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     

Modified tightened two-level continuous sampling plans

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.     

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.     

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.     

Acceptance sampling plans for linear profiles with one-sided specifications

In this study, we propose three new sampling plans based on yield index C_puA for linear profiles with one-sided specifications, including the resubmitted sampling plan, the repetitive group sampling plan, and the multiple dependent state repetitive sampling plan. The operating characteristic functions of our proposed sampling plans are developed. The plan parameters of our proposed sampling plans are determined through nonlinear optimization. The plan parameters are reported for various combinations of acceptable quality level and limiting quality level. The three sampling plans are compared with the existing single sampling plan in terms of the average sample number. A real example is used to illustrate the applications.     

Optimal designing of skip-lot sampling plan of type SkSP-2 with group acceptance sampling plan as reference plan under Burr-type XII distribution

In this paper, skip-lot sampling plan of type SkSP-2 with group acceptance sampling plans is proposed when the lifetime of the product follows the Burr-type XII distributions. The optimal parameters of the proposed plan are determined when two points on operating characteristics curve namely acceptable quality level and limiting quality level and the number of testers are specified. We also considered the Burr-type XII distribution to find the plan parameters. Several tables are given for practical use. We compare the results of proposed plan with the existing plans. Results are explained using real-world examples.     

Developing a variables repetitive group sampling plan based on process capability index C pk with unknown mean and variance

In this paper, variables repetitive group sampling plans are developed based on the process capability index C _pk when the quality characteristic follows a normal distribution with unknown mean and variance. The sampling plan parameters such as the sample size and the acceptance constant are determined to minimize the average sample number. Symmetric and asymmetric cases, in percent defectives due to two specification limits, are dealt with for specified combinations of acceptable quality level and limiting quality level. Tables are provided and examples are given to use proposed plans in practice.     

Procedures and tables for the construction and selection of chain sampling plans ChSP-4A(c1,c2)r—Part 2

In this paper an approach for designing chain sampling plans ChSP-4A(c1,c2)r indexed by acceptable quality level and limiting quality level under the conditions of binomial model and a procedure of designing plans for fixed sample sizes minimizing the sum of weighted risks are described.     

Optimal designing of two-level skip-lot sampling reinspection plan

Skip-lot sampling plan is often applied in industries for reducing the cost and effort of the inspection of the product having excellent quality history. Consequence of skip-lot sampling plans is to reduce the cost of inspection so which are more attractive in economical aspect. In this paper, we develop a sampling plan by incorporating the idea of resampling in two-level skip lot sampling plan and the new plan is designated as SkSP-2L.1-R. This paper presents the Markov chain formulation of the proposed plan along with the derivation of performance measures of the plan. We also provide the designing methodology to determine the optimal parameters of the SkSP-2L.1-R plan so as to minimize the average sample number by using two points on the operating characteristic curve approach. By contemplating various combinations of producer and consumer quality levels along with respective risks, a table is constructed to determine the optimal parameters. An industrial application of the proposed SkSP-2L.1-R plan is discussed. The SkSP-2L.1-R with single sampling plan as a reference plan is compared with the conventional single sampling plan, SkSP-2 plan and SkSP-2-R plan and proved that the proposed SkSP-2L.1-R plan outperforms these plans.KEYWORDS: Consumer quality level, average sample number, producer quality level, resampling scheme, skip-lot sampling     

Acceptance Sampling Plans from Truncated Life Tests Based on the Birnbaum–Saunders Distribution for Percentiles

Time to failure due to fatigue is one of the common quality characteristics in material engineering applications. In this article, acceptance sampling plans are developed for the Birnbaum–Saunders distribution percentiles when the life test is truncated at a pre-specified time. The minimum sample size necessary to ensure the specified life percentile is obtained under a given customer's risk. The operating characteristic values (and curves) of the sampling plans as well as the producer's risk are presented. The R package named spbsq is developed to implement the developed sampling plans. Two examples with real data sets are also given as illustration.     

Optimal designing of an SkSP-R double sampling plan

In this article, we propose a method of planning and determining the optimum parameters of a SkSP-R skip-lot sampling plan by using the attribute double sampling plan as the reference plan. The SkSP-R plan is a new type of skip-lot sampling plan which has a provision for re-inspecting the submitted lots. The optimal plan parameters of the suggested sampling plan are estimated with the target that the average sample number be minimized and satisfying both the specified producer's as well as the consumer's risks simultaneously. In order to obtain the optimum parameters, tables are also built for different combinations of the acceptable quality level and the limiting quality level in conjunctions with different producer's and consumer's risks. An illustrative example is provided for the implementation of the suggested plan. The advantages of the suggested plan over the existing conventional sampling plans and other existing skip-lot sampling plans are also described.     

Developing of a new system of skip-lot reinspection schemes

The skip-lot sampling plans are widely used in industries for quality inspection of products in order to reduce the sampling costs and inspection efforts when products have good quality history. Also, the skip-lot sampling plan concept is sound and useful and it is economically advantageous to use the skip-lot approach in the design of sampling plans. Thus, the skip-lot sampling plans are useful to minimize the cost of the inspection particularly in costly and destructive testing. Hence, a new system of skip-lot sampling plans designated as SkSP-2-R plan is developed in this article by incorporating the idea of resampling procedure in the skip-lot sampling plans of type SkSP-2. A Markov chain formulation and derivation of performance measures for this new plan are presented. The properties and advantages of the SkSP-2-R plan are studied with single sampling plan as the reference plan. The response-to-change characteristics of the SkSP-2-R plan are also investigated, based on the average run length.     

Procedure for the selection of CSP-M one level skip-lot sampling inspection plans that have a single-sampling plan with acceptance number zero as the reference plan

This paper presents a procedure for the selection of CSP-M one-level skip-lot sampling plans, designated as CSP-MSkSP, that have a single-sampling plan with acceptance number zero as the reference plan. The parameters of the plan are determined when two points on the operating characteristic curve are specified, the two points being (p1,) and (p2,), where p1 is the acceptable quality level, is the producer's risk, p2 is the limiting quality level and is the consumer's risk.     

Optimal designing of a new mixed variable lot-size chain sampling plan based on the process capability index

In this paper, a new mixed sampling plan based on the process capability index (PCI) C_pk is proposed and the resultant plan is called mixed variable lot-size chain sampling plan (ChSP). The proposed mixed plan comprises of both attribute and variables inspections. The variable lot-size sampling plan can be used for inspection of attribute quality characteristics and for the inspection of measurable quality characteristics, the variables ChSP based on PCI will be used. We have considered both symmetric and asymmetric fraction non conforming cases for the variables ChSP. Tables are developed for determining the optimal parameters of the proposed mixed plan based on two points on the operating characteristic (OC) approach. In order to construct the tables, the problem is formulated as a non linear programming where the average sample number function is considered as an objective function to be minimized and the lot acceptance probabilities at acceptable quality level and limiting quality level under the OC curve are considered as constraints. The practical implementation of the proposed mixed sampling plan is explained with an illustrative real time example. Advantages of the proposed sampling plan are also discussed in terms of comparison with other existing sampling plans.     

Economic design of quick switching sampling system for assuring Weibull distributed mean life

In this paper, we propose the quick switching sampling system for assuring mean life of a product under time truncated life test where the lifetime of the product follows the Weibull distribution and the mean life is considered as the quality of the product. The optimal parameters of the proposed system are determined using two points on the operating characteristic curve approach for various combinations of consumer's risk and ratio of true mean life time and specified life time. Tables are constructed to determine the optimal parameters for specified acceptable quality level and limiting quality level along with the corresponding probabilities of acceptance. The proposed system is compared with other existing sampling plans under Weibull lifetime model. In addition, an economical design of the proposed system is also discussed.     

Link sampling for attributes

A few lot-by-lot acceptance sampling procedures for attributes are proposed as alternatives to the usual double sampling. In these schemes whenever a second sample is needed, the sample information from neighbouring lots is used. The new plans have the DC identical to that of the comparable double sampling plan. The primary advantage of these plans is a reduction in cost due to a smaller ASN. An empirical study which investigates the effect of sudden shifts in quality level on the probability of acceptance and ARL under the proposed plans is included     

Double and group acceptance sampling plan for truncated life test based on inverse log-logistic distribution

This paper introduces a double and group acceptance sampling plans based on time truncated lifetimes when the lifetime of an item follows the inverse log-logistic (ILL) distribution with known shape parameter. The operating characteristic function and average sample number (ASN) values of the double acceptance sampling inspection plan are provided. The values of the minimum number of groups and operating characteristic function for various quality levels are obtained for a group acceptance sampling inspection plan. A comparative study between single acceptance sampling inspection plan and double acceptance sampling inspection plan is carried out in terms of sample size. One simulated example and four real-life examples are discussed to show the applicability of the proposed double and group acceptance sampling inspection plans for ILL distributed quality parameters.     

Acceptance sampling plan based on an exponentially weighted moving average statistic with the yield index for autocorrelation between polynomial profiles

Acceptance sampling plans based on process yield indices provide a proven resource for the lot-sentencing problem when the required fraction defective is very low. In this study, a new sampling plan based on the exponentially weighted moving average (EWMA) model with yield index for lot sentencing for autocorrelation between polynomial profiles is proposed. The advantage of the EWMA statistic is the accumulation of quality history from previous lots. In addition, the number of profiles required for lot sentencing is more economical than in the traditional single sampling plan. Considering the acceptable quality level (AQL) at the producer's risk and the lot tolerance percent defective (LTPD) at the consumer's risk, we proposed a new search algorithm to determine the optimal plan parameters. The plan parameters are tabulated for various combinations of the smoothing constant of the EWMA statistic, AQL, LTPD, and two risks. A comparison study and two numerical examples are provided to show the applicability of the proposed sampling 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.