Producer's Risk Research Articles

Acceptance sampling plans based on percentiles for extended generalized exponential distribution with real data application

In this paper, when the life test is truncated at a pre-determined time, new acceptance sampling plans (ASP) are developed based on percentile lifetime as a quality parameter for the extended generalized exponential distribution (EGED). An inspection of a representative sample of goods or materials from a big lot or batch is used in quality control testing under acceptance sampling plans to assess whether the lot satisfies predetermined quality requirements. For the suggested new acceptance sampling plans, the minimum sample sizes needed to emphasize the determined lifetime percentile are obtained for a given customer's risk. The sample plans' operating characteristic function values and the producer's risk are built at various quality levels for some distribution parameters. Some numerical examples are presented to show how the suggested ASP can be used. A genuine industrial data set from a top Korean automobile is fitted to the EGED relative to other competitors and the applicability of the suggested ASP is illustrated. It is found that the suggested ASP for the EGED can be applied by the researchers in production engineering fields.

Constructing Optimal Quick Switching System with Hurdle Poisson Distribution

Objectives: Optimizing the sum of risks involved in the selection of acceptance sampling plans playing a vital role. This paper uses the Hurdle Poisson distribution to design an optimal quick switching system attribute plan for a given acceptable quality level (AQL) and limiting quality level (LQL) involving a minimum sum of risks. Methods: The sum of producer's and consumer's risks has been met for the specified AQL and LQL. The sum of these risks, as well as the acceptance and rejection numbers have been calculated using the Hurdle Poisson distribution. The operating characteristic function for the quick switching system attribute plan has also been derived using the Hurdle Poisson distribution. Findings: The producer and the consumer both represent the same party in the final inspection. As a result, the sum of these two risks should be minimized. In this paper, the sum of risks for various operating ratios are tabulated using the Hurdle Poisson distribution. These tabulated values are less than the sum of risks calculated using the Weighted Poisson distribution. Novelty: Reducing the sum of risks is the ultimate aim of the work. In this proposed paper, to attain the minimum sum of risks, the authors make an attempt to approach the Quick Switching System Sampling Plan, when the number of defectives in the submitted lots are very less. In other words, the probability of getting defective is very less. This indicates the quality of the lot selected for the inspection to ensure the protection for the consumer. And the plan is also designed in the way that the producer is also not get affected by rejecting a good lot by the consumer. This is the requirement of minimizing the risks. Keywords: Acceptable Quality Level (AQL), Limiting Quality Level (LQL), Minimum Risk Plan, Quick Switching System Sampling Attribute Plan, Operating Characteristic (OC) Function, Hurdle Poisson Distribution

Acceptance Sampling Plans based on Percentiles of Exponentiated Inverse Kumaraswamy Distribution

Objectives: To prepare the percentile-based acceptance sampling plans for the Exponentiated Inverse Kumaraswamy Distribution (EIKD) at a specific truncation time to inspect the defective lots corresponding to the desired acceptance level. Methods: The failure probability value is estimated using the cumulative probability function F(.) at time ‘t’ which is converted in terms of the scale parameter σ as 100th percentile using quantile function. The minimum size of the sample, Operating Characteristic (OC) and the minimum ratios are calculated for a required levels of consumer’s as well as producer’s risk. Findings: The percentile-based sampling plans are obtained through the minimal size of the sample ‘n’ under a truncated life test with a target acceptance number c in a manner that the proportion of accepting a lot which is not good (consumer’s risk) would not be more than . These values are calculated at The function of probability of acceptance for variations in the quality of a lot (OC function) L(p) of the sample plan are evaluated for the acceptance values of c=1 and c=5. The minimum ratio values are calculated for the acceptability of the lot with producers’ risk of using the sampling plan. Novelty: The modernity of this study is the designing of the acceptance sampling plans to a non-normal data using an asymmetrical distribution that has all three shape parameters. Also, the monitor of the implementation and suitability of statistical quality control and process control aspects using Exponentiated Inverse Kumaraswamy Distribution when compared to other asymmetrical distributions which has at least one scale parameter. Keywords: Sampling plans, Consumer's risk, Operating characteristics function, Truncated life tests, Producer's risk

A variable sampling plan based on the coefficient of variation for lots resubmission

This study focuses on the issue of lots resubmission in inspection processes, which often arises when the initial inspection of a lot is suspected, marked as held, or not accepted. To address this problem, a novel variables sampling plan based on the coefficient of variation is proposed. The objective is to determine the sampling plan parameters that minimize the average sample number while satisfying the two-points of operating characteristic curve. Practical considerations are taken into account by providing tabulated values for the inspection sample size and acceptance criteria of the proposed plan. These tables incorporate various combinations of quality levels, considering commonly used producer's risk and consumer's risk. Furthermore, a comparative analysis between the proposed plan and a single sampling plan is conducted to highlight the advantages of the new approach. To illustrate the practical implementation of the proposed plan, an example is presented.

Optimal Acceptance Sampling Testing Plan With Pivotal Quantity for Log-Location-Scale Distributions

Global market competition has led to manufacturers encountering a decision problem as the reliability of their products exceeds a given standard. Acceptance sampling tests (ASTs) can be expensive and time-consuming, especially for products with high reliability or quality. Thus, careful planning of the acceptance rule and determination of a suitable sample size for the test are important. In this article, an exact method for the optimal planning of ASTs is proposed for cases in which the product lifetimes follow a distribution in the general log-location-scale family of distributions. A novel procedure using the pivotal quantity is established based on the method-of-moments estimators of the model parameters, and the distribution of the reliability estimator is derived. An algorithm for obtaining the optimal sample size and the corresponding acceptability constant is presented in which the producer's and consumer's risks are constrained according to certain acceptance criteria. We apply the proposed method to a censored AST by generating censored observations with a quantile-filling method under Type-II censoring. The performance of the proposed AST with a complete or censored sample is studied and compared with an AST based on the maximum likelihood method. The robustness of the proposed AST is also examined under model misspecification. The results show that the proposed AST performs well under different scenarios.

Barter operations: a multivariate analysis of its use by soybean producers from the state of Minas Gerais

Brazil is the second largest producer of soybeans in the world, in which, in addition to boosting other food industries dependent on this oilseed, it promotes agricultural production in development and technification. The state of Minas Gerais is the seventh largest soybean producing in Brazil and it is responsible for approximately 5% of the total processing of this grain. However, this agricultural activity still lives with risks associated with the production. One of the most important tools for the producer's risk management is the barter, configured as an operation that allows the producer to exchange his future production for inputs, being able to freeze his prices and amortize these values with a fixed volume of production. Although this tool is useful in risk management, there is little information about the knowledge of producers related to this tool and its benefits and possibilities in risk management. In this sense, the present study sought to analyze factors that influence soybean producers in Minas Gerais with regard to barter as a risk management and fundraising tool, based on the application of a questionnaire structured around the variables and specificities of producers in the state. The results obtained show that soybean producers in Minas Gerais, for the most part, do not have a detailed knowledge of the tool and, mainly for this reason, they are afraid of its realization.

Designing two mixed quick switching sampling plans for linear profiles

AbstractThis study compares two proposed mixed quick switching sampling (QSS) plans for linear profiles as the quality characteristic. For the QSS plans, we recommend a binomial attribute plan for normal inspection and then a variable sampling plan for tightened inspection based on capability index CpuA of linear profiles with one‐sided specifications. The difference between the two proposed QSS plans is in the tightened inspection. Tightened inspection of the first proposed plan is a single sampling using CpuA index, but tightened inspection of the second plan is a multiple dependent state repetitive (MDSR) plan based on CpuA index. The optimal parameters are obtained by nonlinear optimization. Simulation study for selecting parameters is conducted with various combinations of specified acceptable quality level (AQL), limited quality level (LQL), producer's risk, and consumer's risk. Simulation results confirm that the second proposed QSS plan which applies variable MDSR at tightened inspection performs better than another proposed plan. Hence, the approach of the second proposed plan is demonstrated in an illustrative example.

Metrics Related to Confusion Matrix as Tools for Conformity Assessment Decisions

Conformity assessment refers to activities undertaken to check whether some product, service or process meets certain criteria and specifications given by internationally accepted standards. The decision on whether a property of interest is aligned with the set standards is made based on measurement. However, uncertainty associated with the measurement results may lead to incorrect decisions. Measurement results may be falsely rejected as non-conforming, although they meet specifications. This is referred to as the producer’s risk. If the measurement result that does not meet the required specifications is accepted as conforming, this is referred to as the consumer’s risk. This paper covers calculations of global consumer's and producer's risk using the Bayesian approach and deals with the application of metrics related to confusion matrices in conformity assessments. These techniques have been used to assess the conformity of the bearing ring diameter with the given specifications. Based on the behavior of these metrics, the optimal length of the guard band was determined with the aim of minimizing the global consumer’s and producer’s risk.

Single Acceptance Sampling Plan Based on Truncated Life Tests for Zubair-Exponential Distribution

In this paper, a single acceptance sampling plan based on a truncated life test is proposed for a lifetime that follows the Zubair-Exponential (ZE) distribution. For some acceptance numbers, confidence levels, values of the ratio of the fixed experiment time to the particular mean lifetime, and the minimum sample sizes required to assert the specified mean life are obtained. The operating characteristic function values of the proposed sampling plans, consumer's and the producer's risk are presented. Other useful tables are presented and the results are discussed.

Zeghdοudi distribution in acceptance sampling plans based on truncated life tests with real data application

The acceptance sampling plan (ASP) is one of the key statistics resources in the industrial sector. It entails the decision-making process for accepting or rejecting the products. The investigated quality parameter is the test unit's mean lifespan. This study develops a new ASP for Zeghdοudi distribution (ZD) when the lifetime is shortened to a specific degree. The optimal plan parameters are accomplished by obtaining the minimum sample size mandatory to ensure the identified mean lifetime for fixing the consumer's risk. Besides, the characteristic operating function (OCF) values for the ASP are displayed, and the producer's risk is determined. Several helpful tables are developed for the suggested ASP based on the ZD for suitable employment. An actual data set is fitted to the Zeghdoudi model and other models to examine the applicability of the suggested ASP in the production sector.

Designing Bayesian new two‐sided group chain sampling plan for quality regions based on beta prior

AbstractAcceptance sampling is used to determine whether to accept or reject the lot that is being inspected. The Bayesian strategy is the ideal method to use when historical data about the product is available in order to make decision. To estimate quality regions, we suggest a Bayesian new two‐sided group chain sampling plan in this study. The operating characteristic function is developed using the binomial distribution, and average probability of acceptance is estimated using beta distribution as prior. Four quality regions are estimated for certain predetermined values of producer's and consumer's risks. Producer's risk and consumer's risk are correlated with acceptable quality level and limiting quality level of quality regions, respectively. For the proposed plan, inflection point values are estimated based on various combinations of design parameters. Operating characteristic curves are use up to compare the current Bayesian group chain sampling plan (BGChSP) with the effects of changing the values of specified parameter values. The suggested plan is a well replacement for current industry plans, according to the operating characteristic curve's findings.

Optimal design of reliability acceptance sampling plan based on constant‐stress accelerated life testing considering the uncertainty of accelerated factor

AbstractWith the increasing marketplace demand for decreasing test time and cost, constant‐stress accelerated life testing (CSALT) is widely used for reliability demonstration in practice. The existing accelerated acceptance sampling plans (AASPs) do not consider the uncertainty of accelerated factor (AF), which makes it difficult to accurately describe the producer's and consumer's risks. Previous AASP studies on CSALT were mainly carried out under a fixed accelerated stress level, and the influence of accelerated stress level is not concerned. Therefore, considering the uncertainty of AF and taking the lognormal distribution as an example, the AASP design method with time‐censoring is proposed, where the life‐stress relationship between the location parameter and stress level is expressed by an inverse power law model. First, considering the uncertainty of AF expressed by a distribution, the acceptance probability can be obtained by the mathematic expectation of conditional acceptance probability, and the producer's and consumer's risks can be accurately expressed. Then, to reduce the total cost furtherly, the accelerated stress level is considered as a new decision variable, the optimum AASP including the sampling plan and the decision‐making criterion can be designed by minimizing the total cost and solving the risk constraint equations of both sides. A real case study of white organic light‐emitting diodes is carried out to verify the effectiveness of the proposed method.

A group acceptance sampling plan for ‘Another Generalized Transmuted‐Exponential Distribution’ based on truncated lifetimes

AbstractThe present paper focuses on the group acceptance sampling plan when the characteristic of interest follows Another Generalized Transmuted‐Exponential distribution. The probability of acceptance is calculated using mean life as a quality parameter for obtaining design parameters such as sample size ‘n’ and acceptance number ‘c’. The values of the operating characteristic function are determined for different quality levels. The plan satisfies both the producer's and consumer's risks at specified quality levels. Relevant r codes using Monte Carlo simulation are appended for use by academia and practitioners. The simulated results of the study are exhibited in the form of tables and explained with relevant examples. Results of the proposed plan are compared with the results generated using maximum likelihood estimates of Another Generalized Transmuted‐Exponential distribution. Easy to follow methodology of the current paper will open new vistas for applying the technique of group acceptance sampling plan to a variety of transmuted probability distributions. For illustration purposes, real data set is also analyzed to show the implementation of the proposed sampling plan.

Amputated Life Testing for Weibull-Fréchet Percentiles: Single, Double and Multiple Group Sampling Inspection Plans with Applications

When a life test is terminated at a predetermined time to decide whether to accept or refuse the submitted batches, the types of group sampling inspection plans (single, two, and multiple-stages) are introduced. The tables in this study give the optimal number of groups for various confidence levels, examination limits, and values of the ratio of the determined experiment time to the fixed percentile life. At various quality levels, the operating characteristic functions and accompanying producer's risk are derived for various types of group sampling inspection plans. At the determined producer's risk, the optimal ratios of real percentile life to a fixed percentile life are obtained. Three case studies are provided to illustrate the processes described here. Comparisons of single-stage and iterative group sampling plans are introduced. The first, second, and third sample minimums must be used to guarantee that the product's stipulated mean and median lifetimes are reached at a certain degree of customer trust. The suggested sample plans' operational characteristic values and the producer's risk are given. In order to show how the suggested approaches based on the mean life span and median life span of the product may function in reality, certain real-world examples are examined.

Optimum degradation test sampling plan for the Wiener process

AbstractIn this paper, we propose degradation test sampling plans (DTSPs) used to determine the acceptability of a product in a Wiener process model. A test statistic and the acceptance criterion based on Wiener process parameter estimates are proposed. The design of a degradation test is investigated using a model incorporating test cost constraint to minimize the asymptotic variance of the proposed test statistic. Some important variables, including the sample size, measurement frequency, and the total test time, are chosen as decision variables in a degradation test plan. The asymptotic variance of the test statistic and the approximate functional forms of the optimal solutions are derived. A search algorithm is also represented in a flow chart for the purpose of finding the optimal DTSPs. In addition, we assess the minimum cost requirement for the result of the test procedure to satisfy the minimum requirements for the producer's risk and the consumer's risk. When the given test budget is not large enough, we suggest some methods to find appropriate solutions. Finally, a numerical example is used to illustrate the proposed methodology. Optimum DTSPs are obtained and tabulated for some combinations of commonly used producer and consumer risk requirements. A sensitivity analysis is also conducted to investigate the sensitivity of the obtained DTSPs to the cost parameters used.

Conformity assessment of medicines containing antibiotics – A multivariate assessment

Pharmaceutical products must meet quality requirements to ensure the efficacy and safety of pharmacological treatment. Non-compliance of medicines can cause economic losses and compromise the patient's health. In this work, the risks of false compliance/non-compliance decisions for parenteral antibiotics (cephalothin, ciprofloxacin and metronidazole) were evaluated on the basis of analytical results, measurement uncertainties and specification limits. Physicochemical and biological quality assays were performed according to pharmacopeial procedures. Measurement uncertainties were determined using the bottom-up approach or the probability of false-positive/false-negative results. The risks of false compliance/non-compliance decisions were estimated using the frequentist approach and Monte Carlo simulations. Guard-bands were determined through a validated spreadsheet for calculating univariate and multivariate acceptance limits. All risk values (particular risks and total risk, consumer's or producer's risk) were below the maximum permissible risk value. The univariate and multivariate guard-bands defined more restrictive specification values, reducing the risks of false compliance/non-compliance decisions. One antibiotic presented unsatisfactory results regarding the drug content and was classified as out of specification product. The application of risk management tools in the pharmaceutical area contributes to improving the quality and safety of products and supports decision-making.

Optimal design of multiple dependent state repetitive group sampling plan for Inverse Power Lomax distribution

A sampling plan named as Multiple Dependent State Repetitive Group Sampling (MDSRGS) plan is introduced for a time-truncated life test given that the underlying distribution of the product's lifetime is Inverse Power Lomax distribution (IPLD). The proposed sampling plan is developed with the help of two already developed sampling plans (MDS and RGS). The two-point approach OC function known as the producer's risk and customer's risk is used to determine the parameters of the proposed plan. An optimization method is used for different values of customer's risk and producer's risk, for static values of experiment termination ratio and mean ratio, to find out plan parameters (minimum size of the sample, the number of acceptance and rejection, and the number of successive lots). Tables are created for different known values of shape parameters of Inverse Power Lomax distribution. The efficiency of the proposed MDSRGS plan is examined by conducting a comparative study. To accompany the results, graphs are also used for visualizing the average sample and acceptance probabilities with the specific mean ratio. Two real-life applications are also incorporated to demonstrate the operating procedure of the proposed plan.

Generalized Family of Group Chain Sampling Plans Using Minimum Angle Method (MAM)

This research develops a generalized family of group chain sampling plans using the minimum angle method (MAM). The MAM is a method whereby both the producer's and consumer's risks are considered when designing the sampling plans. There are three sampling plans nested under the family of group chain acceptance sampling which are group chain sampling plans (GChSP-1), new two-sided group chain sampling plans (NTSGChSP-1), and two-sided group chain sampling plans (TSGChSP-1). The methodology applied is random values of the fraction defectives for both producer and consumer, and the optimal number of groups, <img src=image/13492016_1.gif> is obtained using the Scilab software. The findings reveal that some of the design parameters manage to obtain the <img src=image/13492016_1.gif> corresponding to the smallest angle, <img src=image/13492016_2.gif> and some of the values fail to get the <img src=image/13492016_1.gif>. The <img src=image/13492016_1.gif> obtained in this research guarantees that the producer and the consumer are protected at most 10% from having defective items.

A repetitive group sampling plan based on the lifetime performance index under gamma distribution

AbstractAs technology and living standards improve, people are becoming more concerned with the importance of quality. Quality, thus, becomes the key to company competitiveness, and process capability indices (PCIs) are effective means of measuring process performance. Most PCIs have been developed under the assumption that the quality characteristics are normally distributed; however, the lifetime of products generally possesses a non‐normal distribution. A lifetime performance index (LPI) CL has been proposed and used for measuring product lifetime performance. In this high‐quality era, the use of traditional testing methods incurs very high costs, so acceptance sampling plans have been widely used by industry to perform the inspection. This study considers the product lifetime with a gamma distribution and uses the uniformly minimum‐variance unbiased estimator (UMVUE) of the LPI to develop a repetitive group sampling plan (RGSP). For the practical purpose, this study presents a step‐by‐step procedure and tabulates the plan parameters for various combinations of acceptable and rejectable quality levels, producer's and consumer's risks, and shape parameter. Thus, practitioners can easily know the sample size and the corresponding critical values for decision making. This study also uses the results of the proposed plan to compare with the single sampling plan. Lastly, a practical example is used to illustrate how to apply this acceptance sampling plan.

Single acceptance sampling plans based on truncated lifetime tests for two-parameter Xgamma distribution with real data application.

Recently, the two-parameter Xgamma distribution (TPXGD) is suggested as a new lifetime distribution for modeling some real data. The TPXGD is investigated in different areas and generalized to other forms by many of the researchers. The acceptance sampling plans are one of the main important statistical tools in production and engineering fields. In this paper, modified acceptance sampling plans for the TPXGD are proposed with the assumption that the lifetime is truncated at a predetermined level. The mean of the TPXGD model is utilized as a quality parameter. The variables of the acceptance sampling plans including the acceptance numbers, the minimum sample sizes, operating characteristic function and the producer's risk are investigated for various values of the model parameters. Numerical examples are offered to illustrate the process of the proposed plans. Also, a real data is fitted to the TPXGD and an application based on the suggested acceptance sampling plans is considered for explanation.