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.     

Selection of csp-t plans

Various continuous sampling plans have been proposed for monitoring the quality of continuous production processes. The multi-level continuous sampling plan of MIL-STD-1235C (1988) is designated as CSP-T Plan. CSP-T plan is a three-level tightened continuous sampling plan. It requires a switch to 100% inspection, at any level, whenever a nonconforming unit is found. This provides quick rectification in the event of a shift in quality. In this paper certain performance characteristics of CSP-T plan are derived using the approach of Stephens (1979) under the assumption that the production process is in statistical control. For the selection of CSP-T plans, two tables are given. These tables can be used to obtain parameters i (clearance interval) and f (sampling fraction) of the CSP-T plan for given acceptable quality level (AQL) with producer’ risk α=0.05 or the limiting quality level(LQL) with consumer’ risk β=0.10 and the outgoing quality limit(AOQL). Two examples are also given to illustrate the selection of plans from these tables     

Selection of CSP-V continuous sampling plans

MIL-STD-1235C establishes standard procedures for the selection and implementation of single- and multi-level continuous sampling plans, such as CSP-1, CSP-F, CSP-2, CSP-T and CSP-V. CSP-V is a single-level continuous sampling procedure which provides for alternating sequences of 100%inspection (either at full or reduced clearance number) and sampling inspection. It requires a return to 100% inspection whenever a non-confirming unit is found during sampling inspection, but provides for a reduced clearance number upon demonstration of superior product quality. The CSP-V procedure serves as an alternative to the CSP-T procedure where a reduction in sampling frequency has no economic merit. In this paper, expressions for the average outgoing quality, the average fraction inspected and the operating characteristic function are derived using a Markov chain model. Four tables are given to enable the selection of CSP-V plans when the acceptable quality level or the limiting quality level and the

average outgoing quality limit are specified.     

Designing ChSP-4(c1, c2) plans

In this paper, the notion of average total inspection (ATI) is introduced to ChSP-4(c1,c2) sampling plans. Procedures have been developed for the construction and selection of ChSP-4(c1, c2 plans, minimizing ATI at a given process average, while protection to the consumer is given in terms of the (i) average outgoing quality limit and (ii) limiting quality level.A wide range of c1 and c2 values are considered for developing tables which cover almost all practical situations. The procedure described is similar to that of Dodge and Romig.     

Design and evaluation of skip-lot sampling inspection plans with double-sampling plan as the reference plan

This paper presents a design for skip-lot sampling inspection plans with the double-sampling plan as the reference plan, so as to reduce the sample size and produce more efficient plans in return for the same sampling effort. The efficiency of the proposed plan compared with that of the conventional double-sampling plan is also discussed. The need for smaller acceptance numbers under the plan is highlighted. Methods of selecting the plan indexed by the acceptable quality level and limiting quality level, and by the acceptable quality level and average outgoing quality level are also presented.     

Selection of a sampling plan indexed with maximum allowable average outgoing quality

SUMMARY This paper introduces a new concept of maximum allowable average outgoing quality MAAOQ , which is the average outgoing quality at the inflection point. The procedure for designing a single sampling plan indexed through the maximum allowable per cent defective and MAAOQ is stated. Tables are constructed for the selection of parameters for the plan, and parametric conversions are also studied.     

Generalized tightened two-level continuous sampling plans

In 1955, Lieberman and Solomon introduced multi-level (MLP) continuous sampling plans. Derman et al . then extended the multi-level plans as tightened multi-level plans (MLP-T). In this paper, a generalization of MLP-T with two sampling levels is presented. Using a Markov chain model, expressions for the performance measures of the general MLP-T plans are derived. Tables are also presented for the selection of general MLP-T plans with two sampling levels when the acceptable quality level, limiting quality level, indiff erence quality level and average outgoing quality level are specified.     

Tightened single-level continuous sampling plan

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.     

Single sampling plans indexed by point op control and inflection point

Three tables for selection of single sampling plans with any one of the following combinations of entry parameters are givens.

1) the indifference quality level and the average outgoing quality limit.

2) the indifference quality level with relative slope of the OC curve at that quality leve land.

3) the quality level corresponding to the inflection point with relative slope of the OC curve at that quality level.

A table enabling the transition from one set of parameters to match the OC curve of other similar sets is also given.     

Procedures and tables for the construction and selection of chain sampling plans ChSP-4A(c1, c2,)r-Part 4

In this part of the series, the notion of average total inspection (ATI) is introduced to ChSP-4A(c1, c2)r plans, minimizing ATI at a given process average, while protection to the consumer is given in terms of average outgoing quality limit and limiting quality level. The procedure is similar to that of Dodge and Roming.     

Design of a CSP-1 plan based on regret-balanced criterion

This article explores the problem of designing a CSP-1 plan with the specified average outgoing quality limit (AOQL), the acceptable quality level (AQL), and the limiting quality level (LQL) value. By adopting the regret-balanced criterion under the producer's and consumer's interests of quality, we can design the optimal CSP-1 plan.     

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.     

Minimum average fraction inspected for TCSP-1 plan

This paper presents the calculation of the average outgoing quality limit (AOQL) for the tightened single-level continuous sampling plan (TCSP-1 plan) based on a numerical method. A solution procedure is developed to find the parameters (i, f, k) that will meet the AOQL requirement, while also minimizing the average fraction inspected (AFI) for the TCSP-1 plan when the process average [pbar] (> AOQL) is known.     

Minimum average fraction inspected for short-run CSP-1 plan

This paper presents details of the calculation of the average outgoing quality limit (AOQL) for a short-run CSP-1 plan based on Y ang's renewal process approach. A solution procedure is developed to find the unique combination (i,f) that will meet the AOQL requirement, while also minimizing the average fraction inspected for the shortrun CSP-1 plan when the process average p (> AOQL) and production run length R are known.     

Minimum Average Total Inspection of Variable Lot-size Sampling Plan for Continuous Production

This paper explores the problem of minimizing the average total inspection (ATI) of Read & Beattie's variable lot-size sampling plan for continuous production. The solution procedure is developed to find the optimal parameters (n,  c) that will meet the average outgoing quality limit (AOQL) requirement, while also minimizing the ATI for this variable lot-size plan.     

Minimum Variance and VOQL Chain Sampling Plans–ChSP-4(c 1, c 2)

In this article the outgoing quality and the total inspection for the chain sampling plan ChSP-4(c ₁, c ₂) are introduced as well-defined random variables. The probability distributions of outgoing quality and total inspection are stated based on total rectification of non conforming units. The variances of these random variables are studied. The aim of this article is to develop procedures for minimum variance ChSP-4(c ₁, c ₂) sampling plans and their determination. In addition to minimum variance sampling plans, a procedure is developed for designing plans with a designated maximum variance, a VOQL (Variance of Outgoing Quality Limit) plan. The VOQL concept is analogous to the AOQL (Average Outgoing Quality Limit) except in the VOQL plan, it is the maximum variance which is established instead of the usual maximum AOQ.     

Closed-Form Approximation for the AOQL of Attributes Acceptance Sample Plans

We derive upper and lower bounds at the point at which the average outgoing quality limit (AOQL) of an attributes acceptance sampling plan is achieved. Using a simple average of these bounds to approximate the ordinate of the AOQL, we develop an accurate, closed-form approximation to the AOQL. The bounds and approximation show how the parameters of a sampling plan affect the AOQL and can be used to study the behavior of the AOQL and other measures of the plan's performance.     

Comparison between count of cumulative conforming sampling plans and Dodge–Romig single sampling plan

In this research, a new sampling system is introduced based on the concept of count of cumulative conforming control charts (CCC-charts). The proposed method is based on Markov modeling and negative binomial distribution. The proposed sampling system is compared with traditional sampling methods like Dodge–Romig single sampling plan based on lot tolerance percent defective (LTPD) and Dodge–Romig single sampling plan based on average outgoing quality limit (AOQL) and its superiority for larger values of lot sizes and process average is denoted using a comparison study.     

Modified CSP-C Continuous Sampling Plan for Consumer Protection

Dodge (1943) introduced a single level attribute continuous sampling plan designated as CSP-1 for the application of continuous production processes. Govindaraju & Kandasamy (2000) developed a new single level continuous sampling plan whose sampling inspection phase is characterized by a maximum allowable number of non-conforming units c, and a constant sampling rate f and was designated as CSP-C. In this paper, a modification is proposed on the CSP-C continuous sampling plan. In this modified plan, sampling inspection is continued until the occurrence of c+1 non-conforming units, provided the first m sampled units have been found conforming during the sampling phase. Using a Markov chain model, expressions for the performance measures of the modified CSP-C plan are derived. The main advantage of the modified plan is that it is possible to lower the average outgoing quality limit.     

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.