Average Outgoing Quality Research Articles

A one-sided single screening procedure based on individual unit misclassification error

A procedure is proposed for screening applications in quality control that eliminates overselection (namely, the condition where the proportion of accepted screened items is greater than the proportion of conforming items in the original population) and controls for individual unit misclassification error (IME), namely, the probability of an accepted/selected item being below specification. Screening involves selecting items whose performance is within specifications based on observing one or more correlated screening variables in lieu of observing the performance variable directly. Overselection and an uncontrollably high IME can occur when (1) there is a high correlation between the performance and screening variables and (2) the proportion of conforming items among accepted items (or its complement, average outgoing quality (AOQ)), is prespecified as in, for example, Owen et al. (1975). We instead propose a procedure that prespecifies a maximum tolerable IME (emaxa) for accepted items, which eliminates...

An economic two-stage screening procedure with a prescribed outgoing quality in logistic and normal models

An economic two-stage screening procedure based on a dichotomous performance variable T and a continuous screening variable X is proposed. X is measured first to decide whether an item should be accepted, rejected, or additional observations should be taken. If no terminal decision is reached, T is then observed to classify the undecided items. Two models are considered; (i) the logistic model, where P(T = 1|X = x) is assumed to be a logistic function of x, and (ii) the normal model, where X given T is assumed to be normally distributed. A simple economic model based on inspection and misclassification costs is constructed. Optimal cutoff values on the screening variable are obtained by minimizing the expected cost subject to the constraint that the average outgoing quality attains a pre-specified level. Solutions are provided for both known-parameter and unknown-parameter cases. © 1995 John Wiley & Sons, Inc.

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.

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

Minimum AFI for CSP-2 plan under inspection error

In this paper, we present a modification of Endres's method for minimizing AFI for Continuous Sampling Plan CSP-2 plan under inspection error. The measure of average outgoing quality (AOQ) under both perfect and imperfect replacemant conditions are considered. Both CSP-1 plan and CSP-2 plan under inspection error have the same minimum AFI when the specified process average fraction detective, p , is larger than the average outgoing quality limit, AOQL. Under the same sampling cost, one can use the proposed model to minimize AFI of CSP-I plan under inspection error to replace that of CSP-2 plan under inspection error, because CSP-I plan is more convenient to execut than CSP-2 plan.

Quality Assurance of a Maker-Packer Model

We study a maker-packer production system in cigarette manufacturing where two different types of detectors are installed on the making and packing machines to maintain the product quality. The making machine detector has a continuously adjustable setting which determines the proportion of defective cigarettes removed. The packing machine detector has only discrete settings. We develop an economic model to derive the optimal settings for these detectors to achieve a specified average outgoing quality. The proposed maker-packer model is useful in other industries.

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...

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.

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.

Analysis of two stage sampling plan with imperfect inspection

Acceptance sampling plans used in a typical quality control process, are developed to provide optimal sample size(s) and acceptance (rejection) criterion. In order to apply a sampling plan, a knowledge of acceptable quality level (AQL), a lot tolerance percent defective (LTPD), and the specification of two types of errors (type I and type II) are required. The traditional methods assume that quality control inspectors, inspection tools, and computation processes are free from any errors under normal conditions. However, it has been shown that in practice inspectors, inspection tools as well as computation processes are all erroneous. These errors will have significant impact on sample size(s), decision criterion, average outgoing quality (AOQ), and the operating characteristics curve (OC Curve). The impact of imperfect inspection on AOQ, sample size(s), and OC curves for a two stage sampling plan are presented in this paper. In a two stage sampling plan, the decision to reject or accept a lot is made through two tandem stages of the inspection process. The first stage inspection is performed at the low level component, where m components constitute a single item. An acceptance decision for a single item is made based on the observed number of defects (non-conformities), while an acceptance decision of a given lot depends on the number of defective (non-conforming) items. A simulation program has been developed to investigate the sensitivity of AOQ and OC curves when one or both types of errors (type I and type II) deviate from their specified levels. The computational experiments show that inspection errors cause the discrepancies between the computed values and the specified values. The analysis of simulation results leads us to conclude that, when inspection errors are present, the traditional sampling plans without inclusion of inspection errors are misleading and incorrect.

Computerized continuous sampling plans with finite production

This paper presents two computer programs that assist the decision maker in selecting a proper continuous sampling plan (CSP). The first program calculates both the long-run and approximate short-run average outgoing quality, AOQ and AOQ∗(t), for six continuous sampling plans based on Yang's renewal-process approach. The second is an interactive constrained optimization program using utility theory to determine a feasiable economically-based continuous sampling plan.

The Design of CSP‐2 under the Conditioned Inspection Capacity

Continuous Sampling Plans (CSP) are used where processes are continuous and products are not grouped into lots. The principal design criterion for these plans is the Average Outgoing Quality Limit (AOQL), which is the worst outgoing quality over all possible values of the incoming quality level. These are generally applicable to in‐process and final inspections and have been found to be most effective when administered in such a way as to provide an incentive to clear up the faults promptly. In applying the traditional continuous sampling plans, it is necessary to revert to 100 per cent inspection when the quality deteriorates. Therefore, the inspection rate must be larger than production rate and the unit inspection cost must be low. The plan presented in this article relaxes the 100 per cent inspection restriction while reaching the same AOQL quality assurance as traditional CSP‐1. The Markov chain process and numerical analysis will be used to formulate the plan. Its results are then evaluated against CSP‐2.

Design of a Single Sampling Scheme

Presents a compact table yielding the parameters of a single sampling scheme. The table is compatible with the structure of MIL‐STD‐105D and the switching procedure incorporated in this scheme is relatively simpler than that of MIL‐STD‐105D. The basis for the construction of the table is given. Methods are given for the selection of a scheme having either acceptable quality level, limiting quality level, indifference quality level or average outgoing quality limit as a function of lot size.

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.

Sampling for quality inspection and correction: AOQL performance criteria

By definition, an Average Outgoing Quality Limit (AOQL) sampling plan leads to inspection of the whole population if the sample shows a number of defective items k exceeding an acceptance number k 0. The literature shows how this constant k 0 and other related parameters can be chosen such that the expected value of p ̃ , the fraction of defectives after inspection and possible correction, does not exceed a prespecified constant p ̃ m . This paper studies several other criteria that are ignored in the literature. It is based on an extensive Monte Carlo simulation. Its main conclusion is that AOQL sampling is useful in practice, including applications in auditing. Yet the probability that the average yearly outgoing fraction p ̃ exceeds the given constant p ̃ m can be sizable, if the original before-sampling fraction p exceeds p ̃ m ‘mildly’. The paper further investigates the effects of splitting the yearly population into subpopulations and the effects of underestimating the original fraction.

Impact of quality improvement on optimal buffer designs and productivity in automatic assembly systems

Mismatches between sampling time requirements and production cycle times have automated inspection processes and represent a substantial bottleneck in automatic assembly systems (AASs). Consequently, indirect ways must be developed to assess average outgoing quality in order not to slow the entire line down to the speed of the test process. A clear tradeoff exists between the average outgoing quality limit (AOQL) and the production rate in AASs. In this article, these tradeoffs are analyzed with particular emphasis on the new trends in moving the quality upstream into the products and processes. A simultaneous investigation of product quality and optimal buffer designs is made. Modeling and Monte Carlo optimization approaches involving discrete event simulation and stochastic quasigradient methods are used to carry out the analyses.

Probability Limits on Outgoing Quality for Continuous Sampling Plans

We investigate the performance of Dodge's continuous sampling plan 1 (CSP-1) when production run lengths are short or moderate or when the input process is not iid Bernoulli. For finite run lengths. methods are presented for computing upper and lower percentage points (probability limits) for the distributions of the outgoing quality and fraction inspected when the input process is Markov. Both rectifying and nonrectifying inspection are considered. Particular attention is paid to the special case of iid Bernoulli input. Comparisons are made with long-run maximum averages under various input process assumptions, including Dodge's average outgoing quality limit (AOQL) for the iid case, an AOQL for Markov input, and unrestricted AOQL values, These limits arc proposed as new performance measures. intended to supplement the tables in MIL-STD-1235B for use in selecting CSP-1 plans. We also discuss the problem of interval estimation of the incoming and outgoing quality from CSP-1 inspection data.

Probability Limits on Outgoing Quality for Continuous Sampling Plans

We investigate the performance of Dodge's continuous sampling plan 1 (CSP-1) when production run lengths are short or moderate or when the input process is not iid Bernoulli. For finite run lengths. methods are presented for computing upper and lower percentage points (probability limits) for the distributions of the outgoing quality and fraction inspected when the input process is Markov. Both rectifying and nonrectifying inspection are considered. Particular attention is paid to the special case of iid Bernoulli input. Comparisons are made with long-run maximum averages under various input process assumptions, including Dodge's average outgoing quality limit (AOQL) for the iid case, an AOQL for Markov input, and unrestricted AOQL values, These limits arc proposed as new performance measures. intended to supplement the tables in MIL-STD-1235B for use in selecting CSP-1 plans. We also discuss the problem of interval estimation of the incoming and outgoing quality from CSP-1 inspection data.

Single-sided economic screening models incorporating individual unit misclassification error and risk preference

Screening models are used when it is not technically, physically, or economically feasible to assess a product's conformance to specifications on a performance variable. Under these circumstances, a screening variable is used to infer the quality of a product with respect to the performance variable. Past research efforts have independently addressed the design of screening inspection plans either in terms of average outgoing quality (AOQ), economic consequences, or individual unit misclassification error (IME). A model and procedure are proposed that integrates the economic consequences associated with a screening inspection plan with the concept of IME and AOQ as a basis for selecting the parameters of an optimal inspection plan. A cost function that realistically reflects the risk preference of a decision maker (DM) to the economic consequences of an inspection plan is also proposed. A general methodology, using standardized variables, is used to efficiently derive the optimal screening inspection plan for four different cost functions. A comprehensive empirical study is used to examine the sensitivity of an optimal inspection plan with respect to different cost functions. The results show that the nature of the cost function and its parameters have a significant impact on the screening selection plan and its characteristics.

Renewal Theory Applications to Continuous Inspection of Markovian Production Processes

Theory of renewal processes has been used to study the effectiveness of three continuous sampling schemes, when the quality of the successive units in a continuous production process follows a two-state time-homogeneous Markov chain model which comprises the iid Bernoulli model considered by Dodge. The average outgoing quality and operating characteristics functions have been formulated and some numerical results have been given when the serial correlation coefficient of the Markov chain is assumed to be known a priori.