Risk Aversion in Decision Models

In this dissertation an on-line interactive system for generating and analyzing various acceptance sampling plans is presented. This real-time sampling plan system utilizes a series of algorithms to perform the necessary functions for generating information pertinent to single, double, and multiple sampling plans. These algorithms along with other special programming considerations allow for fast generation of the following information relative to single, double, and multiple sampling plans: (1) the operating characteristic (OC) curve, (2) the average outgoing quality (AOQ) curve, (3) the average sample number (ASN) curve, (4) the average total inspection (ATI) curve, (5) multiple plots per graph, (6) the sample size(s), (7) the acceptance number(s), (8) the rejection number(s), (9) the average outgoing quality number (AOQL), (10) the lot size, (11) the lot quality (p' 95' p' 50' p' 10), and (12) the alpha and bet&adot value&sdot for a specified AQL and LPTD. This information for single, double, and multiple sampling plans can be generated by using either the Poisson, binomial, or hypergeometric distribution. Two procedures are available to the user for generating information pertinent to a particular sampling plan. The first procedure enables the user to generate single, double, and multiple sampling plans given the acceptance quality level (AQL) and the lot tolerance percent defective (LTPD). This procedure allows for the generation of two types of sampling plans: one plan minimizes consumers' risk and the other plan minimizes producers' risk. The second procedure permits the user to specify the sample size(s), the acceptance number(s), the rejection numbers (in case of multiple sampling plans), the lot size, and the percent defective used to scale the x-axis. The system is designed for use by a person with various backgrounds in programming or statistical quality control. Several examples of its use are given to illustrate one or more important points. The sampling plan system was found to be an acceptable means of generating and analyzing various sampling plans on a real-time basis.

This paper presents procedures and tables for the selection of conditional sampling plans, viz. conditional double sampling plan, chain-deferred sampling plan, link sampling plan, and ChSP-4A chain sampling plan for given acceptable quality level (AQL), producer's risk, limiting quality level and consumer's risk giving minimum sample size at AQL under the conditions of the Poisson model for the operating characteristic curve.

Coal serves as a critical energy source for power generation and industrial operations, the demand for coal is rising, yet production levels are declining. In statistical quality control a statistical procedure can play a crucial role in boosting production efficiency and output. Techniques such as proximate and ultimate analysis, calorific value assessments, and ash fusion testing are employed to evaluate coal’s composition and performance. Effective quality control techniques not only maximizes energy output but also reduces environmental impact and operational complications. This article introduces a stochastic approach to designing acceptance sampling techniques, aimed at enhancing the optimization of the Markov method for classifying conforming and non-conforming items. A Bayesian single sampling plan includes a defined sample size, an acceptance number, and a decision rule based on lower and upper thresholds, ensuring compliance with both buyer and vendor specifications for lot acceptance. The design methodology is developed using a Markov model to create a single sampling plan under Gamma-Poisson conditions. The sampling plan’s performance is evaluated using Acceptable Quality Level (AQL) and Limiting Quality Level (LQL), optimizing thresholds through the minimum angle method. The practical applicability of this sampling plan is demonstrated through numerical examples within a coal manufacturing environment.

This paper suggests a novel method for acceptance sampling that integrates fuzzy logic with the negative binomial distribution. In quality control and reliability assessment, acceptance sampling plans play a crucial role in decision-making under uncertainty. Traditional sampling plans often rely on precise information and fixed parameters, which may not reflect real-world vagueness and imprecision. This paper introduces a Fuzzy Acceptance Sampling Plan (FASP) based on the Negative Binomial Distribution (NBD), providing a more flexible and realistic framework for dealing with over-dispersed count data and uncertainty in quality inspection. By incorporating fuzzy set theory, key parameters such as the acceptance number, lot quality, and inspection risks are modeled as fuzzy numbers. The plan allows for soft decision boundaries, enhancing the responsiveness to varying production conditions. Analytical expressions for the operating characteristic (OC) function, the average sample number (ASN) and average outgoing quality (AOQ) are derived in the fuzzy environment using membership functions. Numerical examples illustrate the application and advantages of the proposed plan over classical approaches, particularly in handling uncertain or imprecise inspection data. The proposed FASP-NBD model is especially useful in industries where defective items occur in clusters, and precise parameter estimation is difficult.

: A prediction-interval approach and an assumption of a Gaussian manufacturing process are used to derive a variables sampling plan applicable to finite lots required to be of very high quality. Values tabulated for calculating acceptance regions are such that, with high probability, accepted lots will have zero defects. Further, tables are given for selecting sample size for a specified combination of lot size and acceptable quality level. Comparisons show that, for a fixed risk level, substantial savings in required sample size can be effected over those specified by comparable hypergeometric sampling plans. Lots ranging in size from 5 to 100 are considered. Bounds for the probability of accepting a lot with a fixed number of defects and coming from a prescribed manufacturing process are derived and prove to be very tight. Not only are these bounds useful in defining the required sample size in the sampling plan context, but the method of derivation has application to other areas of sampling, e.g. from truncated or stratified distributions.

Acceptance sampling plan is a product control technique, which plays a vital role in industries to inspect the quality of the raw materials processing at various stages of manufacturing and finished products at the specified quality levels. Various methods are used for monitoring and maintaining the quality of the products and services. Using acceptance sampling techniques, the quality of the products and services are decided, whether to accept or reject the finished product. In this situation the interest is to keep away from wrong selections, which is accepting the product of bad quality and rejecting the product of good quality. Accordingly, the usual objective in these cases is to use the overall risk of a wrong decision as optimization criteria. This situation is called as Minimum Risks Sampling Plan. In this paper, Hurdle Poisson distribution has been used to select the parameters of Repetitive Group Sampling Attribute Plan involving minimum sum of producer’s and consumer’s risks for specified Acceptable Quality Level and Limiting Quality Level.

Double sampling plans are generally superior to corresponding single sampling plans from an economic standpoint. That is because the double sampling plans can give an early decision at the first stage whenever lot quality is extremely good or bad. Further, because this method has five parameters (n 1, n 2, c 1, c 2, c 3), double sampling plans can be developed to accord well with required characteristics of the inspection method (e.g. AOQL, producer's and consumer's risks). Double sampling attribute plan in MIL-STD 105D[6] adopt some convenient constraints for selecting parameters, for example n 1 = n 2 or 2n 2, and c 2=c 3. Design procedures for single sampling attribute plans with given producer's and consumer's risks have been extensively investigated by, among others, PEACH & LITTAURE[9] and HALD [3] [4]. On the other hand, design procedures for double sampling attribute plans with given two risks are not well developed, for it is difficult to determine n 1 and n 2 such that both actual risks close to the specified risks. In this paper, we define two functions λ1 and λ2 with respect to n 1 and n 2, and follow a path that preserves both risks. This is done by describing the changes of λ1 and λ2 with respect to the discrimination ratio (r ≅ p 2/p 1) using a system of differential equations which includes the corresponding single sampling plan as an initial state. Sample sizes (n 1, n 2) of double sampling plans with given acceptance numbers are obtained as numerical solutions of simultaneous differential equations. These double sampling plans have producer's and consumer's risks that are almost equal to the specified risks.

Most sampling activity is concerned with the Acceptable Quality Level (AQL) or Producers' Risk. There exists, however, applications for sampling schemes built around the Limiting Quality Level (LQ) or Consumers’ Risk. Examples include isolated lots or cases where the characteristic being examined in the sample is so severe that extra care must be taken to prevent nonconformances being shipped or used. When the output of nonconformances must be zero or measured in parts per million, a sampling scheme with low consumers’ risk can be effectively used to audit a process. It can be argued that this is a form of process control because rejection of a lot under this scheme is an indication of major problems. In such cases, diagnosis and corrective action are required immediately, in addition to the usual screening of the rejected lot and those immediately preceding it. This paper provides such a sampling scheme. The determining parameter is the average outgoing quality limit (AOQL). LQ's from 0.001 to 0.05 are used. Because of the universal application and popularity of MIL-STD-105D and the ANSI Standard Z1.4 (Ref.), their format and procedure have been followed wherever possible.

Since the first acceptance sampling plans have been developed 80 years ago, a number of selection principles have emerged. The majority of these principles are characterized by the fact that they look upon producer and consumer as two opposing parties. However, in many occasions, e.g., in final inspection, producer and consumer represent the same party and, therefore, the used sampling plan should not make an attempt to discriminate between their interests. In this case the interest is to avoid wrong decisions, i.e., reject product of sufficient quality and accept product of insufficient quality. Thus, the natural objective in these cases is to use overall risk for a wrong decision as optimization criteria. In this paper, a table and procedure are given for finding the Modified Quick Switching Systems QSS − m(n;CN, CT) involving minimum sum of producer's and consumer's risks for specified Acceptable Quality Level and Limiting Quality Level using weighted Poisson distribution.

Although regulatory bodies have standards that manufacturers of rapid diagnostic tests (RDTs) must meet for market approval, RDTs have no specific sampling and testing standards to monitor ongoing lot production, unlike pharmaceuticals and certain devices. With the importance of accurate diagnosis for improved health outcomes, independent quality assurance testing is key to ensuring the availability of high-quality RDTs, particularly in low-resource settings. This work develops an approach for HIV RDT lot testing, involving qualification of specimens to enable testing across various RDTs (namely Determine HIV-1/2, OraQuick HIV-1/2, Bioline HIV-1/2 3.0, UniGold HIV, and HIV Ag/Ab Combo). A sampling plan and acceptance criteria were developed per lot (approximating sensitivity and specificity) based on ISO 2859–1: 1999, using the test line response to a qualified panel (disease-positive and negative specimens) as the attribute. Based on general performance of HIV RDTs, an average % defective tests allowed per lot (acceptance quality limit) of 0.65% within ISO 2859–1: 1999 was selected, where RDTs are tested with 80 positives (accept 1 / reject 2 defective results) and 80 negatives (accept 1 / reject 2 defective results) per lot. Panel qualification was conducted with 83 positive and 84 negative serum specimens to select specimens that consistently provided expected results when tested in quadruplicate with three lots per product. While all products yielded consistent results with at least 80 negative specimens, only 4 products did the same for positive specimens. With this approach, each of these 4 RDT products can be tested with the qualified 80-positive specimen panel, requiring the other product to be tested with 20 specimens in quadruplicate. Additionally, this approach was adapted to evaluate HIV antibody/antigen combination tests with Ag panel qualification using p24 samples. While panels were qualified to monitor ongoing lot consistency of HIV RDTs, this approach could be mimicked with other types of diagnostics for monitoring manufacturing consistency, field investigation, small-scale stability checks, and proficiency testing.

In this study, a variable acceptance sampling plan (ASP) based on best linear unbiased estimator (BLUE) in successive sampling (SS) approach was designed. It was assumed that the underlying characteristic of interest follows normal distribution over the two succeeding occasions. The design of the proposed plan was presented for known and unknown sigma of normal distribution. The plan parameters were determined by using optimization approach for both situations, such that the provided consumer's and producer's risks are satisfied for the assigned values of acceptable quality level (AQL) and the limiting quality level (LQL). The efficiency of the proposed chart over the existing chart was discussed. The proposed plan was more efficient than the existing plan in terms of sample size. Industrial data were used for the application of the proposed sampling plan.

THE MAJOR OBJECTIVE of this study was an effort to develop a foreign dividend decision model that could supplant arbitrary and rule of thumb foreign dividend decision rules with a rational decision model that applies the theory of financial management to the financial decision problems of the multinational corporate system. To accomplish this purpose, a linear resource allocation model was developed. The model is demonstrated in two steps: (1) the uni-subsidiary case and (2) the multisubsidiary case. The uni-subsidiary case describes a corporate system that consists of only one foreign subsidiary and one domestic parent corporation and sets the stage for the subsequent broadening of the model to the more realistic multi-subsidiary and multi-national case. The decision models seek to determine the key decision variables that affect the efficiency of the allocation of foreign generated funds among the alternative uses: foreign dividend remittances to the domestic parent company and foreign investment of these funds in the host country environment. Specifically, the models seek to measure the comparative returns on the available decision alternatives, given a number of internal (corporate policy determined) and external (environmentally determined) constraints. The decision problem thus involves the adjusting of normal returns that may be expected from available decision alternatives for the impact of such factors as foreign and United States taxation of foreign earnings and dividends, and the risks and uncertainties that prevail in the foreign environment. The key foreign host country uncertainties which have been dealt with explicitly in the models are inflation, host currency devaluation, and political risks to which the foreign properties of a multinational corporate system may be exposed. By giving explicit recognition not only to the key decision variables of foreign funds allocation decisions, but also to changes in these variables over time, the models may serve a useful purpose in providing a framework for the actual process of corporate financial decision making under conditions of uncertainty and rapidly changing foreign and domestic environments. One of the uses of the models-possibly in a computerized form-may be the ex post analysis of foreign dividend and foreign funds allocation decisions in order to compare and evaluate actual decisions with those that may have been indicated by the use of the optimizing procedures implicit in the models. Repeated application of the decision models to ex post and ex ante decision situations, as well as the ability of managers to test various decision alternatives by varying input assumptions and parameter estimates in a systematic way, may lead to the development of a decision tool for managers that can simulate financial resource allocation decisions of the type demonstrated in this paper, before the actual decisions must be made. The value of the model lies in its explicit identification of some of the more important foreign dividend variables; in the attempt to measure and adjust investment

A table and a procedure are given for finding the multiple deferred (dependent) state sampling plans of type MDS-(c1, c2) involving minimum sum of producer's and consumer's risks for specified acceptable quality level and limiting quality level.

This chapter addresses the issue of quality assurance for the incoming materials and the role of purchasing in preventing quality problems to crop up. Communicating specifications unambiguously and completely at the time of placing orders and choosing a vendor who has the requisite process capability to supply quality as per those specifications are the preventive strategies in quality assurance of incoming materials. Design of an optimal inspection policy to get the requisite quality protection against defectives being accepted as good with the minimum inspection cost should be the objective of incoming materials quality assurance program. Acceptance sampling plans, OC curve, AQL, and LTPD are described. In double sampling plans, the decision to accept or reject the lot can be taken after the first sample if the lot quality is very good or very bad, respectively. However, in doubtful cases, a second sample is taken, and based on combined inspection outcomes of the two samples, a decision to either accept or reject the lot is taken.KeywordsQuality assuranceVendorProcess capabilitySpecificationsOptimal inspection policySampling plansOC curveAQLLTPDDouble sampling

The results of a long-term, comprehensive CT quality control (QC) program were analyzed to investigate differences in failure rates based on QC test, scanner utilization pattern, and number of channels, as well as explore issues regarding testing frequency. CT QC data were collected over a 4-yr period for 26 CT scanners representing two different vendors and using three different QC programs culminating in over 100 scanner-years of QC data. QC tests analyzed included water tests [mean CT number, standard deviation, and uniformity], linearity tests [air, water, and acrylic], and artifact analysis [water phantom and large phantom]. The data were organized based on scanner use, number of channels, scanner modality, and QC test. Logistic regression model analysis with generalized estimating equation method was used to estimate failure rates for each group. A significant difference between failure rates with respect to QC test was found (p-value = 0.02). Large phantom artifacts, standard deviation of water, and water phantom artifacts had the three highest failure rates. No significant difference was found between failure rates organized by scanner use, scanner modality, or number of channels. Standard deviation of water is the most important quantitative value to collect as part of a daily QC program. Uniformity and linearity tests have relatively low failure rates and, therefore, may not require daily verification. While its failure rates were moderate, daily artifact analysis is suggested due to its potentially high impact on clinical image quality. Weekly or monthly large phantom artifact analysis is encouraged for those sites possessing an appropriate phantom.