A new classes of life distribution, namely harmonic used better than aged in expectation in upper tail (HUBAEUT) is introduced. Testing exponentiality against this class is investigated using kernel method. The limiting null and nonnull distribution of the test statistics is normal and the null variance is calculated exactly. Selected critical values are tabulated for sample sizes of 5(1)40. Power of the test are estimated by simulation. the efficacies of the test statistics used for testing against HUBAEUT are calculated for som common alternatives and are compared to some other procedures. It is shown that proposed test is simple, has high relative efficiency and power for some commonly used alternatives. The set of real data are used as an examples to elucidate the use of the proposed test statistics for practical reliability.

Let E be a set of n quantitative observations under the time control. The interval of time is to be split into several subintervals such that the observations in each subinterval are almost similar, whereas the observations between the subintervals are very dissimilar. The corresponding time-subintervals become periods or phases of the development that exist in the underlying phenomenon. Aboukalam(2005) proposes a robust solution based on some initial subintervals and a technique for combining any two successive groups in that starter using a t-test under a fixed significant level ($\alpha$). The inconvenience is that; the technique reliability is not released from the level $\alpha$ which must not be defined apart from the number of the periods that is, in its turn, unknown. To avoid this, we propose what so called; most significant periods solution. The new technique constructs its own initial subintervals and uses another way for combining the groups. However, the way of determining and treating outliers has not changed. This paper conducts many empirical simulations using different possible time dominated data in order to illustrate the reliability of the proposed technique. Finally, we apply both techniques on some real time dominated data to explain the advantage of the proposal.

This paper introduces different vectors of the reliability equivalence factors of a series system consists of n independent and nonidentical components. The failure rates of the system components are assumed to be constant. The reliability function and mean time to failure are used as performances to derive the reliability equivalences of the system. The results presented here generalize those available in the literatures. Numerical study is given to explain how one can utilize the theoretical results obtained.

AIn this paper we introduce and study a multivariate notions of mean inactivity time (MIT) functions. Basic properties of these functions are derived and their relationship to the multivariate conditional reversed hazard rate functions is studied. A partial ordering, called MIT ordering, of non-negative random vectors is introduced and its basic properties are presented. Its relationship to reversed hazard rate ordering is pointed out. Finally, using the MIT ordering, a bivariate and multivariate notions of IMIT (increasing mean inactivity time) class is introduced and studied.

In this paper, we present the U-Statistic test for testing exponentiality against new renewal better than used (NRBU) based on a goodness of fit approach. Selected critical values are tabulated for sample sizes n=5(1)30(10)50. The asymptotic Pitman relative efficiency relative to (NRBU) test given in the work of Mahmoud et all (2003) is studied. The power estimates of this test for some commonly used life distributions in reliability are also calculated. Some of real examples are given to elucidate the use of the proposed test statistic in the reliability analysis. The problem in case of right censored data is also handled.

Many software reliability growth models (SRGMs) based on nonhomogeneous Poisson process (NHPP) have been developed and applied in practice. NHPP SRGMs are characterized by their mean value functions. Mean value functions are usually derived from differential equations representing the fault detection/removal process during testing. In this paper such differential equations are regarded as frameworks for generating mean value functions. Currently available frameworks are theoretically discussed with respect to capability of representing the fault detection/removal process. Then two general frameworks are proposed.

Effective and quick methods that are easy to carry out even by hand, or easy to be programmed by hand-held calculators are needed for assessing the sizes of contrasts of unreplicated $2^P$ factorial designs. Moreover, they have the advantage to use the original numerical measurements which makes the analysis easier to explain. Basically, Lenth (1989) is one of the most familiar of such quick and powerful methods. Later on, Aboukalam (2001) proposes under constant effects an alternative sophisticated method to Lenth's method. The proposed method is the supreme from two considerable powers. The first utmost indicates less inflation deficiency while the other utmost indicates less shrinkage deficiency. Also under constant effects, Al-Shiha (2006) introduces an alternative quick method which is less shrinkage deficiency while the inflation deficiency is the same. If effects are random, Aboukalam (2005) introduces an alternative quick method in which the first power is favored as long as the second power is within a small margin. In the spirit of quickness and fixed effects, this article adds another method which is supreme from the two considerable powers. The method is based on a one step of the scale-part of a suggested M-estimate for location. Explicitly, we suggest adapting the skipped median (ASKM) estimate. Critical values of ASKM-method, for several sample sizes often used, are empirically computed.

Typical confidence intervals for a mean or mean residual life (MRL) are centered about the mean or mean residual life. We discuss novel confidence intervals that produce statements like "we are 95% confident that the MRL function, e(t), is greater than a prespecified $\mu_o$ for all t in the interval [0, $\hat{\theta})$)" where $\hat{\theta}$ is determined from the sample data, confidence level, and $\mu_o$. Also, we can have statements like 'we are 95% confident that the MRL of population 1, namely $e_1$(t), is greater than the MRL of population 2, $e_2$(t), for all t in the interval [0, $\hat{\theta}$)" where $\hat{\theta}$ is determined from the sample data and confidence level. We illustrate these one and two sample confidence intervals on internal bonds (tensile strengths) for an important modem engineered wood product, called medium density fiberboard (MDF), used internationally.

In this paper, we derive recurrence relations for the single and product moments of progressively Type-II right censored order statistics from half logistic distribution. Next, we derive the maximum likelihood estimators (MLEs) of the location and scale parameters of the half logistic distribution. In addition, we use the setup proposed by Balakrishnan and Aggarwala (2000) to compute the approximate best linear unbiased estimates (ABLUEs) of the location and scale parameters. Finally, we point out a simulation study to compare between the efficiency of the techniques considered for the estimation.