Reliability Acceptance Sampling Plan Research Articles

Integrating order statistics in reliability acceptance sampling plans for a compound distribution: a case study

Integrating order statistics in reliability acceptance sampling plans for a compound distribution: a case study

Performance evaluation study of reliability acceptance sampling plans based on compound exponential-geometric distribution

Performance evaluation study of reliability acceptance sampling plans based on compound exponential-geometric distribution

Two-stage group reliability acceptance sampling plan for Lindley distribution

Two-stage group reliability acceptance sampling plan for Lindley distribution

Bayesian reliability acceptance sampling plans under interval censoring

. This work considers Bayesian reliability acceptance sampling plan (RASP) under interval censoring. It is considered that the consumer and manufacturer agree on a common lifetime distribution of the product. However, they differ in their assessment of the prior distributions and utility functions because of the adversarial nature of the consumer and manufacturer, but the manufacturer knows the consumer’s utility and prior. The consumer accepts or rejects a lot of products based on his/her own priors about the quality of the product and a utility function. If the consumer rejects the lot, the manufacturer gives additional information on lifetime based on a life test to update the consumer’s belief. The consumer decides on accepting or rejecting the lot based on updated information. The life test is conducted under an interval censoring scheme, where the decision on acceptance or rejection of the lot can be taken sequentially at pre-specified inspection times. The manufacturer’s task is to determine the optimal interval-censoring life testing plan which maximizes his/her utility. Last, we discuss a methodology where the manufacturer does not require knowledge of the consumer’s utility function and prior distribution for planning the life test.

A modified reliability acceptance sampling plan with warranty return rate consideration under Weibull‐distributed accelerated lifetime data

AbstractWarranty is a standard and essential policy for today's products. The period and cost of warranty are majorly affected by the reliability of products. Therefore, validation and verification of product reliability are required to control warranty costs and sustain the brand reputation. In this paper, we propose a modified reliability acceptance sampling plan (MRASP) for product reliability validation. The operating characteristic function of the MRASP is derived by considering the accelerated time‐to‐failure data with Type‐II censoring, which follows a Weibull distribution. To minimize the number of failures required for the accelerated life test and consider the sampling risk constraints, we constructed an optimization model to determine the optimal plan design of the proposed MRASP. Following the optimal plan design, practitioners can set the number of failures required in the accelerated life test to estimate the lifetime capability of the submitted lot and decide the lot disposition using the acceptance benchmark. In addition, the lifetime capability estimation can be used to infer the warranty return rate and warranty cost of the lot, which is valuable for practitioners to formulate the warranty budget. Finally, we illustrate a real‐world case to demonstrate the practicality and applicability of the proposed method.

An advanced acceptance reliability sampling plan for heterogeneous items subject to external shocks

Abstract Accepted by: Phil Scarf In practice, many engineering items have more than one failure mode, whereas most of the existing reliability acceptance sampling plans reported in the literature assume that they have only one basic failure mode. To fill the gap, in this paper, we propose a reliability sampling plan for items with an additional failure mode that is due to external shocks. Moreover, heterogeneous populations of items are considered when items’ lifetime distributions differ from subpopulation to subpopulation. A new two-stage reliability sampling plan that takes into account these factors has been developed, where the lifetimes of items in a population are stochastically compared before and after the acceptance test. It is shown that the developed sampling plan improves the reliability characteristic of the population.

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.

Reliability acceptance sampling plan for degraded products subject to Wiener process with unit heterogeneity

The acceptance sampling plan (ASP), designed with the degradation data following the Wiener process, is widely used to verify the reliability requirements of products. Previous studies mainly designed ASPs under the given sampling plan, which lacked the justification of the sampling plan; furthermore, they ignored the unit heterogeneity of products in the degradation modeling, which affects the description accuracy of risks. To solve the above problems, this paper proposes an optimal ASP design method considering the unit heterogeneity. Firstly, the determinant of the Fisher information matrix is used to characterize the parameters estimation accuracy, under the cost requirement, the optimal test time and sample size are determined by maximizing the determinant, and an optimal sampling plan is obtained. Then, with the likelihood ratio order and the monotonicity of the average failure time on the average degradation rate, the average degradation rate is taken as the acceptance index to effectively simplify the original acceptance test problem. On this basis, the decision-making criterion considering the existence of ASP is obtained by solving the risk constraint equations of both parties. Finally, the simulation and a real example are presented to demonstrate the implementation and feasibility of the proposed method.

Construction of minimum cost reliability acceptance sampling plans for multistage process

ABSTRACT In this paper an attempt is made to derive lot acceptance sampling plans based on failure censored data. The items in the lot having multiple quality charecteristics are processed through multistage production process. We assume that quality charecteristics of the units follow exponential distribution with different parameters. The acceptance criterion for the given lot is obtained based on the average-life of units in the sample at every stage. Two nonlinear optimiztion problems which minimize the expected total testing costs at the acceptable quality level are solved. Further, a sensitivity analysis study is conducted to assess the behaviour of testing costs with respect to changes in producer's risk, consumer's risk, and sample sizes. The plan parameters are obtained by solving nonlinear mixed integer programming problem by using genetic algorithm solver in MATLAB. Some numerical exapmles and two case studies are discussed to illustrate our sampling plans.

Two Reliability Acceptance Sampling Plans for Items Subject to Wiener Process of Degradation

Traditionally, in reliability acceptance sampling plans, the decision to accept or reject a lot is made by performing the life tests of items. However, when the item’s deterioration is described by a degradation process, it can be made based on the observed deterioration levels of the items obtained from degradation tests. In this paper, two acceptance sampling plans are developed, based on the observation of the deterioration of the items, accumulated on a given period of time. To model the degradation of the items over time, the Wiener process with positive drift is employed. Algorithms to find the parameters of the proposed sampling plans are suggested. Conditionally on the acceptance in the test, the developed sampling plans are shown to improve the reliability performance of the items in the sense that the lifetimes of the items after the reliability sampling test are stochastically larger than those before the test. Also, we compare the two sampling plans both from a technical and economical points of view.

Optimum reliability acceptance sampling plan using Type-I generalized hybrid censoring scheme for products under warranty

PurposeThe purpose of this paper is to design an optimal reliability acceptance sampling plan (RASP) using the Type-I generalized hybrid censoring scheme (GHCS) for non-repairable products sold under the general rebate warranty. A cost function approach is proposed for products having Weibull distributed lifetimes incorporating relevant costs.Design/methodology/approachFor Weibull distributed product lifetimes, acceptance criterion introduced by Lieberman and Resnikoff (1955) is derived for Type-I GHCS. A cost function is formulated using expected warranty cost and other relevant cost components incorporating the acceptance criterion. The cost function is optimized following a constrained optimization approach to arrive at the optimum RASP. The constraint ensures that the producer's and the consumer's risks are maintained at agreed-upon levels.FindingsOptimal solution using the above approach is obtained for Type-I GHCS. As a special case of Type-I GHCS, the proposed approach is also used to arrive at the optimal design for Type-I hybrid censoring scheme as shown in Chakrabarty et al. (2019). Observations regarding the change in optimal design and computational times between the two censoring schemes are noted. An extensive simulation study is performed to validate the model for finite sample sizes and the results obtained are found to be in strong agreement. In order to analyze the sensitivity of the optimal solution due to misspecification of parameter values and cost components, a well-designed sensitivity analysis is carried out using a real-life failure data set from Lawless (2003). Interesting observations are made regarding the change in optimal cost due to change in parameter values, the impact of warranty cost in optimal design and change in optimal design due to change in lot sizes.Originality/valueThe research presents an approach for designing optimal RASPs using Type-I generalized hybrid censoring. The study formulates optimum life test sampling plans by minimizing the average aggregate costs involved, which makes it valuable in dealing with real-life problems pertaining to product quality management.

Designing variable sampling plans based on lifetime performance index under failure censoring reliability tests

In this paper, we develop two novel variable reliability acceptance sampling (RAS) plans referred to repetitive group sampling (RGS) and resubmitted sampling (RS), for failure censoring reliability tests by considering information obtained during life test using lifetime performance index (LPI) under Weibull distribution assumption for item lifetime. Performances of the proposed plans are compared with the single sampling (SS) plan through real case studies which show the great performances of proposed plans in terms of minimization of the average failure number of tested items.

Optimal reliability acceptance sampling plan based on accelerated life test data

In constant stress accelerated life testing, a unit is tested at a fixed stress level until failure or the termination time point of test. Assuming a log linear life-stress relationship, two different acceptance sampling plans namely: 1) acceptance sampling based on asymptotic distribution of the estimator process capability index (ĈL); 2) acceptance sampling based on exact distribution of ĈL, are developed for exponential distribution based on data obtained from the progressive type-II censoring. Asymptotic and exact distributions of the estimators of the parameters of exponential distribution are obtained. The parameters of the sampling scheme are obtained by minimising expected total testing cost. Some numerical results and comparisons of obtained sampling schemes are presented in tables to illustrate our plans.

Optimal Design of Reliability Acceptance Sampling Plan Based on Sequential Order Statistics

Abstract The concept of sequential order statistics were introduced by Kamps in 1995. In this article, we derive an acceptance sampling plan, for units having exponentially distributed lifetime, using sequential order statistics. Based on data obtained from progressive type II censoring using constant stress accelerated life tests, we obtain the maximum likelihood estimates of the parameters of the exponential distribution. Further, a log linear life-stress relationship is assumed to derive the exact distributions of the estimators of the parameters of exponential distribution. The parameters of the sampling scheme are obtained by minimizing expected total testing cost satisfying usual probability requirements. Some numerical results are presented in a table to illustrate our plans.

Optimal Design of Reliability Acceptance Sampling Plan Based on Data Obtained from Partially Accelerated Life Test (PALT)

In this paper, constant–stress partially accelerated life tests (PALT) are considered for a product with the assumption that the lifetime of the product follows Weibull distribution with known shape parameter and unknown scale parameter. Based on data obtained using Type-II censoring, the maximum likelihood estimates (MLEs) of the Weibull parameters and acceleration factor are obtained assuming linear and Arrhenius relationships with the lifetime characteristics and stress. Exact distributions of the MLEs of the parameters of Weibull distribution are also obtained. Optimal acceptance sampling plans are developed using both linear and Arrhenius relationships. Some numerical results are also presented to illustrate the resulted test plans.

Optimal reliability acceptance sampling plan based on accelerated life test data

In constant stress accelerated life testing, a unit is tested at a fixed stress level until failure or the termination time point of test. Assuming a log linear life-stress relationship, two different acceptance sampling plans namely: 1) acceptance sampling based on asymptotic distribution of the estimator process capability index (ĈL); 2) acceptance sampling based on exact distribution of ĈL, are developed for exponential distribution based on data obtained from the progressive type-II censoring. Asymptotic and exact distributions of the estimators of the parameters of exponential distribution are obtained. The parameters of the sampling scheme are obtained by minimising expected total testing cost. Some numerical results and comparisons of obtained sampling schemes are presented in tables to illustrate our plans.

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

ABSTRACTA 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.

성능특성치의 열화가 와이블 분포를 따를 때 가속열화시험을 활용한 신뢰성 샘플링검사계획의 개발

성능특성치의 열화가 와이블 분포를 따를 때 가속열화시험을 활용한 신뢰성 샘플링검사계획의 개발

Generalized Hybrid Censored Reliability Acceptance Sampling Plans for the Weibull Distribution

SYNOPTIC ABSTRACTThis work considers determination of reliability acceptance sampling plans (RASPs) for the Weibull distribution under generalized hybrid censoring schemes (GHCSs). Sample size and an acceptability constant are determined for specified producer's and consumer's risks, using the asymptotic normality of the maximum likelihood estimators of model parameters. A simulation study is undertaken to verify whether the RASPs meet the specified risks for finite sample size. Optimum RASPs are obtained based on a variance minimization criterion subject to a cost constraint. Suitable algorithms are proposed for computation of optimum RASPs. One data set is analyzed for the purpose of illustration in real-life application.

Design of Control Chart in Presence of Hybrid Censoring Scheme

In this paper, a new reliability testing control chart has been developed using the hybrid censoring scheme for the Weibull distribution. The in-control and out-of-control probabilities are estimated for the desired quality characteristic using the reliability acceptance sampling plan. The performance of the proposed chart has been evaluated by estimating the average run lengths for the shifted process under the simulation. A numerical example has been given for the practical implementation of the proposed chart. It has been observed that the proposed chart is a valuable addition in the process monitoring for the life testing of the products.