, and that the observations at the time of cross-section include the age and phase of each sampled lifetime at the time of sampling. The estimation procedures must allow for length-bias even when the relevant lengths are not recorded. Stronger results are available when certain parametric assumptions are satisfied about the relationship of the phase durations to the total lifetime, or alternatively when it is also possible to record the total lifetime from a follow-up survey.