A New Variable-Censoring Control Chart Using Lifetime Performance Index under Exponential and Weibull Distributions

In reliability theory or life testing, exponential distribution and Weibull distribution are frequently considered to model the lifetime of the components or systems. In this paper, we design a control chart based on the lifetime performance index using Type II censoring for exponential and Weibull distributions. Average run length helps to measure the performance of the proposed control chart. The optimal values of the number of failure items and decision criteria used to decide whether the process is in-control or out-of-control based on the sample results are determined such that the in-control average run length is as close as to the specified average run length values. We simulate the data to illustrate the performance of the proposed control chart.

Effect of Breeding Heavier Romney Ewe Lambs at Seven Months of Age on Lamb Production and Efficiency over Their First Three Breeding Seasons

This experiment examined the effect of breeding heavier ewe lambs on lamb production and their efficiency over their first three breeding seasons. Two groups of ewe lambs were bred at seven months of age at an average pre-breeding live weight of either 47.9 ± 0.36 kg (heavy; n = 135) or 44.9 ± 0.49 kg (control; n = 135). Ewe live weight, number of lambs born and weaned, and lamb live weight were recorded until 39 months of age, and efficiency was calculated for each ewe. Although the number and lamb weaning weight did not differ between treatments over three years, when data were pooled, heavier ewe lambs at breeding weaned a greater number of lambs over the three-year period. The total lamb weaning weight over the three-year period increased by 2% for each additional kilogram at ewe lamb breeding. Breeding heavier ewe lambs had no effect on efficiency. These results suggest that although breeding heavier ewe lambs had a positive effect on lamb production over the three-year period, it had no effect on efficiency. Before final recommendations can be made, lifetime performance and longevity to five years of age of heavier ewe lambs at breeding are required.

Lifetime performance evaluation model based on quick response thinking

In practice, lifetime performance index CL has been a method commonly applied to the evaluation of quality performance. L is the upper or lower limit of the specification. The product lifetime distribution is mostly abnormal distribution. This study explored that the lifetime of commodities comes from exponential distribution. Complete data collection is the primary goal of analysis. However, the censoring type is one of the most commonly used methods due to considerations of manpower and material cost or the timeliness of product launch. This study adopted Type-II right censoring to find out the uniformly minimum variance unbiased (UMVU) estimator of the lifetime performance index CL and its probability density function. Afterward this study obtained the 100×(1-α)% confidence interval of the lifetime performance index CL as well as created the uniformly most powerful (UMP) test and the power of the test for the product lifetime performance index. Last, this study came up with a numerical example to demonstrate the suggested method as well as the application of the model.