Purpose




This paper considers a series system consisting of n different components having unknown and variable failure rates, where the lifetime of components follow exponential distribution having non-constant failure rates. Moreover, the failure rates are bounded by above and are dependent on environmental factors such as temperature, pressure, through linear relationship. The purpose of this paper is to design a component reliability test plan for such a series system with an unknown variable failure rate.




Design/methodology/approach




The reliability of the system is estimated with the help of the unbiased estimator of failure rate. The testing procedure is stopped when a fixed number of failures occur for each component.




Findings




An optimal reliability test plan is designed and the resultant non-linear integer optimization problem is formulated satisfying the constraints of producer’s and consumer’s risks. The obtained results are compared with the results available in the literature. Some examples are considered to illustrate the approach.




Originality/value




It is observed that use of prior information in the form of an upper bound and incorporation of environmental factors have the advantage of savings in the total testing cost.

Reliability test plan for a series system with variable failure rates

The expected lifetime and failure rate of units or products are of great significant for any manufacturing industry. If a statistically significant sample is selected randomly from a lot of similar units and if the selected units are tested till all units fail, then enough data will get generated for confidently predicting the life expectancy of any unit contained in the lot. Life testing is carried out for estimating the mean time to failure and the expected life of units. When units are produced in the manufacturing industry, the manufacturer would like to study the exact behavior of the unit under the normal working environment. For that he needs the data and evaluates Introduction to System Reliability Evaluation through Bayesian Approach

Introduction to System Reliability Evaluation through Bayesian Approach

Consider a series system with n different components. Assume that the lifetime of $$i\text {-}th$$
 component follows exponential distribution with parameter $$ \lambda _{i}(\mathbf {x}), \ \mathbf {x} \in \mathbb {R}^{k} $$
 is a covariate vector, $$ 1\le i \le n $$
 . For example, $$ \mathbf {x} $$
 may be (temperature, pressure, humidity), so that $$ \mathbf {x} \in \mathbb {R}^{3} $$
 represents a three dimensional covariate vector. Assume that each $$ \lambda _{i}(\mathbf {x}),1\le i \le n $$
 , is distinct and depends upon $$ \mathbf {x} $$
 through linear relationship. Prior information available in the form of upper bounds on $$ \lambda _{i}(\mathbf {x}) $$
 are also incorporated in the design. We propose to obtain optimal reliability test plan based on maximum likelihood estimator of system reliability. A non-linear integer optimization problem is formulated for minimizing the maximum of total expected cost involved in testing satisfying usual probability requirements (Type-I and Type-II error constraints). In addition, it is also established through simulation that the derived sampling plan meets the specified producer’s and consumer’s risks as well. A sensitivity analysis is carried out to study the effect of various input parameters on maximum total expected testing cost. Finally, a qualitative analysis is presented at the end to discuss the nature of sampling plan derived. Several numerical examples are discussed to illustrate our test plan, and it is observed that the proposed plan has significant potential to reduce the total number of components to be tested for failure. It is noted that the number of components to be tested for failure is reduced by about 96% as compared to the existing test plans in the literature.

Design of component reliability test plan for a series system having time dependent testing cost with the presence of covariates

Consider a parallel system with n independent components. Assume that the lifetime of ith component follows an exponential distribution with unknown parameter. We assume that each failure rate is distinct and the priori information can be modeled by quasi-density function. Using squared error loss function, a Bayesian estimator for failure rate based on type-II censoring is used to get an estimate of system reliability. An optimal reliability test plan is designed and a non-linear integer optimization problem is formulated satisfying usual probability requirements (type-I and type-II error constraints). Several numerical examples are considered to illustrate the Bayesian approach of obtaining optimal reliability test plan for a parallel system.

Design of Optimal Bayesian Reliability Test Plans for a Parallel System Based on Type-II Censoring

We consider the problem of acceptance testing for a parallel (1-out-of-n:G) system of n different components with constant failure rates. The components are individually tested and the tests are terminated as soon as a preassigned number of each component fails. This paper provides a criterion for accepting or rejecting the system based on the product of the total times on test for each component. The critical level for the test statistic is chosen so as to guarantee that the specified levels of consumer and producer risks on the system reliability are not exceeded. If the testing costs depend on the number of each component tested, aminimum-cost procedure can be found from the feasible set of plans.

M. Kumar

Papers

Optimal component test plans for a parallel system based on Type-II censoring