Multiple states repetitive group sampling plans with process loss consideration

We propose a multiple state repetitive group sampling plan by considering the process loss. The optimal plan parameters of the proposed plan are selected such that producer’s risk and consumer’s risk are satisfied simultaneously by minimizing the average sample number. The advantages of the proposed plan over the existing sampling plans are given. Extensive tables are provided for practical applications of the proposed plan. Two real world examples are given for the illustration purpose.     

Design of progressively censored group sampling plans for Weibull distributions: An optimization problem

Optimization algorithms provides efficient solutions to many statistical problems. Essentially, the design of sampling plans for lot acceptance purposes is an optimization problem with several constraints, usually related to the quality levels required by the producer and the consumer. An optimal acceptance sampling plan is developed in this paper for the Weibull distribution with unknown scale parameter. The proposed plan combines grouping of items, sudden death testing in each group and progressive group removals, and its decision criterion is based on the uniformly most powerful life test. A mixed integer programming problem is first solved for determining the minimum number of failures required and the corresponding acceptance constant. The optimal number of groups is then obtained by minimizing a balanced estimation of the expected test cost. Excellent approximately optimal solutions are also provided in closed-forms. The sampling plan is considerably flexible and allows to save experimental time and cost. In general, our methodology achieves solutions that are quite robust to small variations in the Weibull shape parameter. A numerical example about a manufacturing process of gyroscopes is included for illustration.     

Variable sampling inspection for resubmitted lots based on process capability index Cpk for normally distributed items

In this article, a variables sampling inspection plan for resubmitted lot based on the process capability index C_pk is developed for normally distributed items with unknown mean and variance. The three plan parameters, sample size n, critical acceptance value k_a and the number of resubmissions m, are determined simultaneously by minimizing average sample number (ASN) with two conditions specified by the producer and the consumer. The advantages of the proposed resubmitted sampling plan over the variables single sampling plan are also discussed. Tables of plan parameters for selected values of acceptable quality level (AQL), limiting quality level (LQL), producer’s α-risk and consumer’s β-risk are provided and discussed with the help of an application example.     

Variables sampling inspection scheme for resubmitted lots based on the process capability index Cpk

This paper attempts to develop a sampling inspection scheme by variables based on process performance index for product acceptance determination, which examines the situation where resampling is permitted on lots not accepted on original inspection. The equations for plan parameters, the required sample size and the corresponding critical value, are derived based on the exact sampling distribution rather than an approximation approach hence the decisions made are more accurate and reliable. Moreover, the efficiency of the proposed variables resubmitted sampling plan is evaluated and compared with the existing variables single sampling plan. For illustrative purpose, an example is presented to demonstrate the use of the derived results for making a decision on product acceptance determination.     

Capability-based quick switching sampling system for lot disposition

Various acceptance sampling schemes have been developed for quality control and assurance. In this research, two types of variables quick switching sampling (VQSS) system based on the process capability index C_pk are proposed. The VQSS is composed of two single sampling plans, one is under a normal inspection and the other is under a tightened inspection. Requirements for accepting a lot under the tightened inspection are more stringent than under the normal inspection. The concept of the VQSS system is that the sampling mechanism can adjust flexibly based on the quality history of the preceding submitted lots. A minimization model is constructed to solve the plan parameters for each type of the VQSS system under different mixes of quality levels and risk endurance levels, and several tables are prepared for references. In addition, the performance of the two types of VQSS system are compared with the single sampling plan through the operating characteristic (OC) curve and the average sample number (ASN) required for inspection. Finally, a real example from a dielectric layer coating machine is presented to show the practicality of the proposed system.     

A combined attributes–variables plan

The design of single sampling plans in which the lot acceptance decision is based on both variables and attribute measurement of quality is discussed. A new plan, called the combined attributes–variables plan, is proposed incorporating an acceptance number to the regular variables plan for consumer protection. A design approach for the new plan is also developed for food manufacturing applications in which the sample size cannot be predetermined because of short production lengths and other analytical testing issues. Copyright © 2014 John Wiley & Sons, Ltd.     

Interval censored sampling plans for the gamma lifetime model

In this article, an acceptance sampling procedure for the gamma lifetime model is established under the interval censored test. Both producer and consumer risks are considered to develop the ordinary and approximate sampling plans with grouped data. Some of the proposed sampling plans are tabulated and the use of the tables is illustrated by an example. A sensitivity study is conducted to evaluate the influence of the length of the time interval on the proposed sampling plans.     

Estimation and Design of Sampling Plans for Monitoring Dependent Production Processes

We consider the problem of designing single and the double sampling plans for monitoring dependent production processes. Based on simulated samples from the process, Nelson proposed a new approach of estimating the characteristics of single sampling plans and, using these estimates, designing optimal plans. In this paper, we extend his approach to the design of optimal double sampling plans. We first propose a simple methodology for obtaining the unbiased estimators of various characteristics of single and double sampling plans. This is achieved by defining the various characteristics of sampling plans as explicit random variables. Some of the important properties of the double sampling plans are established. Using these results, an efficient algorithm is developed to obtain optimal double sampling plans. A comparison with a crude search shows that our algorithm leads to about 90% savings, on the average, in computational timings. The procedure is also explained through a suitable example for the ARMA(1,1) model. It is observed, for instance, that an optimal double sampling plan leads to about 23% reduction in average sample number, compared to an optimal single sampling plan. Tables for choosing the optimal plans for certain auto regressive moving average processes at some practically useful values of acceptable quality level and rejectable quality level are also presented.     

Multiple dependent state sampling plans for lot acceptance based on measurement data

This paper proposes a multiple dependent (or deferred) state sampling plan by variables for the inspection of normally distributed quality characteristics. The decision upon the acceptance of the lot is based on the states of the preceding lots (dependent state plan) or on the states of the forthcoming lots (deferred state plan). The lot acceptance probability is derived and the two-point approach to determining the plan parameters is described. The advantages of this new variables plan over conventional sampling plans are discussed. Tables are constructed for the selection of parameters of this plan under the specific values of the producer’s and consumer’s risks, indexed by acceptable quality level and limiting quality level, when the standard deviation is known or unknown.     

A variables sampling plan based on Cpmk for product acceptance determination

Process capability indices are useful management tools, particularly in the manufacturing industry, which provide common quantitative measures on manufacturing capability and production quality. Most supplier certification manuals include a discussion of process capability analysis and describe the recommended procedure for computing a process capability index. Acceptance sampling plans have been one of the most practical tools used in classical quality control applications. It provides both vendors and buyers to reserve their own rights by compromising on a rule to judge a batch of products. Both sides may set their own safeguard line to protect their benefits. Two kinds of risks are balanced using a well-designed sampling plan. In this paper, we introduce a new variables sampling plan based on process capability index C_pmk to deal with product sentencing (acceptance determination). The proposed new sampling plan is developed based on the exact sampling distribution hence the decisions made are more accurate and reliable. For practical purpose, tables for the required sample sizes and the corresponding critical acceptance values for various producer’s risk, the consumer’s risk and the capability requirements acceptance quality level (AQL), and the lot tolerance percent defective (LTPD) are provided. A case study is also presented to illustrate how the proposed procedure can be constructed and applied to the real applications.     

A new system of skip‐lot sampling plans having a provision for reducing normal inspection

The skip‐lot sampling program can be used for reducing the amount of inspection on a product that has excellent quality history. Thus skip‐lot sampling plans are designed to reduce inspection costs. Moreover, the skip‐lot concept is sound and useful and is economically advantageous to use in the design of sampling plans. Hence, a new system of skip‐lot sampling plans designated as the SkSP‐V plan is developed in this paper. The proposed plan requires a return to normal inspection whenever a lot is rejected during sampling inspection, but has a provision for a reduced normal inspection upon demonstration of superior product quality. A Markov chain formulation and derivation of performance measures for this new plan are presented. The properties of SkSP‐V plan are studied with single sampling plan as the reference plan. Advantages of this new plan are also discussed. Finally, certain cost models are given for the economic design of the SkSP‐V plan. Copyright © 2010 John Wiley & Sons, Ltd.     

Generalized beta prior models on fraction defective in reliability test planning

In many reliability analyses, the probability of obtaining a defective unit in a production process should not be considered constant even though the process is stable and in control. Engineering experience or previous data of similar or related products may often be used in the proper selection of a prior model to describe the random fluctuations in the fraction defective. A generalized beta family of priors, several maximum entropy priors and other prior models are considered for this purpose. In order to determine the acceptability of a product based on the lifelengths of some test units, failure-censored reliability sampling plans for location-scale distributions using average producer and consumer risks are designed. Our procedure allows the practitioners to incorporate a restricted parameter space into the reliability analysis, and it is reasonably insensitive to small disturbances in the prior information. Impartial priors are used to reflect prior neutrality between the producer and the consumer when a consensus on the elicited prior model is required. Nonetheless, our approach also enables the producer and the consumer to assume their own prior distributions. The use of substantial prior information can, in many cases, significantly reduce the amount of testing required. However, the main advantage of utilizing a prior model for the fraction defective is not necessarily reduced sample size but improved assessment of the true sampling risks. An example involving shifted exponential lifetimes is considered to illustrate the results.     

Acceptance sampling in a producer—supplier conflicting environment: Risk neutral case

This paper considers a mutual inspection game which follows the signing of a quality delivery contract. The basic strategic decisions considered involve both the supplier and producer acceptance sampling procedure on the same lot. To solve the game, we consider the classical notions of ‘producer’ and ‘consumer’ risks and define a random payoffs game. To simplify our analysis, we assume risk neutrality by both the producer and the supplier. The approach of this paper provides a departure point from traditional acceptance sampling, to an approach which recognizes explicit motivations and the pursuit of self-interest as well as the cost of information for the parties involved. As a result, the traditional formulation of sampling plans, designed in terms of risk considerations based on Neyman—Pearson theory in hypothesis testing, is deemed limited. For demonstration purposes, an example is solved.     

Variables sampling plans with PPM fraction of defectives and process loss consideration

Acceptance sampling plans provide the vendor and the buyer decision rules for lot sentencing to meet their product quality needs. A problem the quality practitioners have to deal with is the determination of the critical acceptance values and inspection sample sizes that provide the desired levels of protection to both vendors and buyers. As today's modern quality improvement philosophy, reduction of variation from the target value is the guiding principle as well as reducing the fraction of defectives. The C_pm index adopts the concept of product loss, which distinguishes the product quality by setting increased penalty to products deviating from the target. In this paper, a variables sampling plan based on C_pm index is proposed to handle processes requiring very low parts per million (PPM) fraction of defectives with process loss consideration. We develop an effective method for obtaining the required sample sizes n and the critical acceptance value C₀ by solving simultaneously two nonlinear equations. Based on the designed sampling plan, the practitioners can determine the number of production items to be sampled for inspection and the corresponding critical acceptance value for lot sentencing.     

Bayesian single and double variable sampling plans for the Weibull distribution with censoring

The sampling inspection problem is one of the main research topics in quality control. In this paper, we employ Bayesian decision theory to study single and double variable sampling plans, for the Weibull distribution, with Type II censoring. A general loss function which includes the sampling cost, the time-consuming cost, the salvage value, and the after-sales cost is proposed to determine the Bayes risk and the corresponding optimal sampling plan. Explicit expressions for the Bayes risks for both single and double sampling plans are derived, respectively. Numerical examples are given to illustrate the effectiveness of the proposed method. Comparisons between single and double sampling plans are made, and sensitivity analysis is performed.     

基于混合Ⅱ型删失数据的Weibull模型精确推断和可接受抽样计划(英文)

本文考虑基于混合Ⅱ型删失数据的Weibull模型精确推断和可接受抽样计划.得到威布尔分布未知参数最大似然估计的精确分布以及基于精确分布的置信区间.由于精确分布函数较为复杂,给出未知参数的另外几种置信区间,基于近似方法的置信区间.为了评价本文的方法,给出一些数值模拟的结果.且讨论了可靠性中的可接受抽样计划问题.利用参数最大似然估计的精确分布,给出一个可接受抽样计划的执行程序和数值模拟结果.     

Classical versus Bayesian risks in acceptance sampling: a sensitivity analysis

Assuming a beta prior distribution on the fraction defective, $p$ , failure-censored sampling plans for Weibull lifetime models using classical (or average) and Bayesian (or posterior) producer’s and consumer’s risks are designed to determine the acceptability of lots of a given product. The average risk criterion provides a certain assurance that good (bad) lots will be accepted (rejected), whereas the posterior risk criterion provides a determined confidence that an accepted (rejected) lot is indeed good (bad). The performance of classical and Bayesian risks are analyzed in developing sampling plans when the lifetime variable follows the Weibull distribution. Several figures and tables illustrate the sensitivity of the risks and optimal sample sizes for selected censoring levels and specifications according to the available prior information on $p$ . The analysis clarifies the distinction among the different risks for a given sampling plan, and the effect of the prior knowledge on the required sample size. The study shows that, under uncertainty in the prior variance of $p$ , the designs using Bayesian risks are more appropriate.     

Developing a sampling plan by variables inspection for controlling lot fraction of defectives

Acceptance sampling has been widely used tool for determining whether the submitted lot should be accepted or rejected. However, it cannot avoid two kinds of risks, accepting undesired poor product lots and rejecting good product lots. Such risks are even more significant as the rapid advancement of the manufacturing technology and stringent customers demand is enforced. A yield index S_pk has been developed to provide an exact measure on process yield or fraction nonconforming for normally distributed processes with two-sided specification limits. Therefore, the aim of this paper is to develop a variables sampling plan for evaluating the lot or process fraction nonconforming based on the yield index. The probability of lot acceptance is derived based on the sampling distribution and two-point condition on OC curve is used to determine the plan parameters. Tables of the plan parameters and step-by-step procedure are provided for the practitioner to make decision on lot sentencing especially for situations of products with very low fraction of nonconformities.