Determination of a new mixed variable lot-size multiple dependent state sampling plan based on the process capability index

This article proposes a new mixed variable lot-size multiple dependent state sampling plan in which the attribute sampling plan can be used in the first stage and the variables multiple dependent state sampling plan based on the process capability index will be used in the second stage for the inspection of measurable quality characteristics. The proposed mixed plan is developed for both symmetric and asymmetric fraction non conforming. The optimal plan parameters can be determined by considering the satisfaction levels of the producer and the consumer simultaneously at an acceptable quality level and a limiting quality level, respectively. The performance of the proposed plan over the mixed single sampling plan based on C_pk and the mixed variable lot size plan based on C_pk with respect to the average sample number is also investigated. Tables are constructed for easy selection of plan parameters for both symmetric and asymmetric fraction non conforming and real world examples are also given for the illustration and practical implementation of the proposed mixed variable lot-size plan.     

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.     

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.     

Repetitive group sampling plan based on the process capability index for the lot acceptance problem

An acceptance sampling plan is a method used to make a decision about acceptance or rejection of a product, based on adherence to a standard. Meanwhile, process capability indices (PCIs) have been applied in different manufacturing industries as capability measures based on specified criteria which include process departure from a target, process consistency, process yield and process loss. In this paper, a repetitive group sampling (RGS) plan based on PCI is introduced for variables’ inspection. First, the optimal parameters of the developed RGS plan are obtained considering constraints related to the risk of consumers and producers and also a double sampling plan, a multiple dependent state sampling plan and a sampling plan for resubmitted lots have been designed. Finally, after the development of variable sampling plans based on the Bayesian and exact approach, a comparison study has been performed between the developed RGS plan and other types of sampling plans and the results are elaborated.     

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     

Design of acceptance sampling plan using a modified EWMA statistic

In this paper, a modified exponentially weighted moving average (EWMA) statistic is proposed. The approximate distribution of the proposed modified EWMA statistic is derived. A variable acceptance sampling plan is designed using the proposed EWMA statistic. The plan parameters of the proposed sampling plan are determined such that the given producer's risk and consumer's risk are satisfied. The efficiency of the proposed plan based on the new EWMA statistic is compared with the existing EWMA plan in terms of the sample size required. The application of the proposed plan is given with the help of an example.     

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 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.     

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.     

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.     

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.     

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.     

Designing an economically optimal repetitive group-sampling plan based on loss functions

Acceptance sampling is a quality assurance tool, which provides a rule for the producer and the consumer to make acceptance or rejection decision about a lot. This paper attempts to develop a more efficient sampling plan, variables repetitive group sampling plan, based on the total loss to the producer and consumer. To design this model, two constraints are considered to satisfy the opposing priorities and requirements of the producer and the consumer by using Acceptable quality level (AQL) and Limiting quality level (LQL) points on operating characteristic (OC) curve. The objective function of this model is constructed based on the total expected loss. In order to illustrate the application of the proposed model, an example is presented. In addition, the effects of process parameters on the optimal solution and the total expected loss are studied by performing a sensitivity analysis. Finally, the efficiency of the proposed model is compared with the variables single sampling plan, the variables double sampling plan and the repetitive group sampling plan of Balamurali and Jun (2006) in terms of average sample number, total expected loss and its difference with ideal OC curve.     

Multiple dependent state repetitive sampling plans with or without auxiliary variable

In this article, a new variable acceptance sampling plan has been developed using the multiple dependent state repetitive sampling scheme for the normal distribution. The plan parameters have been determined so as to minimize the average sample number while satisfying the producer's and the consumer's risks under the operating characteristic function. The multiple dependent state repetitive sampling scheme has also been extended to the case of utilizing an auxiliary variable. The proposed sampling plans are compared with the existing sampling plans.     

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.     

Certain observations on lot sensitive sampling plan

This paper compares the sample size efficiency of the lot sensitive plan over the equivalent double and multiple sampling plans. It is shown that a fully curtailed lot sensitive plan will involve smaller average sample number than the equivalent double and multiple plans.     

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.     

Optimum reliability acceptance sampling plans under progressive type-I interval censoring with random removal using a cost model

A reliability acceptance sampling plan (RASP) is a variable sampling plan, which is used for lot sentencing based on the lifetime of the product under consideration. If a good lot is rejected then there is a loss of sales, whereas if a bad lot is accepted then the post sale cost increases and the brand image of the product is affected. Since cost is an important decision-making factor, adopting an economically optimal RASP is indispensable. This work considers the determination of an asymptotically optimum RASP under progressive type-I interval censoring scheme with random removal (PICR-I). We formulate a decision model for lot sentencing and a cost function is proposed that quantifies the losses. The cost function includes the cost of conducting the life test and warranty cost when the lot is accepted, and the cost of batch disposition when it is rejected. The asymptotically optimal RASP is obtained by minimizing the Bayes risk in a set of decision rules based on the maximum likelihood estimator of the mean lifetime of the items in the lot. For numerical illustration, we consider that lifetimes follow exponential or Weibull distributions.     

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.     

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.