A New Two-Parameter Lifetime Distribution with Increasing Failure Rate

We consider the parameter inference for a two-parameter life distribution with bathtub-shaped or increasing failure rate function. We present the point and interval estimations for the parameter of interest based on type-II censored samples. Through intensive Monte-Carlo simulations, we assess the performance of the proposed estimation methods by a comparison of precision. Example applications are demonstrated for the efficiency of the methods.

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OPTIMAL BURN-IN PROCEDURES IN A GENERALIZED ENVIRONMENT

International Journal of Reliability Quality and Safety Engineering ◽

10.1142/s021853930500177x ◽

2005 ◽

Vol 12 (03) ◽

pp. 189-201 ◽

Cited By ~ 6

Author(s):

JI HWAN CHA ◽

JIE MI

Keyword(s):

Lower Bound ◽

Failure Rate ◽

Rate Function ◽

General Assumption ◽

Lifetime Distribution ◽

Failure Rate Function ◽

Increasing Failure Rate ◽

Bathtub Shape ◽

Early Failures ◽

Special Case

Burn-in procedure is a manufacturing technique that is intended to eliminate early failures. In the literature, assuming that the failure rate function of the products has a bathtub shape the properties on optimal burn-in have been investigated. In this paper burn-in problem is studied under a more general assumption on the shape of the failure rate function of the products which includes the traditional bathtub shaped failure rate function as a special case. An upper bound for the optimal burn-in time is presented under the assumption of eventually increasing failure rate function. Furthermore, it is also shown that a nontrivial lower bound for the optimal burn-in time can be derived if the underlying lifetime distribution has a large initial failure rate.

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Objective Bayesian Snalysis for the Complementary Exponential Geometric Model Applied to Cancer Data

International Journal of Statistics and Probability ◽

10.5539/ijsp.v6n2p122 ◽

2017 ◽

Vol 6 (2) ◽

pp. 122 ◽

Cited By ~ 1

Author(s):

Daniele Cristina Tita Granzotto ◽

Vera Lucia Damasceno Tomazella ◽

Francisco Louzada

Keyword(s):

Geometric Model ◽

Real Data ◽

Lifetime Distribution ◽

Mean Square ◽

Data Set ◽

Increasing Failure Rate ◽

Cancer Data ◽

Credible Intervals ◽

Two Parameter ◽

Common Malignancy

In this paper we provide a reference Bayesian framework to a new two-parameter lifetime distribution with increasing failure rate, the complementary exponential geometric (CEG). To this end, we presented some of the main properties of this model and its characteristics related to the reliability analysis. A simulation study is performed to analyse the frequentist properties of credible intervals from the reference posterior distribution among of the standard error and mean square error (MSE) of estimations. The presented methodology is illustrated by the use of a real data set which presents the study of time until the cure of cervix lesions, that are precursors cancer lesions in the cervix. According to to INCA (Cancer National Institute), cervical cancer stands as the fourth cause of death among women in Brazil. Together with breast cancer, it is one of the most common malignancy affecting women worldwide. For this reason, patients must be carefully evaluated for metastatic disease. These data were collected in the Woman Clinic which is sited in Maring\'{a} city (Paran\'{a} State, Brazil).

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