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     

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.     

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.     

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.     

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.     

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.     

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.     

Designing of a mixed-chain sampling plan based on the process capability index with chain sampling as the attributes plan

In this article, we propose a new mixed chain sampling plan based on the process capability index C_pk, where the quality characteristic of interest having double specification limits and follows the normal distribution with unknown mean and variance. In the proposed mixed plan, the chain sampling inspection plan is used for the inspection of attribute quality characteristics. The advantages of this proposed mixed sampling plan are also discussed. Tables are constructed to determine the optimal parameters for practical applications by formulating the problem as a non linear programming in which 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. The practical application of the proposed mixed sampling plan is explained with an illustrative example. Comparison of the proposed sampling plan is also made with other existing sampling plans.     

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.     

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.     

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.     

Designing Variables Sampling Plans with Process Loss Consideration

For the implementation of an acceptance sampling plan, a problem the quality practitioners have to deal with is the determination of the critical acceptance values and inspection sample sizes that provide the desired levels of protection to both vendors and buyers. Traditionally, most acceptance sampling plans focus on the percentage of defective products instead of considering the process loss, which doesn't distinguish among the products that fall within the specification limits. However, the quality between products that fall within the specification limits may be very different. So how to design an acceptance sampling plan with process loss consideration is necessary. In this article, a variables sampling plan based on L _e is proposed to handle processes requiring low process loss. The required sample sizes n and the critical acceptance value c with various combination of acceptance quality level are tabulated. The proposed sampling plan provides a feasible policy, which can be applied to products requiring low process loss where classical sampling plans cannot be applied.     

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.     

A Design of Attributes Double Sampling Plans for Three-class Products

In this article, a new attributes double sampling plan for three-class products (ADSPTP) is presented, and the corresponding operating characteristic function is constructed based on the given procedure of performing ADSPTP. Average sample numbers (ASN) for complete inspection and curtailed inspection of the second sample are derived and the extreme point is discussed on the three-dimensional ASN surface. In addition, the differences arising from different parameters are studied. Sampling plans are designed by a nonlinear optimization model. Finally, numerical examples and discussions are given to illustrate the obtained results, and tables of the designed plans under various conditions are provided.     

A mixed double sampling plan based on Cpk

Abstract

Acceptance sampling plans are quality tools for the manufacturer and the customer. The ultimate result of reduction of nonconforming items will increase the profit of the manufacturer and enhance the satisfaction of the consumer. In this article, a mixed double sampling plan is proposed in which the attribute double sampling inspection is used in the first stage and a variables sampling plan based on the process capability index C_pk is used in the second stage. The optimal parameters are determined so that the producer’s and the consumer’s risks are to be satisfied with minimum average sample number. The optimal parameters of the proposed plan are estimated using different plan settings using two points on the operating characteristic curve approach. In designing the proposed mixed double sampling plan, we consider the symmetric and asymmetric nonconforming cases under variables inspection. The efficiency of the proposed plan is discussed and compared with the existing sampling plans. Tables are constructed for easy selection of the optimal plan parameters and an industrial example is also included for implementation of the proposed plan.     

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.     

Exponentially weighted moving average control schemes with variable sampling intervals

The idea of using non-constant sampling intervals has been of interest in quality control applications since it was first suggested for the “skip-lot sampling plan” of Dodge. Recent interest has focused on the use of variable sampling interval (VSI) control schemes. VSI control schemes use a short sampling interval is given     

Repetitive group sampling procedure for variables inspection

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.     

Economic design of quick switching sampling system for resubmitted lots

This paper proposes a quick switching sampling system for the inspection of attributes quality characteristics for resubmitted lots. The optimal parameters for both fraction non conforming items and fraction non conformities of the proposed sampling system are determined using an optimization procedure so that producer’s risk and consumer’s risk are simultaneously satisfied. Tables are also constructed for the selection of parameters for specified AQL and LQL. The advantage of the proposed plan over the existing plan is discussed and illustrate. An economic design of the proposed sampling system is also discussed and shown that the proposed sampling system has minimum total cost and average total inspection compared to other existing sampling plans.