Generalized Failure Rate Research Articles

Contributions to nonparametric generalized failure rate function estimation

For a specified distribution functionG with densityg, and unknown distribution functionF with densityf, the generalized failure rate function γ(x)=f(x)/gG −1 F(x) may be estimated by replacingf andF byf n and $$\hat F_n $$ , wheref n is an empirical density function based on a sample of sizen from the distribution functionF, and $$\hat F_n (x) = \int\limits_{ - \infty }^x {f_n (t)dt} $$ . Under regularity conditions we show $$\mathop {\sup }\limits_{x \in C} |\gamma _n (x) - \gamma (x)|\mathop \to \limits^{w.p.l} 0$$ and, under additional restrictions $$\mathop {\sup }\limits_{x \in C} |\gamma _n (x) - \gamma (x)|\mathop = \limits^{w.p.l} o (n^{ - 1/3} \beta _n \log n)$$ whereC is a subset ofR and βn→∞. Moreover, asymptotic normality is derived and the Berry-Esseen type bound is shown to be related to a theorem which concerns the sum of i.i.d. random variables. The order boundO(n−1/2+∈c n 1/2 ) is established under mild conditions, wherec n is a sequence of positive constants related tof n and tending to 0 asn→∞.

Optimal Replacement for Shock Models with General Failure Rate

A device is subject to a series of shocks which arrive as a semi-Markov process. Shocks cause damage and eventually failure will occur at the time of arrival of one of the shocks. The device must be replaced upon failure at some cost but it also can be replaced before failure at a lower cost. We consider the general case where the failure rate need not be increasing and replacement can be made at any time. The form of the optimal replacement policy is found and conditions are determined for which a control limit policy is optimal.

Study on the action of D-norgestrel as a postcoital contraceptive agent

This study was undertaken to investigate possible mechanisms of action of D-norgestrel as a contraceptive agent after the results of large clinical trials on postcoital contraception with D-norgestrel were known. Previously, in a total of 4,631 patients with 41,802 months of use, a general failure rate of 3.5 and a corrected failure rate of 1.7 was observed. In this communication, the action of 400 mcg D-norgestrel was investigated when taken orally by a total of six subjects on day 12, days 10 and 12, days 8, 10, 12 of the cycle, on the 2nd and 4th day, and on the 2nd, 4th and 6th day after the LH-peak. Karyopyknotic index, cervical function, Spinnbarkeit and crystallization of cervical mucus, serum levels of 17β-estradiol, progesterone and LH were studied daily from the 8th day of the cycle. Preovulatory application of the contraceptive agent resulted in the inhibition of peripheral parameters of the menstrual cycle. Furthermore, midcycle elevation of LH was found inhibited and reduced in subjects treated in the follicular phase. Neither preovulatory nor postovulatory application of the progestagen appeared to interfere with the luteal phase of the cycle. It is concluded that one of the possible main actions of this contraceptive agent has to be sought in the inhibition of peripheral function of the menstrual cycle.

Low-dose lynestrenol as a contraceptive method

The use of a continuous low-dose of lynestrenol as an oral contraceptive has been investigated in a total of 274 women during 2702 cycles. A daily dose of 0.5 mg ** was found to give a satisfactory contraceptive protection; a total of two pregnancies occurred giving a general failure rate of 0.88 per 100 woman-years. ** Trade name Exlution R (Organon, Oss, The Netherlands) The computer analysis showed that the cycle length was more or less a normal one in 80 per cent of participants after 6 cycles. Irregular bleeding occurred in 244 out of 2702 cycles (9%). The incidence of spotting was higher in the initial cycles, decreasing with the duration of treatment. Less women experienced break-through bleeding. The method was acceptable to most of the subjects and side-effects, other than menstural irregularity, were minimal.

Postcoital contraception with D-norgestrel

This study consists of results of a large clinical trial in which a single dose of D-norgestrel was taken within three hours after each sexual intercourse. Studied patients totaled 4,631 with 41,802 months of use. Five doses of drug were tested from 150 up to 400 micrograms per tablet. Contraceptive efficacy was poor with the lowest dose but improved with each higher dose reaching with 400 mcg a general failure rate of 3.5 and a corrected failure rate of 1.7. Main side-effects were cycle disorders consisting chiefly of shortened cycles and break-through bleeding. However, the incidence of irregular bleeding did not vary significantly with the different doses. Side effects unrelated to menstrual cycles were extremely infrequent. Drop-out rates due to side effects were 5–8 percent. The acceptability of the method was very rewarding, and its chances as a basis for routine large-scale family planning are promising.

Remarks on Non-Parametric Estimates for Density Functions and Regression Curves

Remarks on Non-Parametric Estimates for Density Functions and Regression Curves

Mathematical Theory of Reliability

Preface to the Classics Edition Preface 1. Introduction. Historical Background of the Mathematical Theory of Reliability Definitions of Reliability 2. Failure Distributions. Introduction Typical Failure Laws The Exponential as the Failure Law of Complex Equipment Monotone Failure Rates Preservation of Monotone Failure Rate Additional Inequalities General Failure Rates 3. Operating Characteristics of Maintenance Policies. Introduction Renewal Theory Replacement Based on Age Comparison of Age and Block Replacement Policies Random Replacement Repair of a Single Unit 4. Optimum Maintenance Policies. Introduction Replacement Policies Inspection Policies 5. Stochastic Models for Complex Systems. Introduction Markov Chains and Semi-Markov Processes Repairman Problems Marginal Checking Optimal Maintenance Policies under Markovian Deterioration 6. Redundancy Optimization. Introduction Optimal Allocation of Redundancy Subject to Constraints Application to Parallel Redundancy Model Application to Standby Redundancy Model Complete Families of Undominated Allocations Optimal Redundancy Assuming Two Types of Failure 7. Qualitative Relationships for Multicomponent Structures. Introduction Achieving Reliable Relay Circuits Monotonic Structures S-shaped Reliability Functions for Monotonic Structures k-out-of-n Structures Relationship between Structures Failure Rate and Component Failure Rates Appendix 1. Total Positivity Appendix 2. Test for Increasing Failure Rate Appendix 3. Tables Giving Bounds on Distributions with Monotone Failure Rate References Index.