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     

Minimum average fraction inspected for continuous sampling plan CSP-1 under inspection error

SUMMARY In this paper, we present a further modification of Endres's method to construct the problem of minimizing the average fraction inspected (AFI) for the continuous sampling plan CSP-1 under inspection error. The measures of average outgoing quality under perfect and imperfect replacement conditions are considered. The formulae for searching the smallest clearance number i for minimizing the AFI for a CSP-1 plan are also provided. The solution procedure of the proposed method is more reliable, clearer and easier than that of Endres.     

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.     

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.     

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.     

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.     

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.     

Continuous inspection of Markov processes with a clearance interval

Dodge's continuous sampling plan-1 (CSP-1) with clearance interval zero may be inefficient if there is serial correlation between successive units which are Markov dependent and a clearance interval greater than zero is appropriate. For such a situation, the average outgoing quality limit (AOQL) expression has been obtained and, when the serial correlation coefficient of the Markov chain is assumed to be known a priori, it is numerically demonstrated that smaller AOQL values are achieved numerically for values of the clearance interval from 1 to 4, by improving the perform-ance ofCSP-L     

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.     

Average outgoing quality of CSP-C continuous sampling plan under short run production processes

A CSP-C continuous sampling plan is a new single-level continuous sampling procedure developed by Govindaraju & Kandasamy (2000) by incorporating the concept of acceptance number to the CSP-1 plan for the application of continuous production processes. In this new plan, the sampling inspection phase is characterized by a maximum allowable number of non-conforming units, c, and a constant sampling rate, f. Govindaraju & Kandasamy (2000) derived the performance measures such as average outgoing quality (AOQ), average fraction inspected (AFI) etc, of the CSP-C plan using a Markov chain model for long run production processes. Yang (1983) has observed that the AOQ and AFI, being long run average measures, are not satisfactory measures of performance for short run production processes. Hence, formulas are derived in this paper, using the renewal theory approach enabling one to compute AOQ and AFI for both long run and short run production processes. Numerical illustrations are also given. By simulation, the accuracy of the short run measures is studied.     

Construction and selection of skip-lot sampling inspection plans of type SkSP-2 indexed by indifference quality level and maximum allowable per cent defective

This paper presents tables based on the Poisson model, for the selection of skip-lot sampling plans of type SKSP-2, with a single-sampling plan which has a zero acceptance number as a reference plan. The indifference quality level (IQL) and the maximum allowable per cent defective (MAPD) are the criteria used for fixing the plan. Procedures for the selection of plans for given conditions of (IQL, average outgoing quality limit) and (MAPD, average outgoing quality limit) are also discussed.     

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.     

Comments on a simple test for new better than used in expectation1 by borges,proschan and rodrigues

Procedures and tables are givenfor construction and selection of continuous sampling plans of the type CSP-2 for a given pair of conditions.     

Economic design of continuous sampling plan under linear inspection cost

The article explores the problem of an economically based type I continuous sampling plan (CSP-1 plan) under linear inspection cost. By assuming that the per unit inspection cost is linearly proportional to the average number of inspections per inspection cycle, and by solving the modified Cassady et al.'s model, we not only have the required level of product quality but also obtain the minimum total expected cost per unit produced.     

Design and evaluation of skip-lot sampling plans of type SkSP-3

This paper presents a system of skip-lot sampling inspection plans designated as SkSP-3 based on the principle of a continuous sampling plan of type CSP-2. Expressions for performance measures such as Operating Characteristic function and ASN function are derived by the Markov chain approach. Selection of SkSP-3 with a single sampling plan having acceptance number zero as the reference plan is discussed.     

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.     

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.     

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.     

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.