Reliability Demonstration Test Plan Research Articles

Reliability demonstration test plan for degraded products subject to Gamma process with unit heterogeneity

Reliability demonstration test plan for degraded products subject to Gamma process with unit heterogeneity

Overdispersion Effects on Reliability Test Planning

The impact of overdispersion on the design of optimal reliability demonstration test plans for beta-binomial models with Weibull, gamma, and lognormal lifetime distributions is analyzed. Assuming limited producer and consumer risks, fixed-duration test plans with minimal sample sizes and optimal-duration test plans with minimum costs based on failure count data are determined by solving the corresponding nonlinear programming problems when the fluctuation of the failure probability is described by a beta distribution. If the test time is fixed, the overdispersion effect on the optimal sample size and decision criterion is important in most situations. The influence is less relevant when the engineer also wants to find the minimum-cost test time. Optimal-duration plans usually outperform fixed-duration schemes in terms of costs and robustness against overdispersion. The use of lot inspection schemes with optimal reliability test times is strongly recommended when the presence of overdispersed failure count data is suspected. Applications of the developed methodology to the manufacturing of microelectronic chips and semiconductor lasers are provided for illustrative and comparative purposes.

A reliability demonstration test plan derivation method based on subsystem test data

A reliability demonstration test (RDT) has been used to determine whether a product meets pre-specified reliability requirements and to decide whether a batch of products should be accepted or rejected. For systems with high reliability, standard RDTs are no longer preferred because test plans often require long test durations and pose high risks to producers and consumers. Related reliability information, such as subsystem test data, which is often available prior to system testing, is often neglected. For the widely applied assumptions of exponentially distributed subsystems and systems, this paper proposes a reliability demonstration test plan derivation method that makes use of subsystem test data to derive the probability density function of system failure rate for small-sized sample data. In comparison with conventional RDT plans that make decisions solely based on system test data, a system test plan can be derived with much shorter test durations while keeping producer and consumer risks under control. The case study shows that our proposed method can reduce risk and shorten test duration when a test plan needs to be derived for a system with subsystem test data.

Gamma Reliability Test Times With Minimal Costs and Limited Risks

Minimum-cost reliability test durations based on gamma failure count data are found by solving mixed integer nonlinear programming problems. The optimal numbers of test units and failures allowed are also determined. A linear combination of test time and sample size is minimized assuming that producer and consumer risks are controlled. A quite accurate approximation of the smallest feasible acceptance number is deduced in closed-form. Moreover, a fast and efficient iterative algorithm is presented in order to obtain the optimal reliability demonstration test plan, which provides the best criterion to decide the acceptability of submitted lots and production processes. Furthermore, some descriptive analyses of the proposed inspection schemes, as well as applications of the developed methodology to the manufacturing of deep groove ball bearings, semiconductor lasers, and water pumps, are provided for illustrative and comparative purposes.

Optimum lot inspection based on lognormal reliability tests

Improved lognormal reliability test plans are proposed for lot sentencing. A mixed integer nonlinear programming problem is stated and solved in order to find the duration of the reliability test based on lognormal failure count data that minimises the inspection effort. The maximum number of failures tolerated by the decision maker and the necessary number of devices to be tested are also determined. The producer and consumer risks are limited in advanced, whereas the cost function is essentially a linear combination of the required sample size and test time. The minimum-cost test for device reliability demonstration provides the best criterion to decide the acceptability of manufacturing processes and submitted lots. A quick and effective iterative algorithm is suggested to obtain the optimal reliability demonstration test plan. The developed methodology is applied to the production of microelectronic chips, semiconductor lasers and ball bearings for illustrative purposes.

Planning reliability demonstration tests with limited expected risks

Optimal reliability demonstration test plans with controlled expected producer and consumer risks are computed. Device failure times follow Weibull distributions, whereas prior information on device reliability is described by limited beta models. Minimum-cost test durations, sample sizes and acceptance numbers are found by solving mixed integer nonlinear programming problems. Lower and upper bounds on the minimal feasible number of failures allowed, as well as a reasonable approximation, are first deduced. An iterative method is then presented for determining the optimal lot inspection plan. Numerical and graphical analyses and several applications in industrial manufacturing are also provided for illustrative and comparative purposes. The inclusion of substantial prior knowledge allows the reliability engineer to reduce test time, sample size and cost, and leads to improved risk assessments for both producers and consumers. The proposed approach also enables the practitioners the flexibility to define precise limits of the device reliability and to combine multiple experts’ opinions. In addition, the best plan can continually be updated as more subjective or objective information becomes available.

Optimal lot sentencing based on defective counts and prior acceptability

Optimal inspection schemes for lot sentencing based on defective counts and prior lot acceptability, which provide appropriate protections to manufacturers and customers, are derived by minimizing the sampling inspection effort. An efficient computational procedure to determine the best test plan is presented. Moreover, an explicit approximation of the optimal scheme is deduced and its accuracy is analyzed. The achieved results practically solve the underlying constrained optimization problem in closed-form. The developed methodology is applied to the design of reliability demonstration test plans using failure count data and posterior odds ratios. Some illustrative examples are also presented. In most practical cases, the suggested approach is quite robust to small deviations in the prior acceptability, and allows the practitioners to substantially reduce the required sample size for screening lots of incoming and outgoing goods, as well as to appreciably improve the evaluations of the actual producer and consumer risks. Furthermore, it provides straightforward ways to combine multiple expert opinions and to update the optimal inspection scheme using the current estimate of the prior lot acceptability. In addition, the proposed test plans usually outperform the noninformative/frequentist schemes in terms of sampling cost and are quasi-optimal when the previous knowledge is slightly modified.

Optimal attribute sampling plans in closed-forms

Lot sampling inspection based on the number of defective units observed in selected random samples is widely used in reliability and quality control. An integer nonlinear programming problem is formulated to determine the most powerful binomial sampling plan for the disposition of large lots with limited producer and consumer risks. An appealing approximation of the optimal test plan is then explicitly deduced. The minimum number of units to be tested per lot in order to achieve the desired protections for manufacturers and customers, as well as the best decision rule for lot sentencing, is derived in closed-form. The procedure is simple, quick and accurate in most practical cases, and clearly improves the classical normal approximation. The suggested perspective allows the practitioners to greatly simplify the determination of the best attribute inspection scheme. In addition, it can be used to find the optimal reliability demonstration test plan based on the number of observed failures in a given time period. The developed methodology is applied to some examples in industrial manufacturing for illustrative and comparative purposes. A useful approximation of the optimal attribute sampling plan with given expected risks is also provided.

New statistical formulations for determination of qualification test plans of safety instrumented systems (SIS) subject to low/high operational demands

This paper aims to develop new statistical formulations to design efficient reliability demonstration test (RDT) plans for electrical/electronic and programmable electronic (E/E/ES) safety instrumented systems (SIS) subject to requirements of IEC 61508-1 (2010) standard.11IEC 61508-1:2010. Functional safety of electrical/electronic/programmable electronic (E/E/ES) safety-related systems. Source: http://www.iec.ch/functionalsafety/standards/ A case study is presented to show how the proposed statistical formulations can be employed to design RDT plans to validate whether SIS target mission reliability (TMR) can be met under a specified confidence level. Discussions includes trade-offs between test duration and number of units on test and sensitivity studies showing how the demonstrated reliability at end of mission life is impacted by SIS operational mode and key statistical parameters. The major contributions that this research offers are: (i) A framework to guide reliability practitioners in applying the proposed statistical formulations to design optimum RDT plans and articulate mission reliability statements (MRS) to support regulatory certification of new SIS designs. (ii) A methodology, demonstrated by a practical case study, to show how RDT plans can be designed to meet targets set by the applicable standards. The developed framework is robust and can support certification of safety systems in a wide variety of industrial applications.

Reliability demonstration test for load-sharing systems with exponential and Weibull components.

Conducting a Reliability Demonstration Test (RDT) is a crucial step in production. Products are tested under certain schemes to demonstrate whether their reliability indices reach pre-specified thresholds. Test schemes for RDT have been studied in different situations, e.g., lifetime testing, degradation testing and accelerated testing. Systems designed with several structures are also investigated in many RDT plans. Despite the availability of a range of test plans for different systems, RDT planning for load-sharing systems hasn’t yet received the attention it deserves. In this paper, we propose a demonstration method for two specific types of load-sharing systems with components subject to two distributions: exponential and Weibull. Based on the assumptions and interpretations made in several previous works on such load-sharing systems, we set the mean time to failure (MTTF) of the total system as the demonstration target. We represent the MTTF as a summation of mean time between successive component failures. Next, we introduce generalized test statistics for both the underlying distributions. Finally, RDT plans for the two types of systems are established on the basis of these test statistics.

An Approach for Reliability Demonstration Test Based on Power‐Law Growth Model

Reliability demonstration test (RDT) is a critical and necessary step before the acceptance of an industrial system. Generally, a RDT focuses on designing a test plan through which one can judge whether the system reliability indices meet specific requirements. There are many established RDT plans, but few have incorporated the reliability growth aspects of the corresponding products. In this paper, we examine a comprehensive test plan that involves information concerning the reliability growth stage. An approach for RDT under the assumption of the power‐law model is proposed. It combines data related to the growth stage with those pertaining to the test stage of the product to reduce the cost of the test. Through simulation studies and numerical examples, we illustrate the characteristics of the test plan and significant reduction in test costs through our approach. Copyright © 2017 John Wiley & Sons, Ltd.

Accelerated reliability demonstration under competing failure modes

The conventional reliability demonstration tests are difficult to apply to products with competing failure modes due to the complexity of the lifetime models. This paper develops a testing methodology based on the reliability target allocation for reliability demonstration under competing failure modes at accelerated conditions. The specified reliability at mission time and the risk caused by sampling of the reliability target for products are allocated for each failure mode. The risk caused by degradation measurement fitting of the target for a product involving performance degradation is equally allocated to each degradation failure mode. According to the allocated targets, the accelerated life reliability demonstration test (ALRDT) plans for the failure modes are designed. The accelerated degradation reliability demonstration test plans and the associated ALRDT plans for the degradation failure modes are also designed. Next, the test plan and the decision rules for the products are designed. Additionally, the effects of the discreteness of sample size and accepted number of failures for failure modes on the actual risks caused by sampling for the products are investigated.

Reliability Demonstration for Long-Life Products Based on Degradation Testing and a Wiener Process Model

<?Pub Dtl=""?> In this paper, the degradation based reliability demonstration test (RDT) plan design problems for long life products under a small sample circumstance are studied. Fixed sample method, sequential probability ratio test (SPRT) method, and sequential Bayesian decision method are provided based on univariate degradation testing. The simulation examples show the superiority of degradation based RDT methods compared with the traditional failure based methods, and the sequential-type methods have more test power than their fixed sample counterparts. The test power can be further improved by combining the test data of a reliability indicator with the data of its marker, based on which the bivariate fixed sample method and the sequential Bayesian decision method are defined. The simulation study shows the benefit from the combination. The degradation based RDT plan optimization model, and the corresponding searching-based solution algorithm using some heuristic rules discovered in the paper, are also presented. The case study of Rubidium Atomic Frequency Standard with a RDT plan design demonstrates the effectiveness of our methods on overcoming the difficulties of small samples in reliability demonstration of long life products.

Heuristic Degradation Test Plans for Reliability Demonstration

Reliability demonstration is an important task in the product development process. The commonly used reliability demonstration test methods include bogey test, life test, and degradation test, among which the degradation test is known to be most efficient. However, its application in industry is still limited primarily due to the lack of appropriate test plans. This paper presents heuristic reliability demonstration test plans for the products whose performance characteristics can be modeled with the Weibull distribution. In particular, the paper describes degradation models, test method, test termination rules, and the calculation of reliability and confidence interval from degradation data. The paper delineates test plan models, which are solved for optimal sample size and test time using the proposed heuristic algorithm. The algorithm results in the lowest test cost and the shortest test time for the products that are expected to pass or fail the test at a high degree of confidence. A case study is presented to illustrate the proposed method, and shows that the heuristic test plan reduced the test time, and cost by 27%, and 29%, respectively. The paper also numerically compares the three test methods, and concludes that the degradation test method is most efficient in terms of test time, cost, and sample size.

Optimal Reliability Demonstration Test Plans for $k$-out-of-$n$ Systems of Gamma Distributed Components

Constrained optimization problems are solved to determine the best reliability sampling plans for <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$k$</tex> </formula> -out-of- <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$n$</tex> </formula> :F systems of gamma distributed components. As usual, the constraints are related to the quality levels required by the producer and the consumer, whereas the decision criterion is based on the uniformly most powerful reliability test. Excellent approximate solutions are derived in closed-forms assuming a frequentist perspective. This classical methodology is generalized to those situations in which the prior information on the fraction effective, <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$r$</tex></formula> , is appreciable. Because prior knowledge on <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$r$</tex> </formula> often suggests a restricted parameter interval, a limited beta distribution is used to describe the probabilistic behavior of <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$r$</tex></formula> . Optimal sample sizes and acceptance factors are obtained by solving mixed integer nonlinear programming problems. Lower and upper bounds on the smallest sample size, as well as a quite accurate approximation, are also provided. An efficient step-by-step procedure, which only needs a few iterations in most practical cases, is proposed for solving the optimization problem. The incorporation of prior knowledge into the reliability analysis provides better assessment of the true producer's and consumer's risks, and considerable savings in sample size and test duration. The optimal solutions are usually quite robust to small variations in the gamma shape parameter and the prior information. An example concerning a system composed of five water pumps for cooling a reactor is included for illustration. The proposed component test sampling plans can be recommended for use in practical applications, particularly when it is economically infeasible, or even impossible, to test a whole system.

Design of a Zero-Failure Reliability Test Plan Based on Customer Usage and Bench Life Test Data

Reliability tests are mandatory to evaluate new products prior to their release. The proper determination of a reliability test plan is crucial because an erroneous test plan can be very costly and misleading. This paper describes a probability-based method of designing a reliability demonstration test plan using both field customer usage and historical bench life test data. Statistical distribution analysis, Monte Carlo simulation (MCS) technique, and zero-failure test method are integrated into the probability-based method to create test plans that can more accurately evaluate product reliabilities for the required product service life using a small number of test samples.

Reliability demonstration test planning: A three dimensional consideration

Increasing customer demand for reliability, fierce market competition on time-to-market and cost, and highly reliable products are making reliability testing more challenging task. This paper presents a systematic approach for identifying critical elements (subsystems and components) of the system and deciding the types of test to be performed to demonstrate reliability. It decomposes the system into three dimensions, (i.e. physical, functional and time) and identifies critical elements in the design by allocating system level reliability to each candidate. The decomposition of system level reliability is achieved by using criticality index. The numerical value of criticality index for each candidate is derived based on the information available from failure mode and effects analysis (FMEA) document or warranty data from a prior system. It makes use of this information to develop reliability demonstration test plan for the identified (critical) failure mechanisms and physical elements. It also highlights the benefits of using prior information in order to locate critical spots in the design and in subsequent development of test plans. A case example is presented to demonstrate the proposed approach.

BAYESIAN SINGLE-LEVEL BINOMIAL AND EXPONENTIAL RELIABILITY DEMONSTRATION TEST PLANS

Bayesian reliability demonstration test plans are developed for binomial and exponential sampling distributions using mixtures of beta and inverse gamma prior distributions, respectively. Both types of plans consider a single specified target reliability and rectify an important drawback of an existing well-known classical single-level test planning procedure. The plans are developed in such a way that they attain a specified probability of passing the test when the target reliability has been met as well as provide desired confidence that the target reliability has been met given that the test has been passed.