tailieunhanh - Engineering Statistics Handbook Episode 10 Part 4

Tham khảo tài liệu 'engineering statistics handbook episode 10 part 4', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Exponential The Exponential distribution shape The Exponential CDF http div898 handbook apr section1 2 of 5 5 1 2006 10 41 32 AM Exponential Below is an example of typical exponential lifetime data displayed in Histogram form with corresponding exponential PDF drawn through the histogram. Histogram of Exponential Data The Exponential models the flat portion of the bathtub curve -where most systems spend most of their lives Uses of the Exponential Distribution Model 1. Because of its constant failure rate property the exponential distribution is an excellent model for the long flat intrinsic failure portion of the Bathtub Curve. Since most components and systems spend most of their lifetimes in this portion of the Bathtub Curve this justifies frequent use of the exponential distribution when early failures or wear out is not a concern . 2. Just as it is often useful to approximate a curve by piecewise straight line segments we can approximate any failure rate curve by week-by-week or month-by-month constant rates that are the average of the actual changing rate during the respective time durations. That way we can approximate any model by piecewise exponential distribution segments patched together. 3. Some natural phenomena have a constant failure rate or occurrence rate property for example the arrival rate of cosmic ray alpha particles or Geiger counter tics. The exponential model works well for inter arrival times while the Poisson distribution describes the total number of events in a given period . When these events trigger failures the exponential life distribution model will naturally apply. http div898 handbook apr section1 3 of 5 5 1 2006 10 41 32 AM . Exponential Datapỉot and EXCEL functions for the Exponential model DATAPLOT and EXCEL Functions for the Exponential The Dataplot commands EXPPDF and EXPCDF calculate the exponential PDF and CDF for the standardized case with 1. To