Trend changes in failure rate and mean residual life: Its relations and applications

The classes of life distributions which exhibit the trend change in its aging properties, such as failure rate, mean residual life, have attracted a great deal of interest among the reliability analysts and engineers. Such classes of life distributions include IDFR, DIFR, DIMRL and IDMRL, among others.;We consider certain parametric models that show the trend change in either its failure rate or its mean residual life. The conditions that characterize the relations between failure rate and mean residual life are derived in general and we apply these results to Hjorth model, Dhillon model, lognormal distribution and inverse Gaussian distribution to study such relations in detail. We compute the values and percentiles of change points for both failure rate and mean residual life functions and provide graphical comparisons for the shapes of both functions for selected combinations of parameter values in each model. We observe the influence of each parameter value on the location of trend change. It is shown that the trend change of mean residual life takes place before the failure rate changes its trend.;Another objective is to suggest new bootstrap confidence intervals for several process capability indices. Our confidence intervals are based on the method of percentile-t and work as the competitors to the existing confidence intervals. We also show that our confidence intervals are better than the percentile and standard bootstrap confidence intervals for various underlying distributions by comparing the mean length of confidence intervals and coverage probabilities. Our method is especially effective when the original sample size is small.