Geometric imperfect preventive maintenance and replacement (GIPMAR) model for aging repairable systems

PurposeThis work seeks to develop a geometric imperfect preventive maintenance (PM) and replacement model (GIPMAR) for aging repairable systems due to age and prolong usage that would meet users need in three phases: within average life span, beyond average life span and beyond initial replacement age of system.Design/methodology/approachThe authors utilized the geometric process (GP) as the hazard function to characterize the increasing failure rate (IFR) of the system. The GP hazard function was incorporated into the hybridized preventive and replacement model of Lin et al. (2000). The resultant expected cost rate function was optimized to obtain optimum intervals for PM/replacement and required numbers of PM per cycle. The proposed GIPMAR model was applied to repairable systems characterized by Weibull life function and the results yielded PM/replacement schedules for three different phases of system operation.FindingsThe proposed GIPMAR model is a generalization of Lin et al. (2000) PM model that were comparable with results of earlier models and is adaptive to situations in developing countries where systems are used across the three phases of operation depicted in this work. This may be due to economic hardship and operating environment.Practical implicationsThe proposed model has provided PM/Replacement schedules for different phases of operation which was never considered. This would provide a useful guide to maintenance engineers and end-users in developing countries with a view to minimizing the average cost of maintenance as well as reducing the number of down times of systems.Social implicationsA duly implemented GIPMAR model would ensure efficient operation of systems, optimum man-hour need in the organization and guarantee customer's goodwill in a competitive environment.Originality/valueIn this work, the authors have extended Lin et al. (2000) PM model to provide PM/replacement schedules for aging repairable systems which was not provided for in earlier existing models and literature.

Importance of Normalization of Carbohydrate Antigen 19-9 in Patients With Intrahepatic Cholangiocarcinoma

BackgroundAlthough carbohydrate antigen 19-9 (CA19-9) is an established prognostic marker for intrahepatic cholangiocarcinoma (ICC) patients, the significance of elevated preoperative CA19-9 that normalized after resection remains unknown. This study aimed to investigate whether elevated preoperative CA19-9 that normalized after curative resection had an impact on prognosis among patients with ICC.MethodsPatients who underwent curative resection for stage I to III ICC between 2009 and 2018 were identified. Patients were categorized into three cohorts: normal preoperative CA19-9, elevated preoperative CA19-9 but normalized postoperative CA19-9, and persistently elevated postoperative CA19-9. Overall survival (OS), recurrence-free survival (RFS), and hazard function curves over time were analyzed.ResultsA total of 511 patients (247 [48.3%] male; median age, 58 years) were included. Patients with elevated preoperative CA19-9 (n = 378) were associated with worse RFS and OS than those with normal preoperative CA19-9 (n = 152) (both p < 0.001). Patients with persistently elevated postoperative CA19-9 (n = 254) were correlated with lower RFS and OS than the combined cohorts with normal postoperative CA19-9 (n = 257) (both p < 0.001). The hazard function curves revealed that the risk of recurrence and mortality peaked earlier and higher in the elevated postoperative CA19-9 group than the other 2 groups. Multivariate analyses identified persistently elevated, rather than normalized, postoperative CA19-9 as an independent risk factor for shorter RFS and OS in ICC.ConclusionsElevated preoperative serum CA19-9 that normalizes after curative resection is not an indicator of poor prognosis in ICC. Patients with persistently elevated postoperative CA19-9 are at increased risk of recurrence and death.

Asymmetric Density for Risk Claim-Size Data: Prediction and Bimodal Data Applications

A new, flexible claim-size Chen density is derived for modeling asymmetric data (negative and positive) with different types of kurtosis (leptokurtic, mesokurtic and platykurtic). The new function is used for modeling bimodal asymmetric medical data, water resource bimodal asymmetric data and asymmetric negatively skewed insurance-claims payment triangle data. The new density accommodates the “symmetric”, “unimodal right skewed”, “unimodal left skewed”, “bimodal right skewed” and “bimodal left skewed” densities. The new hazard function can be “decreasing–constant–increasing (bathtub)”, “monotonically increasing”, “upside down constant–increasing”, “monotonically decreasing”, “J shape” and “upside down”. Four risk indicators are analyzed under insurance-claims payment triangle data using the proposed distribution. Since the insurance-claims data are a quarterly time series, we analyzed them using the autoregressive regression model AR(1). Future insurance-claims forecasting is very important for insurance companies to avoid uncertainty about big losses that may be produced from future claims.

A Two Parameters Rani Distribution: Estimation and Tests for Right Censoring Data with an Application

In this paper, we developed a new distribution, namely the two parameters Rani distribution (TPRD). Some statistical properties of the proposed distribution are derived including the moments, moment-generating function, reliability function, hazard function, reversed hazard function, odds function, the density function of order statistics, stochastically ordering, and the entropies. The maximum likelihood method is used for model parameters estimation. Following the same approach suggested by Bagdonavicius and Nikulin (2011), modified chi squared goodness-of-fit tests are constructed for right censored data and some tests for right data is considered. An application study is presented to illustrate the ability of the suggested model in fitting aluminum reduction cells sets and the strength data of glass of the aircraft window.

Change points in the hazard function of survival models

In this work, a chronological presentation of the main results and applications of the different investigations that analyze the problem of the change point in the hazard function of survival models is made, these include the constant hazard function by parts and Cox-type regression models with change points.

The Lindy effect in psychology: Network dynamics reinforce depression over time

This paper studies the factors that sustain mental disorders by taking a network approach. The network theory suggests that mental disorders are networks of symptoms that causally interact (Borsboom, 2017). Symptom networks share certain dynamics with other complex systems: abrupt transitions between stable states, critical slowing down and hysteresis (Cramer et al., 2016). These findings suggest that symptom networks that have transitioned to a pathological state tend to remain that state. We argue that this tendency leads to the Lindy effect in symptom networks. The Lindy effect means that the conditional probability of surviving beyond a time point, given survival until that time point, increases over time (Taleb, 2014). In other words, time benefits future survival. A symptom network is considered to have survived until a time point if it has remained in a pathological state until that point. We first show how the Lindy effect is formalised by examining the stopping time distribution of Brownian motion with an absorbing barrier (Cook, 2012; Taleb, 2018). Specifically, we describe the hazard function of the stopping time distribution and make a distinction between "strong Lindy" and "weak Lindy". Strong Lindy is a monotonically decreasing hazard function whereas weak Lindy means an inverted-U shaped hazard function. Then, major depressive disorder (MDD) networks were simulated, manipulating the level of symptom connectivity. As before, the presence of the Lindy effect in these networks were tested using hazard functions, and in addition, survival probabilities conditioned on time. Afterwards, we fit a distribution to the network lifetimes. The lifetime distribution of strongly connected networks were heavy tailed and showed the Lindy effect; the longer a network had been depressed, the more likely it was to remain depressed. The lifetime distribution of weakly connected networks were light tailed and did not show the Lindy effect. After discussing caveats and alternative explanations of the findings, we conclude that network dynamics and the resulting Lindy effect can explain several findings in psychology such as the chronicity of depression (Swaminath, 2009) and the frequency distribution of remission times (Simon, 2000; Patten et al., 2010).

Computing the Number of Failures for Fuzzy Weibull Hazard Function

The number of failures plays an important factor in the study of maintenance strategy of a manufacturing system. In the real situation, this number is often affected by some uncertainties. Many of the uncertainties fall into the possibilistic uncertainty, which are different from the probabilistic uncertainty. This uncertainty is commonly modeled by applying the fuzzy theoretical framework. This paper aims to compute the number of failures for a system which has Weibull failure distribution with a fuzzy shape parameter. In this case two different approaches are used to calculate the number. In the first approach, the fuzziness membership of the shape parameter propagates to the number of failures so that they have exactly the same values of the membership. While in the second approach, the membership is computed through the α-cut or α-level of the shape parameter approach in the computation of the formula for the number of failures. Without loss of generality, we use the Triangular Fuzzy Number (TFN) for the Weibull shape parameter. We show that both methods have succeeded in computing the number of failures for the system under investigation. Both methods show that when we consider the function of the number of failures as a function of time then the uncertainty (the fuzziness) of the resulting number of failures becomes larger and larger as the time increases. By using the first method, the resulting number of failures has a TFN form. Meanwhile, the resulting number of failures from the second method does not necessarily have a TFN form, but a TFN-like form. Some comparisons between these two methods are presented using the Generalized Mean Value Defuzzification (GMVD) method. The results show that for certain weighting factor of the GMVD, the cores of these fuzzy numbers of failures are identical.

Numerical solution of a Gamma - integral equation using a higher order composite Newton-Cotes formulas

The paper aims at solving a complex equation with Gamma - integral. The solution is the infected size (p) at equilibrium. The approaches are both numerical and analytical methods. As a numerical method, the higher-order composite Newton-Cotes formula is developed and implemented. The results show that the infected size (p) increases along with the shape parameter (k). But the increase has two phases: an increasing rate phase and a decreasing rate phase; both phases can be explained by the instantaneous death rate characteristics of the Gamma distribution hazard function. As an analytical method, the Extreme Value Theory consolidates the numerical solutions of the infected size (p) when k ≥ 1 and provides a solution limit ( p = 1 − 1 2 R ) as k goes to +∞.