A note on the operating characteristic curve of the known sigma single sampling variables plan

The operating characteristic curves of certain known sigma variables sampling plans may not be satisfactory in that they have a tendency to reject even lots of acceptable quality. This note presents the theory and a method to identify such known sigma variables plans possessing unsatisfactory operating characteristic curves.     

Selection of tightened two-level continuous sampling plans

Lieberman and Solomon (1955) introduced multi-level continuous sampling plans and Derman et al. (1957) extended them as tightened multi-level continuous plans. MLP-T plan is one of the three tightened multi-level continuous sampling plans of Derman et al. (1957). In this paper, we restrict our discussion to MLP-T plans with two sampling levels. Using a Markov chain model, expressions for the average outgoing quality, the average fraction inspected and the operating characteristic function are derived. Four tables are given to enable selection of MLP-T plans with two sampling levels when the acceptable quality level or the limiting quality level and the average outgoing quality limit are specified.     

On equivalence of oc functions of certain conditional sampling plans

In this paper equivalence of operating characteristic ( OC ) functions of certain conditional sampling plans viz., ChSP-4, ChSP~4A, Conditional Double Sampling Plan, Link sampling Plan and Chain Deferred State Sampling Plans have been established. A common procedure to select these plans have been suggested.     

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.     

Procedures and tables for the construction and selection of conditional double sampling plans

Procedures and tables for the selection of conditional double sampling plans for various entry parameters are given. A search procedure is also developed to determine the parameters of the plans when two points on the operating characteristic curve are specified.     

Some sampling plans with identical operating characteristic curves

The properties of three sampling inspection plans with identical operating characteristic curves are discussed. Relative merits and demerits are studied and an eficient plan is identiJied. Tables yielding parametric values for designing plans for various entry parameters are provided.     

Acceptance Sampling Plans from Truncated Life Tests Based on the Birnbaum–Saunders Distribution for Percentiles

Time to failure due to fatigue is one of the common quality characteristics in material engineering applications. In this article, acceptance sampling plans are developed for the Birnbaum–Saunders distribution percentiles when the life test is truncated at a pre-specified time. The minimum sample size necessary to ensure the specified life percentile is obtained under a given customer's risk. The operating characteristic values (and curves) of the sampling plans as well as the producer's risk are presented. The R package named spbsq is developed to implement the developed sampling plans. Two examples with real data sets are also given as illustration.     

ASN-minimax double sampling plans for variables

X be a continuous quality characteristic, with one-sided lower specification limit, having either normal distribution with known σ or exponential distribution. We report on an algorithm allowing the calculation of the so-called ASN-Minimax plan. This plan has minimal maximal average sample size among all double sampling plans for variables that obey the classical two-points-condition on the operating characteristic. We give examples and tables of the ASN-Minimax plans in the normal as well as in the exponential case. Received: March 20, 2000; revised version: January 22, 2001     

Reliability sampling plans for the two-parameter exponential distribution under progressive censoring

This paper presents reliability sampling plans for the two-parameter exponential distribution under progressive censoring. These sampling plans are quite useful to practitioners, because they provide savings in resources and in total test time. Furthermore, they off er the flexibility to remove functioning test specimens from further testing at various stages of the experimentation. In the construction of these sampling plans, the operating characteristic curve is derived using the exact distributional properties of maximum likelihood estimators. An example is given to illustrate the application of the proposed sampling plans.     

Improved attribute acceptance sampling plans based on maxima nomination sampling

This paper demonstrates the use of maxima nomination sampling (MNS) technique in design and evaluation of single AQL, LTPD, and EQL acceptance sampling plans for attributes. We exploit the effect of sample size and acceptance number on the performance of our proposed MNS plans using operating characteristic (OC) curve. Among other results, we show that MNS acceptance sampling plans with smaller sample size and bigger acceptance number perform better than commonly used acceptance sampling plans for attributes based on simple random sampling (SRS) technique. Indeed, MNS acceptance sampling plans result in OC curves which, compared to their SRS counterparts, are much closer to the ideal OC curve. A computer program is designed which can be used to specify the optimum MNS acceptance sampling plan and to show, visually, how the shape of the OC curve changes when parameters of the acceptance sampling plan vary. Theoretical results and numerical evaluations are given.     

Minimum Size Double Sampling Plans for Large Isolated Lots

A common approach to the design of an acceptance sampling plan is to require that the operating characteristic (OC) curve should pass through two designated points that would fix the curve in accordance with a desired degree of discrimination. This paper presents a search procedure for the selection of double sampling inspection plans of type DSP - (0, 1) for specified two points on the OC curve, namely acceptance quality limit, producer's risk, limiting quality and consumer's risk. Selection of the plans is discussed for both the cases of fraction non-conforming and the number of non-conformities per unit.     

Optimal exact design of double acceptance sampling plans by attributes

The design of double acceptance sampling (AS) plans for attributes based on the operating characteristic curve paradigm is usually addressed by enumeration algorithms. These AS plans may be non optimal regarding the sample size to inspect as they were obtained without the requirement that the constraints at the OC curve controlled points are not violated for minimum Average Sample Number (ASN) scenarios. An approach based on mathematical programming is proposed to systematically design double AS plans for attributes, where the characteristics controlled are modelled by binomial or Poisson distributions. Specifically, Mixed Integer Nonlinear Programming (MINLP) formulations are developed and combined with an enumeration algorithm that allows finding ASN minimax optimal plans. A theoretical result is developed with the purpose of assuring the global optimum design is reached by iteration where a convenient solver is used to find local optima. To validate the algorithm, we compare our results with those of tables commonly used for practical purposes, consider different rates of risk, and setups commonly used in Lot Quality Assurance Plans (LQAS) for health monitoring programmes. Finally, we compare AS plans determined for processes described by binomial and Poisson distributions.     

The operating characteristic of double sampling plans by variables when the standard deviation is unknown

Summary We deal with double sampling plans by variables for a one-sided specification limit when the quality characteristic is normally distributed with unknown standard deviation. An algorithm is presented that allows to calculate the OC of the sampling plans proposed by Bowker and Goode (1952). We give several examples. Furthermore, it is shown that the algorithm carries over to calculating the OC of the double-stage t-test. The authors wish to thank Yvonne K?llner and Timor Saffary for technical support.     

A Design of Attributes Double Sampling Plans for Three-class Products

In this article, a new attributes double sampling plan for three-class products (ADSPTP) is presented, and the corresponding operating characteristic function is constructed based on the given procedure of performing ADSPTP. Average sample numbers (ASN) for complete inspection and curtailed inspection of the second sample are derived and the extreme point is discussed on the three-dimensional ASN surface. In addition, the differences arising from different parameters are studied. Sampling plans are designed by a nonlinear optimization model. Finally, numerical examples and discussions are given to illustrate the obtained results, and tables of the designed plans under various conditions are provided.     

Matching Performance of Continuous Sampling Plans with Single Sampling Plans

Single sampling plans are widely used for appraising incoming product quality. However, for situations where a continuous product flow exists, lot-by-lot demarcations may not exist, and it may be necessary to use alternate procedures, such as CSP-1, for continuous processes. In this case, one would like to be able to understand how average performance of the continuous sampling procedures compares to the more commonly used single sampling plans.

In this study, a model is devised which can be used to relate plan performance between single sample lot acceptance procedures and Dodge's(1943) CSP-1 continuous sampling plan. It is shown that it is generally not possible to match up performance based upon operating characteristic curve expressions for the two plans. Instead, the plans are matched by equating expressions for π(p), the long run proportion of product which is accepted, under both procedures. This is shown to be equivalent to matching up properties on an average outgoing quality basis. The methodology may be extended for any derivative plan under MIL-STD-1235B (1982), the military standard for continuous acceptance sampling.     

Acceptance sampling plans for linear profiles with one-sided specifications

In this study, we propose three new sampling plans based on yield index C_puA for linear profiles with one-sided specifications, including the resubmitted sampling plan, the repetitive group sampling plan, and the multiple dependent state repetitive sampling plan. The operating characteristic functions of our proposed sampling plans are developed. The plan parameters of our proposed sampling plans are determined through nonlinear optimization. The plan parameters are reported for various combinations of acceptable quality level and limiting quality level. The three sampling plans are compared with the existing single sampling plan in terms of the average sample number. A real example is used to illustrate the applications.     

Acceptance Sampling Plans from Truncated Life Tests Based on the Generalized Birnbaum–Saunders Distribution

In this article, we develop acceptance sampling plans when the life test is truncated at a pre-fixed time. The minimum sample size necessary to ensure the specified median life is obtained by assuming that the lifetimes of the test units follow a generalized Birnbaum–Saunders distribution. The operating characteristic values of the sampling plans as well as producer's risk are presented. Two examples are also given to illustrate the procedure developed here, with one of them being based on a real data from software reliability.     

Optimal design of accelerated degradation tests based on Wiener process models

Optimal accelerated degradation test (ADT) plans are developed assuming that the constant-stress loading method is employed and the degradation characteristic follows a Wiener process. Unlike the previous works on planning ADTs based on stochastic process models, this article determines the test stress levels and the proportion of test units allocated to each stress level such that the asymptotic variance of the maximum-likelihood estimator of the qth quantile of the lifetime distribution at the use condition is minimized. In addition, compromise plans are also developed for checking the validity of the relationship between the model parameters and the stress variable. Finally, using an example, sensitivity analysis procedures are presented for evaluating the robustness of optimal and compromise plans against the uncertainty in the pre-estimated parameter value, and the importance of optimally determining test stress levels and the proportion of units allocated to each stress level are illustrated.     

Designing of variables quick switching sampling system by considering process loss functions

This paper proposes a variables quick switching system where the quality characteristic of interest follows a normal distribution and the quality characteristic is evaluated through a process loss function. Most of the variables sampling plans available in the literature focus only on the fraction non-conforming and those plans do not distinguish between the products that fall within the specification limits. The products that fall within specification limits may not be good if their mean is too away from the target value. So developing a sampling plan by considering process loss is inevitable in these situations. Based on this idea, we develop a variables quick switching system based on the process loss function for the application of the processes requiring low process loss. Tables are also constructed for the selection of parameters of variables quick switching system for given acceptable quality level and limiting quality level. The results are explained with examples.     

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.