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 Designing of Variables Sampling Plan for Resubmitted Lots

This article proposes a variables sampling plan that can be applied for sampling inspection of resubmitted lots when the quality characteristic of interest follows the normal distribution. Resubmission of lots for inspection is allowed in some situations where the original inspection results are suspected or when the supplier or producer is allowed to opt for resampling as per the provisions of the contract, etc. The advantages of this proposed variables sampling plan over the existing single sampling variables plan are discussed. Tables are also constructed for the selection of optimal parameters of known and unknown standard deviation variables resampling scheme for specified two points on the operating characteristic curve, namely, the acceptable quality level and the limiting quality level along with the producer and consumer's risks. The optimization 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 acceptable quality level and limiting quality level under the operating characteristic curve.     

Attribute-variable Inspection Policy for Lots Using Resampling Based on EWMA

A new mixed sampling plan which is a combination of the attribute single sampling plan and variables resampling scheme based on EWMA statistic is proposed in this paper. The operating characteristic function of the proposed plan is derived and the plan parameters are determined such that the probability of acceptance of good lot is larger than the specified producer's confidence level and the bad lot acceptance probability is smaller than the consumer's confidence level. The efficiency and the advantages of the proposed plan are discussed over the existing attribute sampling plan. The extensive tables are provided for industrial applications. The use of tables is discussed with the help of a real-time industrial example.     

A Sequential Markov Chain Monte Carlo Approach to Set-up Adjustment of a Process over a Set of Lots

We consider the problem of adjusting a machine that manufactures parts in batches or lots and experiences random offsets or shifts whenever a set-up operation takes place between lots. The existing procedures for adjusting set-up errors in a production process over a set of lots are based on the assumption of known process parameters. In practice, these parameters are usually unknown, especially in short-run production. Due to this lack of knowledge, adjustment procedures such as Grubbs' (1954, 1983) rules and discrete integral controllers (also called EWMA controllers) aimed at adjusting for the initial offset in each single lot, are typically used. This paper presents an approach for adjusting the initial machine offset over a set of lots when the process parameters are unknown and are iteratively estimated using Markov Chain Monte Carlo (MCMC). As each observation becomes available, a Gibbs Sampler is run to estimate the parameters of a hierarchical normal means model given the observations up to that point in time. The current lot mean estimate is then used for adjustment. If used over a series of lots, the proposed method allows one eventually to start adjusting the offset before producing the first part in each lot. The method is illustrated with application to two examples reported in the literature. It is shown how the proposed MCMC adjusting procedure can outperform existing rules based on a quadratic off-target criterion.