Average Total Inspection Research Articles

Optimal and economic design of modified double sampling plan under new Weibull–Pareto distribution

PurposeThe purpose of this paper is to design a modified version of the double sampling plan to handle the inspection processes requiring a minimum sample size to assure the median life for the products under the new Weibull–Pareto distribution. The economic design of the proposed plan is also considered to assure the product's lifetime with minimum cost.Design/methodology/approachThe authors have developed an optimization model for obtaining the required plan parameters by solving simultaneously two non-linear inequalities and such inequalities have been formed based on the two points on the operating characteristic curve approach.FindingsThe results show that the average sample number, average total inspection and total inspection cost under the proposed plan are smaller than the same of a single sampling plan. This means that the proposed plan will be more efficient than a single sampling plan in reducing inspection effort and cost while providing the desired protection.Originality/valueThe proposed modified double sampling plan designed to assure the median life of the products under the new Weibull–Pareto distribution is not available in the literature. The proposed plan will be very useful in assuring the product median lifetime with minimum sample size as well as minimum cost in all the manufacturing industries.

Construction and Selection of Double Inspection Single Sampling Plan for an Independent Process Using Bivariate Poisson Distribution

There are more sampling concepts active in production Industries, for inspecting the samples and analysing performance of the population. Also the sampling plans reduce errors in the production and produce the error free products. In this study, construction and selection of Double Inspection with reference to Single Sampling Plan i.e., DISSP, by attribute are investigated by using the Bivariate Poisson distribution. The Methodology, DISSP, was proposed based on two quality characteristics of the same sample size, and the planning parameters (n, C₁, C₂) are based on the operating characteristics, the conventional two-point condition by the planning table parameters (AQL and LQL). It is based on selected quality requirements and risks designed to allow manufacturers to easily determine the required sample size and corresponding acceptance criteria. A Comparison was done based on the efficiency of the plan with an existing single sampling plan and gave a numerical example to expose the operating tables. Also, the study shows the advantages of the proposed plan, and performance of the curves like, Operating characteristics, Average Outgoing Quality, and Average Total Inspection to expose the proposed double inspection sampling plan.

Design of single and double acceptance sampling plans based on neutrosophic sets

Although traditional acceptance sampling plans (ASPs) need certain mass quality characteristics, it is not easy to define them as crisp value in some real case problems. The fuzzy set theory (FST) is one of the popular techniques to model uncertainties of the process and therefore fuzzy ASPs have been offered in the literature. Fuzzy set extensions have been proposed recently for better modeling of the uncertainties having different sources and characteristics. One of these extensions named neutrosophic sets (NSs) can be used to increase the sensitiveness and flexibility of ASPs. The ASPs based on NSs can give ability to classify the items as defective, non-defective and indeterminate. Since the operator can become indecisive for slightly defective items, these plans can provide a good representation of human evaluations under uncertainty. In this study, single and double ASPs are designed based on NSs by using binomial and poisson distributions that are also re-analyzed based on NSs. For this aim, some characteristics functions of ASPs such as probability of accepting a lot (Pa), average outgoing quality (AOQ), average total inspection (ATI) and average sample number (ASN) have also been analyzed based on NSs. Numerical examples are presented to analyze the proposed plans.

Optimal design of a skip-lot sampling reinspection plan with a double sampling plan as a reference plan

Skip-lot sampling plans have the provision of inspecting only a fraction of lots, which reduces time and cost of the inspection. Thus, the skip-lot sampling plan is more cost-effective. The intention of this article is to propose the designing methodology to determine the optimal parameters of skip-lot sampling plan of type 2 with a double sampling plan as a reference plan for resubmitted lots by using two points on the operating characteristic curve. Tables summarize the optimal parameters determined under binomial and Poisson distributions for various combinations of producer quality level and consumer quality level by minimizing the average sample number and subject to satisfying both producer’s risk and consumer’s risk. The execution of the proposed plan is provided with an illustrative example. By comparison, it is proved that the proposed plan is an outstanding plan than the existing skip-lot and conventional sampling plans in terms of probability of acceptance, average sample number, and average total inspection.

(2012-6338) Design and Analysis of Acceptance Sampling Plans Based on Intuitionistic Fuzzy Linguistic Terms

Acceptance sampling plans (ASPs) offer inspection of a small set of items from a lot within a predefined plan to procure a certain output quality level with minimum cost in terms of time, effort, and damage to the inspected items. Although traditional ASPs use crisp plan parameters, quality characteristics of the incoming items or human evaluations about inspection process may contain uncertainties and may not always be defined as crisp values in real life problems. The fuzzy set theory (FST) is one of the most popular techniques to model these uncertainties by defining plan parameters as fuzzy numbers. Despite the advantages, traditional fuzzy sets are not flexible enough to model all kinds of uncertainties. For example, it has some disadvantages because of defining the status of any item based on defectiveness or non-defectiveness conditions and presuming the parts as non-defective whose defectiveness is not indeed determined. New extensions of FST can improve the quality of uncertainty modeling of ASPs. Intuitionistic Fuzzy Sets (IFSs) allow slackness for non-determination about the membership and give more sensitive modeling opportunity in human-related evaluations by the help of this ability. Since the inspection procedure of the ASPs depends on human-related judgements, IFSs have been used to define the defectiveness degree of the items in this study. ASPs based on interval-valued IFSs (IVIFSs) have also been designed and some characteristic functions of ASPs, such as acceptance probability ($P_a$), average sample number ($ASN$) and average total inspection ($ATI$) have been reformulated. Intuitionistic binomial and Poisson distributions have been defined to be able to formulate the ASPs. Additionally, the defectiveness of the items has been represented by using linguistic terms to overcome the difficulty of quantifying the verbal evaluation results as numerical measures. The $alpha$-cut technique has been combined with the linguistic approach to allow defining with multiple $alpha$ values for different product segments. Finally, some numerical examples have been presented to analyze the effectiveness of proposed ASPs and discuss the obtained results.

Economic Design of Quick Switching Sampling System for Resubmitted Lots under Gamma-Poisson Distribution

In this paper, a method of designing quick switching sampling system for resubmitted lots for inspection of attribute quality characteristics based on the gamma-Poisson distribution is proposed. We determine the required parameters by using two-points on the operating characteristic curve approach such that both producer’s and the consumer’s risks are satisfied for some specified values of acceptable quality level and limiting quality level. Tables are constructed for optimal sample size and two acceptance numbers of the proposed sampling system. The relative efficiency of the proposed system over conventional plans is also discussed. In addition, an economic design of the above mentioned sampling system to minimize total cost is also investigated. Consequently, it is proved that the proposed system minimizes the total inspection cost and average total inspection.

Generalized Multiple Dependent State Sampling Plans in Presence of Measurement Data

This article introduces a generalized version of the multiple dependent state sampling plan based on the measurement data, that is, when the quality characteristic is measured in a numerical scale. The conditions of application and the operating procedures of the proposed plan are discussed sequentially. A few important performance measures, such as operating characteristic curve, average total inspection and average sample number, are developed. The advantage of the proposed plan over the multiple dependent state sampling and single sampling plan is demonstrated through numerical example. Finally, one real-life data set is analyzed to illustrate the application of the proposed sampling plan.

Determination and economic design of a generalized multiple dependent state sampling plan

In this paper, we have introduced a generalized version of multiple dependent state sampling plan called generalized multiple dependent state sampling plan. The conditions of application and operating procedure of this new plan are also proposed. The performance measures such as the probability of acceptance, average sample number and average total inspection are derived. The optimal parameters are determined based on two points on the operating characteristic curve approach under both fraction non-conforming and fraction non-conformities. The efficiency of proposed plan is also discussed over the existing attribute sampling plans. Finally economic aspect of designing of the proposed plan is discussed.

Variable stage-independent double sampling plan with screening for acceptance quality loss limit inspection scheme

The quality loss suggested by Taguchi has been recognised as a new quality evaluation based on variable property instead of the quality evaluation based on traditional attribute property such as the proportion of nonconforming items. Some variable sampling inspection plans in order to assure the quality have been considered. As one of those sampling inspection plans, the single sampling plan with screening (SSPS) has been constructed for acceptance quality loss limit inspection scheme. Further, the repetitive group sampling plan with screening (RGSPS) has been developed for reducing the average total inspection (ATI). Although ATI by RGSPS has successfully been reduced in comparison with ATI by SSPS, RGSPS may sometimes increase the average sampling frequency (ASF) in return for reducing ATI. In this study, the stage-independent double sampling plan with screening (SIDSPS) based on the concept of the acceptance quality loss limit inspection scheme is proposed under the consideration of the trade-off between ATI and ASF. Through some numerical comparisons about ATI and ASF in SSPS, RGSPS, and SIDSPS, the usefulness of SIDSPS proposed in this study is confirmed.

Economic design of quick switching sampling system for resubmitted lots

This paper proposes a quick switching sampling system for the inspection of attributes quality characteristics for resubmitted lots. The optimal parameters for both fraction non conforming items and fraction non conformities of the proposed sampling system are determined using an optimization procedure so that producer’s risk and consumer’s risk are simultaneously satisfied. Tables are also constructed for the selection of parameters for specified AQL and LQL. The advantage of the proposed plan over the existing plan is discussed and illustrate. An economic design of the proposed sampling system is also discussed and shown that the proposed sampling system has minimum total cost and average total inspection compared to other existing sampling plans.

An Inventory Model with Embeeded Acceptance Sampling Plan

The classical inventory model assumes that the quality of the items received matches with the quality required. In many cases the deviation in quality results in additional costs to the stockiest and sometimes lead to rejection of the received lot. The cost of inspection along with the other inventory costs can be unified into a single model by embedding an acceptance sampling plan into the inventory model. When the lot is accepted there is a possibility of unseen defectives, which may reach the customer leading to loss of goodwill. If the lot is rejected on inspection, the model suggests rectification and removal of non-confirming units. In this paper a model is developed to determine (i) the Economic Order Quantity and (ii) a single sample plan of the attribute type, which minimizes the Average Total Inspection. The model utilizes spreadsheet solutions to handle statistical functions.

平均検査個数最小化を考慮したTaguchiの品質損失のもとでの計量選別型検査方式のための設計法(理論・技術)

平均検査個数最小化を考慮したTaguchiの品質損失のもとでの計量選別型検査方式のための設計法(理論・技術)

Rectifying inspection for PAOSQLL scheme based on variable repetitive group sampling plan

The concept of the quality loss derived by Taguchi has been accepted as the evaluation measure of quality instead of the traditional attribute property such as the proportion of non-conforming items. Since the variable single sampling plan having the desired operating characteristics indexed by the quality loss was proposed in 1997, various kinds of sampling plans indexed by the quality loss have been considered. Among them, there are two kinds of rectifying variable single sampling (RVSS) plans indexed by the quality loss. In the RVSS plans, two inspection schemes called the acceptance quality loss limit (AQLL) scheme and the permissible average outgoing surplus quality loss limit (PAOSQLL) scheme have been formulated. Note that the concepts of the AQLL and PAOSQLL schemes in the RVSS plans indexed by the quality loss are equivalent to those of the lot tolerance percent defective (LTPD) and the average outgoing quality limit (AOQL) schemes in the traditional rectifying attribute single sampling plans, respectively. On the other hand, in the sampling plan having the desired operating characteristics, an attribute repetitive group sampling plan was proposed for the purpose of reducing the average sampling number in the inspection. Recently, by applying the repetitive group sampling to the rectifying variable sampling plan for the AQLL scheme, the rectifying variable repetitive group sampling (RVRGS) plan for the AQLL scheme has been considered for the purpose of reducing the average total inspection (ATI). However, the RVRGS plan for the PAOSQLL scheme has not been investigated yet. Accordingly, the RVRGS plan for the PAOSQLL scheme must be investigated to complete the RVRGS plans indexed by the quality loss. In this article, the RVRGS plan for the PAOSQLL scheme is addressed. Then, the design procedure in the RVRGS plan for the PAOSQLL scheme is proposed for the purpose of reducing ATI. Through some numerical investigations, the effectiveness to reduce ATI by the RVRGS plan for the PAOSQLL scheme is confirmed.

On Dodge-Romig Single Sampling Inspection Tables under Average Quality Protection

Objectives: This paper aims at presenting an easy method of designing Single Sampling Plans (SSP) by attributes inspection based on Dodge-Romig method under Average Quality Protection. Methods/Statistical Analysis: A computational algorithm is developed for obtaining the parameters of the SSP, viz., the sample size and the acceptance number. A simple computer programme under the Poisson model for the OC function is developed for the computational algorithm using which the parameters of the SSP for desired levels of Average Outgoing Quality Limit (AOQL). Findings: The sample size and acceptance number constituting the SSP obtained using the procedure described in this paper are found to provide closer values of the desired AOQL and the minimum Average Total Inspection (ATI) than those obtainable from Dodge and Romig. The simple computer programme replaces the huge volumes of tables of Dodge and Romig. The procedure avoids the approximations involved in the original Dodge-Romig method and thus results in better plans. Application/ Improvements: The Single Sampling Plans under average quality protection are applicable in attributes inspection where ever rectification is possible.

A Modified Single Sampling Plan for the Inspection of Attribute Quality Characteristics

In this manuscript, a modified single sampling plan is proposed for the inspection of products in which the nonconforming items can be classified in to two categories namely critical and non-critical; and explained with the help of industrial example. The operating procedure of this plan is also proposed and the performance measures such as the probability of acceptance, average sample number, average total inspection and average out going quality are also derived. The optimal parameters are determined which will have minimum sample size. The efficiency of the proposed plan is also discussed over the conventional single sampling plan. The extensive tables for selecting a modified single sampling plan based on AQL and LQL are provided for both Binomial and Poisson distributions and explained with the help of industrial data.

Practitioner advice: Dodge and Romig sampling tables: Revisited, refined, and extended-practitioner advice

ABSTRACTExcel templates together with some VBA code permit great refinements in deriving the sample sizes, n, and acceptance numbers, c, for single sampling plans of the Dodge and Romig (1944, 1959) type that were developed many years ago to achieve optimization via minimum average total inspection (ATI), for ranges of lot sizes, N, and process averages, , classified by two indices defined as lot tolerance percent defective (LTPD) and average outgoing quality limit (AOQL). Two Excel templates are presented here by which optimum single sampling plans are derived for specific values of N and , rather than for ranges of these quantities. The templates also allow for tweaking results to achieve desired properties and provide numerous additional characteristics of the derived sampling plans. While the D & R tables are limited to 8 LTPD values and 13 AOQL values, the templates are unlimited.

A new economical scheme of acceptance sampling plan in a two-stage approach based on the maxima nomination sampling technique

An acceptance sampling plan plays a very important role in any quality assurance system. In this new economical design of acceptance sampling plan, three types of costs are included in the objective function by considering average outgoing quality limit (AOQL), average quality level (AQL) and lot tolerance percent defective (LTPD) constraints based on the maxima nomination sampling (MNS) method in a two-stage approach. The design of this sampling inspection plan involves the minimum average total inspection (ATI). The model is designed to minimize the summation of costs and the proposed MNS economical sampling plan is compared with the classical one. Practitioners can use the proposed model to decrease the total cost of inspection.

Rectifying inspection for acceptable quality loss limit based on variable repetitive group sampling plan

It is usually assumed that a quality characteristic in an item obeys a normal distribution in the case that the quality of items is evaluated based on the variable property. Then, the concept of Taguchi’s quality loss has been accepted as the evaluation measure of quality instead of the traditional attribute property such as the proportion of nonconforming items. From this viewpoint, some variable sampling plans indexed by the quality loss have been investigated before now. As a study earliest among them, the variable single sampling plan based on operating characteristics (OC) indexed by the quality loss was considered. On the other hand, the attribute repetitive group sampling plan on OC was proposed for reducing the sampling number in the inspection. Recently, the variable repetitive group sampling (VRGS) plan on OC indexed by the quality loss has been considered. By the way, the rectifying inspection is known as one of the schemes of acceptance sampling inspection. Then, Dodge-Romig single sampling plans are known as the traditional rectifying inspection based on attribute sampling plans. Dodge-Romig rectifying attribute sampling plans provide the lot tolerance percent defective (LTPD) scheme on each lot and the average outgoing quality limit (AOQL) scheme for many lots. Furthermore, the rectifying variable single sampling (RVSS) plan indexed by the quality loss was investigated. In conformity with the traditional rectifying attribute sampling plans for the LTPD and AOQL schemes, the acceptance quality loss limit (AQLL) and specified permissible average outgoing surplus quality loss limit (PAOSQLL) schemes are respectively proposed in the RVSS plans indexed by the quality loss. In this article, we suppose that the quality characteristic in an item obeys a normal distribution. Under this condition, the rectifying variable repetitive group sampling (RVRGS) plan for AQLL is considered for the purpose of reducing the average total inspection (ATI). Specifically, the design procedure for finding out the required sample size and inspection criteria for satisfying the constraint of the quality assurance is derived. Lastly, it is shown that ATI of the RVRGS plan is reduced in comparison with that of the RVSS plan under the same condition.

Variable sampling inspection plans with screening indexed by Taguchi’s quality loss for optimising average total inspection

There are some conventional attribute sampling inspection plans designed with respect to attribute property, such as the proportion of nonconforming items. Among them, the attribute sampling inspection plans with screening are defined under the lot tolerance percent defective (LTPD) inspection scheme and the average outgoing quality limit (AOQL) inspection scheme. On one hand, Taguchi has proposed the concept of quality loss as a measure to evaluate the quality of items based on the variable property instead of the traditional attribute quality evaluation. Hereby, in this article, the design procedures for variable sampling inspection plans with screening indexed by Taguchi’s quality loss in conformity with the conventional attribute sampling inspection plans with screening composed of the LTPD and AOQL inspection schemes are represented.

Chain Sampling Scheme under Constant Inspection Errors

AbstractThe primary aim of this paper is to extend the inspection error consideration to chain sampling schemes, an area that has not been dealt with in the literature. A mathematical model is developed to investigate the performance of chain sampling schemes under constant inspection errors. Expressions of performance measures, such as operating characteristic function, average total inspection and average outgoing quality, are derived to aid the analysis of a general chain sampling scheme, ChSP‐4A ($c_1,\,c_2$) r, developed by Frishman. This study reveals that as Type I inspection error increases the probability of acceptance will decrease and as Type II inspection error increases the acceptance probability will increase. The effect of Type II error on the probability of acceptance is very marginal compared with that of Type I error, especially when the true fraction non‐conforming is small. In addition, the effects of inspection errors can be ‘eliminated’ by transforming to its equivalent perfect inspection counterpart, hence greatly reducing the complexity of the analysis. The effects of other sampling parameters are also studied to serve as a foundation for future plan designing purposes. Copyright © 2006 John Wiley & Sons, Ltd.