Effect of inspection errors on imperfect production inventory model with warranty and price discount dependent demand rate

2020 ◽  
Vol 54 (4) ◽  
pp. 1189-1213 ◽  
Author(s):  
Amalesh Kumar Manna ◽  
Jayanta Kumar Dey ◽  
Shyamal Kumar Mondal
Keyword(s):  
Type I Error ◽  
Time Dependent ◽  
Selling Price ◽  
Type I ◽  
Development Cost ◽  
Price Discount ◽  
Dependent Development ◽  
Inspection Errors ◽  
Production Inventory ◽  
Inspection Process

This paper deals with selling price-discount and warranty period dependent demand in an imperfect production inventory model under the consideration of inspection errors and time dependent development cost. Normally, due to long-run, a production process deteriorates with time and here we assume that the process shifts from "in-control" to "out-of-control" state at any random time. A time dependent development cost has been constructed to increase the reliability of the production system i.e., to decrease the deterioration of the system during the production process. As a result, a few items are rejected. Here, two types of inspection errors such as Type-I error and Type-II error, have been considered during the period of product inspection process. In Type-I error, an inspector may choose falsely a defective item as non-defective and in Type-II error an inspector may choose falsely a non-defective item as defective. Due to these phenomena, the inspection process would consist of the following costs: cost of inspection, cost of inspection errors. The purpose of this paper is to investigate the effects of time dependent development cost on the defective items, selling price-discount and warranty policy on the market demand and finally optimize the expected average profit under consideration of such inspection costs in infinite time horizon. Some numerical examples along with graphical illustrations and sensitivity analysis are provided to test the feasibility of the model.

scholarly journals The Use of Mixed Models for the Analysis of Mediated Data with Time-Dependent Predictors

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
Emily A. Blood ◽  
Debbie M. Cheng
Keyword(s):  
Longitudinal Data ◽  
Mixed Models ◽  
Structural Equation ◽  
Structural Equation Models ◽  
Type I Error ◽  
Time Dependent ◽  
Type I ◽  
Delayed Effects ◽  
Causal Pathways ◽  
Observational Cohort

Linear mixed models (LMMs) are frequently used to analyze longitudinal data. Although these models can be used to evaluate mediation, they do not directly model causal pathways. Structural equation models (SEMs) are an alternative technique that allows explicit modeling of mediation. The goal of this paper is to evaluate the performance of LMMs relative to SEMs in the analysis of mediated longitudinal data with time-dependent predictors and mediators. We simulated mediated longitudinal data from an SEM and specified delayed effects of the predictor. A variety of model specifications were assessed, and the LMMs and SEMs were evaluated with respect to bias, coverage probability, power, and Type I error. Models evaluated in the simulation were also applied to data from an observational cohort of HIV-infected individuals. We found that when carefully constructed, the LMM adequately models mediated exposure effects that change over time in the presence of mediation, even when the data arise from an SEM.

scholarly journals Production Inventory Model under Time Dependent Demand, Uneven Manufacturing Rate and Manufacture Time Dependent Selling Price

2021 ◽  
Vol 23 (04) ◽  
pp. 225-237
Author(s):  
G.S. Buttar ◽  
◽  
Ruchi Sharma Sharma ◽  
Keyword(s):  
Production Rate ◽  
Production Efficiency ◽  
Inventory Model ◽  
Time Dependent ◽  
Selling Price ◽  
Production Inventory ◽  
Efficiency Cost ◽  
Manufacturing Time ◽  
Variable Production ◽  
Dependent Demand

In this paper, an inventory model for production of a single article with an uneven manufacturing rate and manufacturing time subsidiary selling cost has been considered. The considered production inventory model is accepted to create perfect items in beginning however because of different elements, after some time the production begins diminishing exponentially with time, i.e., the variable production rate has been thought of. The demand is time subordinate. Initially up to certain time, production rate remains constant. But after some time, due to various factors, production will decrease. Therefore, the efficiency (E) of such factors must be increased to get more production which can maintain the production efficiency cost which has been applied. Considering this fact inverse efficiency λ has been introduced in production rate. By utilizing differential calculus, expected maximum profit has been resolved. The goal of the examination is to decide the ideal arrangement for a production framework that expands the total benefit subject to certain limitations viable. Results are examined by means of a mathematical example to outline the hypothesis.

Inventory and pricing decisions for imperfect quality items with inspection errors, sales returns, and partial backorders under inflation

2020 ◽  
Vol 54 (1) ◽  
pp. 287-306 ◽  
Author(s):  
Aditi Khanna ◽  
Aakanksha Kishore ◽  
Biswajit Sarkar ◽  
Chandra K. Jaggi
Keyword(s):  
Optimal Solution ◽  
Selling Price ◽  
Type I ◽  
Discounted Cash Flow ◽  
Screening Process ◽  
Imperfect Quality ◽  
Decision Variables ◽  
Proposed Model ◽  
Price Order ◽  
Inspection Process

In this paper, an optimal replenishment inventory policy for imperfect quality items is presented with a selling price-dependent demand under inflationary conditions using a discounted cash flow (DCF) approach. Due to the presence of defectives in the system, all items go through a 100% inspection process. However, the screening process is also considered to be imperfect and involves errors, namely Type-I and Type-II. In addition, shortages are allowed and are partially backlogged. An optimal solution for the proposed model is derived by maximizing the expected profit function by jointly optimizing three decision variables: selling price, order quantity, and backorder level. To validate the theoretical results, a numerical example along with comprehensive sensitivity analysis is offered. The model has pertinence in industries like textiles, electronics, furniture, footwear, automobiles, and plastics.

An EPQ Model for Deteriorating Items With Imperfect Production, Two Types of Inspection Errors and Rework Under Complete Backordering

2020 ◽  
Vol 22 (02) ◽  
pp. 2040011
Author(s):  
Chayanika Rout ◽  
Debjani Chakraborty ◽  
Adrijit Goswami
Keyword(s):  
Type I Error ◽  
Type I ◽  
Lot Size ◽  
Inventory Cost ◽  
Inspection Errors ◽  
Imperfect Production ◽  
Constant Rate ◽  
Epq Model ◽  
Total Inventory ◽  
Production Lot Size

This paper presents an EPQ model which illustrates imperfect production and imperfect inspection processes for items that are subject to a constant rate of deterioration. The model considers two types of inspection errors, namely, Type I error of falsely screening out a proportion of nondefects, thereby passing them on for rework and Type II error of falsely not screening out a proportion of defects, thus selling those to customers which results in defect sales returns. The screened and returned items are then reworked and the proportion that could not be reworked successfully is scrapped. Shortages are allowed and are completely backlogged. Finally, we calculate the optimal production lot size and the optimal backordering quantity in order to minimize the total inventory cost per unit time. A numerical example is also considered to exemplify the obtained theoretical results which is followed by the complete sensitivity analysis of the involved parameters for even better managerial insights.

scholarly journals Supply Chain with Customer-Based Two-Level Credit Policies under an Imperfect Quality Environment

Mathematics ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 299 ◽  
Author(s):  
Aditi Khanna ◽  
Aakanksha Kishore ◽  
Biswajit Sarkar ◽  
Chandra Jaggi
Keyword(s):  
Supply Chain ◽  
Trade Credit ◽  
Type I Error ◽  
Type I ◽  
Purchase Cost ◽  
Misclassification Errors ◽  
Inspection Process ◽  
Total Profit ◽  
The Impact ◽  
New Retailers

The present model develops a three-echelon supply chain, in which the manufacturer offers full permissible delay to the whole seller, while the latter, in turn, adopts distinct trade credit policies for his subsequent downstream retailers. The type of credit policy being offered to the retailers is decided on the basis of their past profiles. Hence, the whole seller puts forth full and partial permissible delays to his old and new retailers respectively. This study considers bad debts from the portion of new retailers who fail to make up for the delayed part of the partial payment. The analysis shows that it is beneficial for the whole seller to make shorter contracts, particularly with new retailers, along with the fetching of a higher fraction of initial purchase cost from them. In addition to the above-described scenario, the lot received by the whole seller from the manufacturer is not perfect, and it contains some defects for which he employs an inspection process before selling the items to the retailers. In order to make the study more realistic, Type-I, as well as Type-II misclassification errors, and the case of out-of-stock are considered. The impact of Type-I error has been found to be crucial in the study. The present paper determines the optimal policy for the whole seller by maximizing the expected total profit per unit time. For the optimality of the solution, theoretical results are provided. Finally, a numerical example and a sensitivity analysis are done to validate the model.

Smoothing Facilitates the Detection of Coupled Responses in Psychophysiological Time Series

2000 ◽  
Vol 14 (1) ◽  
pp. 1-10 ◽  
Author(s):  
Joni Kettunen ◽  
Niklas Ravaja ◽  
Liisa Keltikangas-Järvinen
Keyword(s):  
Time Series ◽  
Type I Error ◽  
Electrodermal Activity ◽  
Moving Average ◽  
Type I ◽  
Facial Electromyography ◽  
Response Characteristics ◽  
Smoothing Methods ◽  
Response Systems ◽  
Different Response

Abstract We examined the use of smoothing to enhance the detection of response coupling from the activity of different response systems. Three different types of moving average smoothers were applied to both simulated interbeat interval (IBI) and electrodermal activity (EDA) time series and to empirical IBI, EDA, and facial electromyography time series. The results indicated that progressive smoothing increased the efficiency of the detection of response coupling but did not increase the probability of Type I error. The power of the smoothing methods depended on the response characteristics. The benefits and use of the smoothing methods to extract information from psychophysiological time series are discussed.

One Size Fits All?

Methodology ◽  
2012 ◽  
Vol 8 (1) ◽  
pp. 23-38 ◽  
Author(s):  
Manuel C. Voelkle ◽  
Patrick E. McKnight
Keyword(s):  
Repeated Measures ◽  
Structural Equation ◽  
Type I Error ◽  
Equation Modeling ◽  
Type I ◽  
Finite Sample ◽  
Traditional Methods ◽  
Repeated Measures Anova ◽  
Special Cases ◽  
Latent Curve

The use of latent curve models (LCMs) has increased almost exponentially during the last decade. Oftentimes, researchers regard LCM as a “new” method to analyze change with little attention paid to the fact that the technique was originally introduced as an “alternative to standard repeated measures ANOVA and first-order auto-regressive methods” (Meredith & Tisak, 1990, p. 107). In the first part of the paper, this close relationship is reviewed, and it is demonstrated how “traditional” methods, such as the repeated measures ANOVA, and MANOVA, can be formulated as LCMs. Given that latent curve modeling is essentially a large-sample technique, compared to “traditional” finite-sample approaches, the second part of the paper addresses the question to what degree the more flexible LCMs can actually replace some of the older tests by means of a Monte-Carlo simulation. In addition, a structural equation modeling alternative to Mauchly’s (1940) test of sphericity is explored. Although “traditional” methods may be expressed as special cases of more general LCMs, we found the equivalence holds only asymptotically. For practical purposes, however, no approach always outperformed the other alternatives in terms of power and type I error, so the best method to be used depends on the situation. We provide detailed recommendations of when to use which method.

Assessing Person Fit With the Information Matrix Test

Methodology ◽  
2015 ◽  
Vol 11 (1) ◽  
pp. 3-12 ◽  
Author(s):  
Jochen Ranger ◽  
Jörg-Tobias Kuhn
Keyword(s):  
Simulation Study ◽  
Type I Error ◽  
Information Matrix ◽  
Small Samples ◽  
Type I ◽  
Person Fit ◽  
Power Of The Test ◽  
Order Expansion ◽  
Trait Stability ◽  
Information Matrix Test

In this manuscript, a new approach to the analysis of person fit is presented that is based on the information matrix test of White (1982) . This test can be interpreted as a test of trait stability during the measurement situation. The test follows approximately a χ2-distribution. In small samples, the approximation can be improved by a higher-order expansion. The performance of the test is explored in a simulation study. This simulation study suggests that the test adheres to the nominal Type-I error rate well, although it tends to be conservative in very short scales. The power of the test is compared to the power of four alternative tests of person fit. This comparison corroborates that the power of the information matrix test is similar to the power of the alternative tests. Advantages and areas of application of the information matrix test are discussed.

How to Detect Publication Bias in Psychological Research

2019 ◽  
Vol 227 (4) ◽  
pp. 261-279 ◽  
Author(s):  
Frank Renkewitz ◽  
Melanie Keiner
Keyword(s):  
Publication Bias ◽  
Effect Size ◽  
Statistical Power ◽  
Type I Error ◽  
Psychological Research ◽  
Type I ◽  
True Effect Size ◽  
Questionable Research Practices ◽  
True Effect ◽  
Meta Analyses

Abstract. Publication biases and questionable research practices are assumed to be two of the main causes of low replication rates. Both of these problems lead to severely inflated effect size estimates in meta-analyses. Methodologists have proposed a number of statistical tools to detect such bias in meta-analytic results. We present an evaluation of the performance of six of these tools. To assess the Type I error rate and the statistical power of these methods, we simulated a large variety of literatures that differed with regard to true effect size, heterogeneity, number of available primary studies, and sample sizes of these primary studies; furthermore, simulated studies were subjected to different degrees of publication bias. Our results show that across all simulated conditions, no method consistently outperformed the others. Additionally, all methods performed poorly when true effect sizes were heterogeneous or primary studies had a small chance of being published, irrespective of their results. This suggests that in many actual meta-analyses in psychology, bias will remain undiscovered no matter which detection method is used.

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