搞下英文

高手帮忙搞一下英文的翻译 悬赏分：5 - 离问题结束还有 14 天 23 小时这个是一个关于物流的英文文献的其中一部分，可能有点长，真的麻烦大家拉，中间的公式不需要翻译。 366 RAHIM AND OHTA and LCLR = k2lσ0 (6) where k2u and k2l are the upper and lower control limits coefficients for the R-chart, respectively. We obtain expressions for the Type I error and the power of the R-chart as follows: αR = 1 − Fn(k2u) + Fn(k2l ) (7) - and PR = 1 − Fn(k2uσ0/σ1) + Fn(k2lσ0/σ1) (8) where Fn(•) is the cumulative distribution function for the standardized range w = R/σ0, is given by Fn(w) = {_(w/2) − _(−w/2)}n + 2n _ ∞ w/2 ϕ(u){_(u) − _(u − w)}n−1du. (9) Joint probability of Type I and power for the combined charts In interpreting patterns on ¯X and R charts, one should consider two charts jointly (Montgomery, 1991)). If the underlying distribution is normal, then the random variables ¯X and R computed from the same sample are statistically independent. The joint Type I error, α, and power, P, respectively, for the joint ¯X and R control charts can be obtained as follows: α = α¯X + αR − α¯X • αR (10) and P = P¯X + PR − P¯X • PR (11) Weibull shock and inspection intervals In Duncan’s approach, a fixed length of sampling interval and a constant failure rate over each interval were assumed. However, when the process fails at an increasing rate (as in a Weibull distribution), the frequency of sampling should increase according to the age of the system. Duncan’s model was extended by Banerjee and Rahim (1988), assuming a process with a Weibull distribution time shift and an increasing hazard rate. They found AN INTEGRATED OPTIMIZATION MODEL 367 thatthat increasing the sampling frequency according to the age of the system results in a lower operational cost per hour.