‎In manufacturing industries‎, ‎the lifetime of an item is usually‎ ‎characterized by a random variable X, ‎and considered to be‎ ‎satisfactory if X exceeds a given lower lifetime limit L. ‎The‎ ‎probability of a satisfactory item is then eta_L:=P(X> L), ‎called‎ ‎{\\\\em conforming rate}‎. ‎In industrial companies‎, ‎however‎, ‎the lifetime‎ ‎performance index, ‎proposed by Montgomery [1] and‎ ‎denoted by C_L, ‎is widely used as a process capability index‎ ‎instead of the conforming rate‎. ‎Assuming a parametric model for the‎ ‎random variable X, ‎we show that there is a‎ ‎connection between the conforming rate and the lifetime‎ ‎performance index‎. ‎Consequently‎, ‎the statistical inferences about eta_L and C_L are equivalent‎. ‎Hence‎, ‎we restrict ourselves to statistical inference for C_L based on generalized order statistics which contains several ordered data models such as usual order statistics‎, ‎progressively Type-II censored data and records‎. ‎Various point and interval estimators for the parameter‎ C_L are obtained and optimal critical regions for the hypothesis testing problems‎ ‎concerning C_L are proposed‎. ‎Finally‎, ‎two real data sets on the‎ ‎lifetimes of insulating fluid and ball bearings‎, ‎due to Nelson [2] and Caroni [44], ‎respectively‎, ‎and a‎ ‎simulated sample are analyzed‎.

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