Journal of Quality Engineering and Management

Abstract Purpose: The objective of the present study is to determine an optimal configuration in terms of the type and number of components in order to maximize system availability and reduce costs, using an active redundancy allocation strategy, while considering load-sharing capability and the use of maintenance personnel under maintenance and leave policies, in the electrical power distribution system of a marine vessel. In the active redundancy strategy, all additional components and subsystems are operated simultaneously from the start of system operation, and the system fails only when all components have failed.
Methodology: In this study, a bi-objective model is developed for an electrical power distribution system with active redundancy in a marine vessel, where the first objective is minimization of total cost and the second objective is maximization of system availability. System behavior is simulated using a Markov chain and a phase-type distribution, and the model is solved using the Non-dominated Sorting Genetic Algorithm II (NSGA-II). Failure of one component affects the failure rates of other components within the same subsystem, leading to an increase in their failure rates. In other words, the problem is analyzed under a load-sharing condition. A single repairman is considered for equipment repair. The maintenance and leave policy is defined such that if a component fails during the repairman’s leave period, the leave is terminated and repair of the failed component begins immediately. If another component fails while a component is under repair, it is placed in a repair queue, and the repairman starts repairing the next failed component immediately after completing the repair of the previous one. When the repairman is on leave and no component failure occurs, the repairman may resume the leave period.
Findings: The results of the study identify the optimal combination of the type and number of electrical power distribution panels in each subsystem of the vessel’s electrical power distribution system, aimed at increasing system availability and reducing costs through the use of active redundancy. In addition, the results provide the probability of the repairman being busy, which can support managerial decision-making regarding maintenance and leave policies.
Originality/Value: Considering the innovative aspects of the study, the results can be effectively used for engineering analyses, particularly in evaluating system availability, as well as for managerial analyses, including cost estimation and the allocation of maintenance personnel.

Abstract Purpose: This study aims to determine the optimal model within the family of queueing models, where interarrival times follow an exponential distribution and service times follow an Erlang distribution, under a finite stopping time TTT. The significance of this research lies in its application to optimizing the performance of service systems using queueing theory.
Methodology: To select the optimal model, a cost function and a performance metric, namely the average customer satisfaction level, are first defined. Subsequently, a new index, named ORS, is introduced based on the cost function, average customer satisfaction, and the system's stability probability. The optimal model is identified as the one with the highest ORS value. Numerical analysis is employed to demonstrate the procedure for determining the optimal model.
Findings: The numerical results indicate that the ORS index is an effective criterion for evaluating and comparing different queueing models, enabling optimal model selection by incorporating multiple performance aspects.
Originality/Value: The main contribution of this research is the introduction of the ORS index as a novel and comprehensive measure for optimal model selection in queueing systems. This approach can enhance service system design and improve customer satisfaction levels in practical applications.

Abstract Purpose: This paper aims to estimate the parameters of the Weibull distribution using a genetic algorithm and compare its performance with traditional estimation methods.
Methodology: A simulation study was conducted under different sample sizes and censoring levels. The genetic algorithm was applied to maximize the likelihood function.
Findings: The results show that the genetic algorithm provides more accurate and stable parameter estimates compared to the maximum likelihood method, especially in the presence of censored data.
Originality/Value: This study presents a novel application of genetic algorithms in reliability analysis, demonstrating their effectiveness in parameter estimation for censored datasets.

Abstract Purpose: This paper aims to compare and examine the statistical properties of four common estimators of process standard deviation for grouped data in statistical quality control.
Methodology: To achieve the research objectives, the bias and the Mean Squared Error (MSE) of the estimators will first be presented. Then, the estimators will be compared based on their MSEs.
Findings: It is shown that two estimators out of four estimators belong to two different classes of linear unbiased estimators with the minimum variance. Furthermore, numerical calculations show that the estimator based on the arithmetic mean of the group standard deviations is more efficient than the other estimators.
Originality/Value: Based on the results obtained in this study, it is suggested that for estimating the standard deviation of the process in grouped data, an estimator based on the arithmetic mean of the standard deviations of the groups should be used instead of estimators that are based on the arithmetic mean of the ranges of the groups.

Abstract Purpose: This study aims to optimize warranty periods for complex products by examining the role of warranties in customer retention and cost management. The proposed model uses a mixed statistical distribution to simultaneously model minor and major failures, seeking to minimize the product's life-cycle cost while maintaining customer satisfaction.
Methodology: The mathematical model defines life-cycle costs, establishes an objective function to minimize total costs, and determines the optimal warranty period. A numerical example and sensitivity analysis are used for validation, and the model is solved using Maple 2024.
Findings: The optimal warranty period was identified as 3.5-4.5 time units, and the model achieved a 23% cost reduction compared to conventional methods. Sensitivity analysis showed that changes in failure probability and failure rate directly affect the optimal warranty length.
Originality/Value: Using a mixed statistical distribution to model different failure types simultaneously offers an innovative, more realistic approach. This model provides a practical tool for adjusting warranty policies and reducing life-cycle costs, with potential for further development by incorporating dependent failures and real-world data.

Abstract Purpose: In statistical data analysis and modeling, assessing the similarity or divergence between two probability distributions is of great importance. One of the most widely used metrics for this purpose is the Kullback-Leibler (KL) divergence, which quantifies the informational distance between distributions. This study aims to analyze the KL divergence between two normal distributions with equal variance and to compare the performance of different estimation methods for this measure.
Methodology: In this study, the exact value of the Kullback–Leibler divergence between two normal distributions with equal variance is first analytically derived, and then three estimation methods (maximum likelihood, Bayesian, and shrinkage) are proposed to estimate this measure. The performance of each estimator is evaluated via Monte Carlo simulations using the Mean Squared Error (MSE) criterion.
Findings: The simulation results indicate that the Bayesian estimator outperforms the MLE in terms of estimation accuracy. Furthermore, the shrinkage estimator performs best, achieving the lowest MSE among the three methods. This argument suggests that incorporating prior information or penalization techniques can significantly improve estimation quality.
Originality/Value: This study contributes to the literature by providing a detailed comparison of classical and modern estimation techniques for KL divergence in the context of normal distributions with equal variance. The novelty lies in integrating shrinkage methodology and demonstrating its superior performance, which is quantitatively validated through simulations. The findings have practical implications across fields such as machine learning, signal processing, and information theory.

Abstract Purpose: Reliability is one of the most critical quality characteristics of components, products, and systems. Unlike other attributes, it cannot be directly measured and is usually evaluated only after significant operational time under real conditions. However, waiting for long-term field data may reduce market competitiveness in commercial industries and pose serious safety risks in sensitive systems such as military equipment. Therefore, reliability prediction plays a vital role in key decision-making areas such as product release timing, warranty policies, and maintenance planning. This study aims to present an integrated model based on accelerated degradation testing and accelerated life testing to predict the lifetime of a turbine engine nozzle under operational conditions.
Methodology: Initially, the ADT was designed and conducted to monitor the degradation trend of the nozzle's critical feature at various temperature and time levels. Using the power-law and Arrhenius acceleration models, acceleration parameters and the activation energy were estimated. Subsequently, the ALT was performed under high-stress thermal conditions using the extracted parameters, and the corresponding failure times were recorded. Finally, by integrating the results of both tests and applying statistical methods such as maximum likelihood estimation and degradation path modeling, the system's lifetime distribution was modeled.
Findings: The implementation of the proposed model on a turbine engine nozzle demonstrated its ability to predict lifetime accurately and to reduce testing time and cost significantly.
Originality/Value: This model introduces a novel analytical framework that systematically combines two testing methods (ADT and ALT), with the output of one serving as input to the other. The proposed approach can be generalized and applied to other critical industrial and defense-related products.

Abstract Purpose: This study aims to develop a mathematical model for flexible job shop scheduling. The primary focus is on optimizing three objectives: the makespan, the maximum machine workload, and the total workload. The ultimate goal is to enhance productivity and flexibility in manufacturing systems.
Methodology: Two metaheuristic algorithms, NSGA-II and MOGWO, were used to solve the model. The model was first validated on a small scale, and then a sensitivity analysis was conducted on larger instances. The performance of the algorithms was compared based on accuracy and solution quality metrics.
Findings: The results indicate that MOGWO performs better on medium-sized problems, whereas in large-scale cases, the difference between the two algorithms is not significant. The highest sensitivity was observed among the objectives regarding production and maintenance costs. Additionally, a resource-allocation pattern and an optimal sequence of operations were derived.
Originality/Value: The originality of this research lies in developing and applying a multi-objective mathematical model for flexible job-shop scheduling that considers real-world constraints, including costs and resource limitations. The simultaneous use and detailed comparison of NSGA-II and MOGWO across different problem sizes is another contribution. Furthermore, the proposed operational pattern improves the applicability of the results in industrial environments.

Abstract Purpose: The main goal of this study is to propose a realistic and practical model for the economic-statistical design of control charts in the presence of multiple independent assignable causes under the Burr Type XII shock model. The model aims to minimize the underestimation of the actual cost per unit time of the quality cycle.
Methodology: This research utilizes the Burr Type XII distribution as a shock model to develop the RED model for optimal design of control charts. The Lorenz and Van cost function is also extended to account for multiple assignable causes, and a numerical example is provided to demonstrate the solution approach.
Findings: Numerical results reveal that the proposed model outperforms existing models in accurately estimating the real cost per unit time of the quality cycle. Furthermore, an increase in the shock probability leads to a non-decreasing trend in the average cost, underscoring the importance of accounting for this probability in E(A) calculations.
Originality/Value: This is the first study to employ the Burr Type XII distribution as a shock model in the economic-statistical design of control charts. By extending existing cost models, the paper introduces a novel and realistic approach to designing control charts in the presence of multiple independent shocks.

Abstract Purpose: In many industrial processes, there are situations where simultaneous monitoring and control of two or more dependent variables are necessary. In such cases, univariate control of quality characteristics can be misleading when considered independently. In the classical approach, when a quality characteristic falls outside the specified technical limits, the quality loss is regarded as a cost. All products within the technical limits of the quality characteristic are assumed to have similar quality, regardless of the deviation of the quality characteristic from its target value. However, it is essential to distinguish between products that fall within the technical limits of the quality characteristic, as any deviation from the target value incurs a proportional loss.
Methodology: This paper introduces, for the first time in the literature, a reflected normal loss function to determine the average cost of producing non-conforming products when two quality characteristics are evaluated. In summary, this study focuses on the statistical-economic design of a multivariate T²-Hotelling control chart with multivariate variable sampling intervals in the presence of a reflected normal multivariate loss function (RNLMVSIT²). Additionally, a sensitivity analysis is conducted to examine the effects of time and cost parameters on the design parameters and the average cost.
Findings: The results demonstrate the satisfactory performance of the proposed models.
Originality/Value: This paper introduces, for the first time in the literature, a reflected normal loss function to determine the average cost of producing non-conforming products when two quality characteristics are evaluated.

Abstract Purpose: This study aims to improve diesel engine reliability estimation by using a risk-based model that incorporates key environmental factors, especially wear particles in engine oil, for more accurate analysis than traditional time-based methods.
Methodology: The Proportional Hazards Model (PHM) was used to assess engine reliability based on wear particles in oil. The Harrell and Lee test checked model assumptions, and the Wald test validated coefficients. Reliability was then compared across two engine groups under different conditions.
Findings: The study's results showed that incorporating risk factors, such as the level of wear particles in engine oil, increases the accuracy of reliability estimation for diesel engines. Specifically, it was found that engine age, maintenance status, and operational conditions significantly impact reliability, such that worn-out engines reach lower levels of reliability more quickly. The proposed model, by providing a more precise analysis, can serve as an effective tool for optimizing maintenance scheduling and preventing unexpected failures in industrial systems.
Originality/Value: This research's primary distinction lies in the integration of qualitative data related to the internal condition of the engine (wear particles in oil) with advanced statistical models of PHM, which has been less addressed in previous studies. This approach, by creating a link between condition-based data analysis and reliability analysis, opens new horizons for condition-based maintenance planning.

Abstract Purpose: Calculating the optimal target mean for a process is recognized as an essential research area, with many proposed models in the literature. Previous studies have typically focused on a single market. The main difference in this research lies in the number of markets considered; unlike previous works, this study examines n different markets simultaneously.
Methodology: This study aims to determine the optimal process quality mean for a limited number of markets based on the target values of quality characteristics in each market. We propose a model to calculate this optimal mean across n markets with different price/cost structures. A key innovation of this research is the incorporation of probability distributions that reflect the likelihood of the quality characteristic falling within specific quality ranges in each market.
Findings: The model considers the probability that the quality characteristic falls within each market's defined quality range. To analyze and solve the model, absorbing Markov chains are used. A numerical example is presented in which the model is applied to two markets, and the optimal target mean and corresponding optimal revenue are obtained.
Originality/Value: Based on the results from the numerical example, the optimal target mean and revenue were determined for the two markets. A sensitivity analysis was conducted to assess the influence of various model parameters on these parameters, demonstrating how changes in parameters impact the model's outcomes.