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.