A first course in stochastic processes

This paper introduces the concept of repetitive group sampling (RGS) for variables inspection. The repetitive group sampling plan for variables inspection will be useful when testing is costly and destructive. The advantages of the variables RGS plan over variables single sampling plan, variables double sampling plan and attributes RGS plan are discussed. Tables are also constructed for the selection of parameters of known and unknown standard deviation variables repetitive group sampling plan indexed by acceptable quality level and limiting quality level.

Repetitive group sampling procedure for variables inspection

Acceptance sampling plans have been utilised predominantly for the inspection of outgoing and incoming lots; these plans provide effective rules to vendors and buyers for making decisions on product acceptance or rejection. Multiple dependent state (MDS) sampling plans have been developed for lot sentencing and are shown to be more efficient than traditional single sampling plans. The decision criteria of MDS sampling plans are based on sample information not only from the current lot but also from preceding lots. In this study, we develop a variables MDS sampling plan for lot sentencing based on the advanced process capability index, which was developed by combining the merits of the yield-based index and loss-based index. The operating characteristic function of the developed plan is derived based on the exact sampling distribution. The determination of plan parameters is formulated as an optimisation model with non-linear constraints, where the objective is to minimise the sample size required for insp...

Developing a variables multiple dependent state sampling plan with simultaneous consideration of process yield and quality loss

This article proposes a variables two-plan sampling system called tightened-normal-tightened (TNT) sampling inspection scheme where the quality characteristic follows a normal distribution or a lognormal distribution and has an upper or a lower specification limit. The TNT variables sampling inspection scheme will be useful when testing is costly and destructive. The advantages of the variables TNT scheme over variables single and double sampling plans and attributes TNT scheme are discussed. Tables are also constructed for the selection of parameters of known and unknown standard deviation variables TNT schemes for a given acceptable quality level (AQL) and limiting quality level (LQL). The 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 AQL and LQL under the operating characteristic curve.

Designing of a variables two-plan system by minimizing the average sample number

In this paper, a new variable sampling plan using the exponentially weighted moving average (EWMA) statistic based on the yield index is developed for lot sentencing. The proposed plan considers the quality of the current lot as well as the preceding lots through the EWMA statistic. The sample size and the critical value of the proposed plan are determined by considering the acceptable quality level at the producer’s risk and the lot tolerance percent defective at the consumer’s risk. The plan parameters are tabulated according to the smoothing constant of the EWMA statistic and various combinations of two risks. An example is provided for illustrating the proposed plan.

A lot inspection sampling plan based on EWMA yield index

Summary This paper extends the concept of chain sampling to variables inspection when the standard deviation of the normally distributed characteristic is known. A discussion of the shape of the known sigma single-sampling variables plan is given. The chain sampling plan for variables inspection will be useful when testing is costly or destructive.

Chain sampling plan for variables inspection

In this paper, a new tightening concept has been incorporated into the single-level continuous sampling plan CSP-1, such that quality degradation will warrant sampling inspection to cease beyond a certain number of sampled items, until new evidence of good quality is established. The expressions of the performance measures for this new plan, such as the operating characteristic, average outgoing quality and average fraction inspected, are derived using a Markov chain model. The advantage of the tightened CSP-1 plan is that it is possible to lower the average outgoing quality limit.

Tightened single-level continuous sampling plan

In this paper, a modification is proposed on the tightened two-level continuous sampling plan. The tightened two-level plan is one of the three tightened multi-level continuous sampling plans of Derman et al. (1957) with two sampling levels. A modified tightened two-level continuous sampling plan is considered, for which the rules concerning partial inspection depend, in part, on the length of time it takes to decide that the process quality is good enough that 100% inspection may be suspended (e.g. the time required to find i consecutive items free of defects). Using a Markov chain model, expressions for the performance measures of the modified MLP-T-2 plan are derived. The modified MLP-T-2 plan is shown to be identical to the MLP-T-2 plan. Tables are also presented for the selection of the modified MLP-T-2 plan when the AQL or LQL and AOQL are specified.

S. Balamurali

Papers

Chain sampling plan for variables inspection

Tightened single-level continuous sampling plan

Modified tightened two-level continuous sampling plans