## A dynamic analysis of a class of deteriorating systems |

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### Contents

The OneStepDown Transition Matrix | 16 |

The Infinite Horizon Problem | 93 |

The Infinite Horizon Problem When a 1 | 110 |

### Common terms and phrases

aAgN(i ae|AL(i AfN(i AfN+l(i AG(i AGn(Tn-l AL(i AL(i*+l AL(j analysis Appendix argument As(i As(j assume At(i behavior binomial distribution changes sign completes the proof concave conclude consider continuous state space convex decreases definition desired result deterioration equation 1.1 exactly once example exists expected cost fact fgCi finite fM(j functional equation fx(i gN+1 Horizon Problem induction assumption infinite case let inventory model inventory problem Karlin L(TM Lemma Let S t(i main results member of class member of group n-period non-decreasing obtained one-step-down transition matrix optimal maintenance optimal policy optimal stationary policy period problem Pi+l,i+l problem is characterized proceed by induction property p1 proposed model prove Theorem real valued function Recall requirements s(j)Pij Section shown smallest integer sufficient to show Theorem 2.1 tion matrix TM+1 TN+1 transition probabilities valued function defined w=TM+l yields