故障率
ISBN 0471511919
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故障率をより小さな時間間隔で計算すると、ハザード関数(hazard function、ハザード率(hazard rate)とも呼ばれる) h ( t ) {\displaystyle h(t)} が得られる。これは、 Δ t {\displaystyle \Delta t} がゼロに近づくにつれて、瞬間故障率(instantaneous failure rate)あるいは瞬間ハザード率(instantaneous hazard rate)と呼ばれるものになる。
h ( t ) = lim Δ t → 0 R ( t ) − R ( t + Δ t ) Δ t ⋅ R ( t ) . {\displaystyle h(t)=\lim _{\Delta t\to 0}{\frac {R(t)-R(t+\Delta t)}{\Delta t\cdot R(t)}}.}
連続故障率は、時刻 t {\displaystyle t} まで(少なくとも)の故障確率 Pr {\displaystyle \operatorname {Pr} } を表す累積分布型の故障分布関数 F ( t ) {\displaystyle F(t)} に依存しており、
Pr  ( T ≤ t ) = F ( t ) = 1 − R ( t ) , t ≥ 0 {\displaystyle \operatorname {Pr} (T\leq t)=F(t)=1-R(t),\quad t\geq 0\!}