Double and group acceptance sampling plan for truncated life test based on inverse log-logistic distribution

This paper introduces a double and group acceptance sampling plans based on time truncated lifetimes when the lifetime of an item follows the inverse log-logistic (ILL) distribution with known shape parameter. The operating characteristic function and average sample number (ASN) values of the double acceptance sampling inspection plan are provided. The values of the minimum number of groups and operating characteristic function for various quality levels are obtained for a group acceptance sampling inspection plan. A comparative study between single acceptance sampling inspection plan and double acceptance sampling inspection plan is carried out in terms of sample size. One simulated example and four real-life examples are discussed to show the applicability of the proposed double and group acceptance sampling inspection plans for ILL distributed quality parameters.     

Modified CSP-C Continuous Sampling Plan for Consumer Protection

Dodge (1943) introduced a single level attribute continuous sampling plan designated as CSP-1 for the application of continuous production processes. Govindaraju & Kandasamy (2000) developed a new single level continuous sampling plan whose sampling inspection phase is characterized by a maximum allowable number of non-conforming units c, and a constant sampling rate f and was designated as CSP-C. In this paper, a modification is proposed on the CSP-C continuous sampling plan. In this modified plan, sampling inspection is continued until the occurrence of c+1 non-conforming units, provided the first m sampled units have been found conforming during the sampling phase. Using a Markov chain model, expressions for the performance measures of the modified CSP-C plan are derived. The main advantage of the modified plan is that it is possible to lower the average outgoing quality limit.     

Modified tightened two-level continuous sampling plans

In this paper, a modification is proposed on the tightened two-level continuous sampling plan. The tightened two-level plan is one of the three tightened multi-level continuous sampling plans of Derman et al. (1957) with two sampling levels. A modified tightened two-level continuous sampling plan is considered, for which the rules concerning partial inspection depend, in part, on the length of time it takes to decide that the process quality is good enough that 100% inspection may be suspended (e.g. the time required to find i consecutive items free of defects). Using a Markov chain model, expressions for the performance measures of the modified MLP-T-2 plan are derived. The modified MLP-T-2 plan is shown to be identical to the MLP-T-2 plan. Tables are also presented for the selection of the modified MLP-T-2 plan when the AQL or LQL and AOQL are specified.     

Designing of a variables two-plan system by minimizing the average sample number

This article proposes a variables two-plan sampling system called tightened-normal-tightened (TNT) sampling inspection scheme where the quality characteristic follows a normal distribution or a lognormal distribution and has an upper or a lower specification limit. The TNT variables sampling inspection scheme will be useful when testing is costly and destructive. The advantages of the variables TNT scheme over variables single and double sampling plans and attributes TNT scheme are discussed. Tables are also constructed for the selection of parameters of known and unknown standard deviation variables TNT schemes for a given acceptable quality level (AQL) and limiting quality level (LQL). The problem is formulated as a nonlinear programming where the objective function to be minimized is the average sample number and the constraints are related to lot acceptance probabilities at AQL and LQL under the operating characteristic curve.     

Design and Construction of a Variables Repetitive Group Sampling Plan for Unilateral Specification Limit

This paper attempts to develop a repetitive group sampling (RGS) plan by variables inspection for controlling the process fraction defective or the number of nonconformities when the quality characteristic follows a normal distribution and has only the lower or upper specification limit. The proposed sampling plan is derived by the exact sampling distribution rather than the approximation approach. The plan parameters are solved by a nonlinear optimization model which minimizes the average sample number required for inspection and fulfills the classical two-point conditions on the operating characteristic (OC) curve. The efficiency of the proposed variables RGS is examined and also compared with the existing variables single sampling plan in terms of the sample size required for inspection. The results indicate that the proposed variables RGS plan could significantly reduce samples required for inspection compared to the traditional variables single sampling plan.     

Repetitive group sampling procedure for variables inspection

This paper introduces the concept of repetitive group sampling (RGS) for variables inspection. The repetitive group sampling plan for variables inspection will be useful when testing is costly and destructive. The advantages of the variables RGS plan over variables single sampling plan, variables double sampling plan and attributes RGS plan are discussed. Tables are also constructed for the selection of parameters of known and unknown standard deviation variables repetitive group sampling plan indexed by acceptable quality level and limiting quality level.     

The Consumer’s Risk and Costs in Zero-Acceptance Number Sampling

The primary purpose of sampling inspection is the protection of consumer’s interests. Although under simple cost models, sampling inspection never serves the producer’s interest, some form of sampling inspection can be beneficial to the consumer under the same assumptions. We consider the case of isolated lot inspection and examine the consumer risk, economic sample design, and errors in the inspection process. Acceptance sampling is shown to be cost-effective to the consumer whenever the lot quality is less than perfect, and even for perfect lot quality in the presence of inspection errors.     

Efficient ascertainment schemes for maximum likelihood estimation

While well chosen sampling schemes may substantially increase efficiency of observational studies, some sampling schemes may instead decrease efficiency. Rules of thumb how to choose sampling schemes are only available for some special cases. In this paper we provide tools to compare efficiencies, and cost adjusted efficiencies, of different sampling schemes, in order to facilitate this choice. The method can be used for both categorical and continuous outcome variables. Some examples are presented, focusing on data from ascertainment sampling schemes. A Monte Carlo method is used to overcome computational issues wherever needed. The results are illustrated in graphs.     

Minimum average fraction inspected for continuous sampling plan CSP-1 under inspection error

SUMMARY In this paper, we present a further modification of Endres's method to construct the problem of minimizing the average fraction inspected (AFI) for the continuous sampling plan CSP-1 under inspection error. The measures of average outgoing quality under perfect and imperfect replacement conditions are considered. The formulae for searching the smallest clearance number i for minimizing the AFI for a CSP-1 plan are also provided. The solution procedure of the proposed method is more reliable, clearer and easier than that of Endres.     

New acceptance sampling plans based on life tests for Birnbaum–Saunders distributions

In this paper, we consider the Birnbaum–Saunders distribution as a life model to develop various acceptance sampling schemes based on the truncated life tests. We develop the double sampling plan and determine the design parameters satisfying both the producer's and consumer's risks simultaneously for the specified reliability levels in terms of the mean ratio to the specified life. We also propose a group sampling plan and determine the parameters by the above-mentioned two-point method. Tables are constructed for the proposed sampling plans and results are explained with examples.     

Lot Sampling Distributions for Bounded Number of Nonconformities

Attributes sampling is an important inspection tool in areas like product quality control, service quality control or auditing. The classical item quality scheme of attributes sampling distinguishes between conforming and nonconforming items, and measures lot quality by the lot fraction nonconforming. A more refined quality scheme rates item quality by the number of nonconformities occurring on the item, e.g., the number of defective components in a composite product or the number of erroneous entries in an accounting record, where lot quality is measured by the average number of nonconformities occurring on items in the lot. Statistical models of sampling for nonconformities rest on the idealizing assumption that the number of nonconformities on an item is unbounded. In most real cases, however, the number of nonconformities on an item has an upper bound, e.g., the number of product components or the number of entries in an accounting record. The present study develops two statistical models of sampling lots for nonconformities in the presence of an upper bound a for the number of nonconformities on each single item. For both models, the statistical properties of the sample statistics and the operating characteristics of single sampling plans are investigated. A broad numerical study compares single sampling plans with prescribed statistical properties under the bounded and unbounded quality schemes. In a large number of cases, the sample sizes for the realistic bounded models are smaller than the sample sizes for the idealizing unbounded model.     

Developing of a new system of skip-lot reinspection schemes

The skip-lot sampling plans are widely used in industries for quality inspection of products in order to reduce the sampling costs and inspection efforts when products have good quality history. Also, the skip-lot sampling plan concept is sound and useful and it is economically advantageous to use the skip-lot approach in the design of sampling plans. Thus, the skip-lot sampling plans are useful to minimize the cost of the inspection particularly in costly and destructive testing. Hence, a new system of skip-lot sampling plans designated as SkSP-2-R plan is developed in this article by incorporating the idea of resampling procedure in the skip-lot sampling plans of type SkSP-2. A Markov chain formulation and derivation of performance measures for this new plan are presented. The properties and advantages of the SkSP-2-R plan are studied with single sampling plan as the reference plan. The response-to-change characteristics of the SkSP-2-R plan are also investigated, based on the average run length.     

Confidence interval estimation for negative binomial group distribution

Negative binomial group distribution was proposed in the literature which was motivated by inverse sampling when considering group inspection: products are inspected group by group, and the number of non-conforming items of a group is recorded only until the inspection of the whole group is finished. The non-conforming probability p of the population is thus the parameter of interest. In this paper, the confidence interval construction for this parameter is investigated. The common normal approximation and exact method are applied. To overcome the drawbacks of these commonly used methods, a composite method that is based on the confidence intervals of the negative binomial distribution is proposed, which benefits from the relationship between negative binomial distribution and negative binomial group distribution. Simulation studies are carried out to examine the performances of our methods. A real data example is also presented to illustrate the application of our method.     

Exponentially weighted moving average control schemes with variable sampling intervals

The idea of using non-constant sampling intervals has been of interest in quality control applications since it was first suggested for the “skip-lot sampling plan” of Dodge. Recent interest has focused on the use of variable sampling interval (VSI) control schemes. VSI control schemes use a short sampling interval is given     

Repetitive group sampling plan based on the process capability index for the lot acceptance problem

An acceptance sampling plan is a method used to make a decision about acceptance or rejection of a product, based on adherence to a standard. Meanwhile, process capability indices (PCIs) have been applied in different manufacturing industries as capability measures based on specified criteria which include process departure from a target, process consistency, process yield and process loss. In this paper, a repetitive group sampling (RGS) plan based on PCI is introduced for variables’ inspection. First, the optimal parameters of the developed RGS plan are obtained considering constraints related to the risk of consumers and producers and also a double sampling plan, a multiple dependent state sampling plan and a sampling plan for resubmitted lots have been designed. Finally, after the development of variable sampling plans based on the Bayesian and exact approach, a comparison study has been performed between the developed RGS plan and other types of sampling plans and the results are elaborated.     

Dorfman-sterrett screening (group testing) schemes and the effects of faulty inspection

The Dorfman screening procedure is based on first testing a group of items as a whole, proceeding to individual testing only if the group-test indicates existence of at least one nonconforming item. A modification suggested by Sterrett allows for reintroduct-ion of group testing of all items, not yet tested individually, when an item is classified as nonconforming by an individual test. Effects of faulty test inspection on the properties of the modified procedures are studied.     

Sampling schemes for price index construction: a performance comparison across the classification of individual consumption by purpose food groups

Five sampling schemes (SS) for price index construction – one cut-off sampling technique and four probability-proportional-to-size (pps) methods – are evaluated by comparing their performance on a homescan market research data set across 21 months for each of the 13 classification of individual consumption by purpose (COICOP) food groups. Classifications are derived for each of the food groups and the population index value is used as a reference to derive performance error measures, such as root mean squared error, bias and standard deviation for each food type. Repeated samples are taken for each of the pps schemes and the resulting performance error measures analysed using regression of three of the pps schemes to assess the overall effect of SS and COICOP group whilst controlling for sample size, month and population index value. Cut-off sampling appears to perform less well than pps methods and multistage pps seems to have no advantage over its single-stage counterpart. The jackknife resampling technique is also explored as a means of estimating the standard error of the index and compared with the actual results from repeated sampling.     

Zero Acceptance Number Chained Quick Switching System

Zero acceptance number sampling inspection plans are commonly employed for compliance sampling and audit inspection purposes. The discriminatory power of zero acceptance number sampling plans is rather poor. This article remedies this disadvantage by chaining past lot results within a quick switching system.     

The geometric CUSUM chart with sampling inspection for monitoring fraction defective

The detection of an upward shift in the fraction defective of a repetitive process is considered using the geometric CUSUM. This CUSUM makes use of the information provided by the run-lengths of non-defective items between successive defective items, and was initially developed for the case of 100% inspection. This paper considers the geometric CUSUM under sampling inspection, and emphasizes that the pattern of sampling inspection can be quite haphazard without causing any difficulty for the operation of the CUSUM. Two separate mechanisms for the occurrence of a shift are considered. Methods for evaluating zero-state and steady-state ARL are presented for both 100% inspection and sampling inspection. Parameter choice is also considered, and recommendations made. Comparisons with some np -charts are provided.