A two-pronged truncated deferred sampling plan (TTDSP) for log-logistic distribution

This paper is aimed at developing a new truncated sampling plan that uses information from precedent and successive lots for lot disposition with a pretention that the life-time of a particular product assumes a Log-logistic distribution. A new Two-pronged Truncated Deferred Sampling Plan (TTDSP) for Log-logistic distribution is proposed when the testing is truncated at a precise time. The best possible sample sizes are obtained under a given Maximum Allowable Percent Defective (MAPD), Test Suspension Ratios (TSR) and acceptance numbers (c). A formula for calculating the operating characteristics of the proposed plan is also developed. The operating characteristics and mean-ratio values were used to measure the performance of the plan. The findings of the study show that: Log-logistic distribution has a decreasing failure rate; furthermore, as mean-life ratio increase, the failure rate reduces; the sample size increase as the acceptance number, test suspension ratios and maximum allowable percent defective increases. The study concludes that the new minimum sample sizes were smaller which makes the plan a more economical plan to adopt when cost and time of production is costly and the experiment being destructive.

Mathematical modelling to industrial repair and maintenance policy system for its reliability

The present paper is an initiative taken by emerging reliability model to a automobile repair industries for its products by dividing repair policy into two categories as (a) regular/normal service and (b) strategy for accidental or additional failure. The concept of inspection process has been introduced for proper verification of failure and also to its repairing strategy with time and cost. The maintenance cost for regular services are fixed but for the case of additional failures the additional cost will be decided upon the level of damage. The stochastic analysis for system been numerically and graphically analyzed by calculating reliability variables like MTSF, availability, inspection and maintenance analysis of the system with the concept of geometric distribution, Markov process and regenerative technique. The results been proved beneficial for fulfilling the objective of calculating profit function that increases with increasing repair and decreasing failure rate.

The Gompertz Gumbel II Distribution: Properties and Applications

In this paper we introduced Gompertz Gumbel II (GG II) distribution which generalizes the Gumbel II distribution. The new distribution is a flexible exponential type distribution which can be used in modeling real life data with varying degree of asymmetry. Unlike the Gumbel II distribution which exhibits a monotone decreasing failure rate, the new distribution is useful for modeling unimodal (Bathtub-shaped) failure rates which sometimes characterised the real life data. Structural properties of the new distribution namely, density function, hazard function, moments, quantile function, moment generating function, orders statistics, Stochastic Ordering, Renyi entropy were obtained. For the main formulas related to our model, we present numerical studies that illustrate the practicality of computational implementation using statistical software. We also present a Monte Carlo simulation study to evaluate the performance of the maximum likelihood estimators for the GGTT model. Three life data sets were used for applications in order to illustrate the flexibility of the new model.

Phalangeal Osteotomy…To Perform or Not to Perform

Category: Bunion Introduction/Purpose: As the hallux valgus deformity progresses, patients can get mild to moderate arthritis of the metatarsophalangeal (MTP) joint. The degenerative process of MTP arthritis results in reactive tissue formation and proliferation of osseous and cartilaginous structures. For some patients, the results in dorsal bone spurs and pain with great toe dorsiflexion of irritation from shoes. Reconstructive procedures provide a surgical option for patients to address pain and functional limitations, prior to subchondral bone cyst formation and loss of joint space. Patients who underwent cheilectomy alone have been shown to have a high failure rate and progress to advanced disease. A phalangeal dorsiflexion osteotomy has become increasingly more popular amongst foot and ankle surgeons with the hopes of decreasing failure rate and improving early outcomes. Methods: This study was a retrospective review of prospectively collected data from 385 patients treated for hallux rigidus at a large academic medical center between July 2015 and November 2016. All patients underwent either a cheilectomy or cheilectomy with phalangeal osteotomy of the MTP joint. Collected patient reported outcomes (PROs) included in this study were SF12 M, SF12P, FAAM, VAS and PASS scores. Mann-Whitney t-test was performed using GraphPad Prism version 7.0b for Mac to compare procedure groups. Exclusion criteria included poly-trauma, revision of same procedure, and lack of pre or post- operative. Results: Eighteen patients met criteria, 8 underwent cheilectomy and 10 had a cheilectomy with osteotomy procedure. The average age was 51.9 amongst the cohort, with a total of 13 female and 5 males. Patients who underwent cheilectomy with osteotomy procedure had better outcomes across all outcome measure scores. When comparing postoperative scores, cheilectomy with osteotomy patients showed significantly higher scores compared to cheilectomy alone patients: SF12-M (56 vs 36, respectively; p=0.0333), and SF12P (52 vs 30, respectively p=0.0095). VAS scores and FAAM scores showed no statistical difference between the two cohorts. Despite surgical intervention, 50% of patients who received cheilectomy alone reported more pain post-operatively compared to no reports of worsening pain in patients who received cheilectomy with osteotomy. Conclusion: Patients with moderate to severe hallux rigidus demonstrate improved functional outcomes with phalangeal osteotomy in conjunction with cheilectomy compared to cheilectomy alone. Further research with larger cohorts would be beneficial to confirm the reports of this study and expand upon aspects of care that contribute to patient satisfaction and performance.

The DFR Property for Counting Processes Stopped at an Independent Random Time

In this paper we consider general counting processes stopped at a random timeT, independent of the process. Provided thatThas the decreasing failure rate (DFR) property, we present sufficient conditions on the arrival times so that the number of events occurring beforeTpreserves the DFR property ofT. In particular, when the interarrival times are independent, we consider applications concerning the DFR property of the stationary number of customers waiting in queue for specific queueing models.

The DFR Property for Counting Processes Stopped at an Independent Random Time

In this paper we consider general counting processes stopped at a random time T, independent of the process. Provided that T has the decreasing failure rate (DFR) property, we present sufficient conditions on the arrival times so that the number of events occurring before T preserves the DFR property of T. In particular, when the interarrival times are independent, we consider applications concerning the DFR property of the stationary number of customers waiting in queue for specific queueing models.