Desirability functions are popular as a simple computationally-efficient way of combining multiple objectives onto a common scale for comparison and optimization. They are flexible, intuitive and encourage consideration of more than one criterion when choosing a winner. However, they are also prone to flawed implementation as they are sensitive to scaling and choice of user priorities, may lead to mediocre solutions for any individual criterion, and can discourage thoughtful consideration of the merits and weaknesses of individual solutions. In this paper we present the strengths and weaknesses of desirability functions, as well as some alternatives that can lead to better, more natural and thoughtful decision-making. We also highlight some applications where desirability functions are indeed useful tools for achieving desired outcome.
Modern engineering components, such as wind turbine blades, satellite parts, roofing systems, and infrastructure materials, are expected to remain operational for decades despite being prone to gradual degradation. Standard reliability tests under normal service conditions are often infeasible because of the long service life, high costs, and low failure rates of these systems. Accelerated tests have been widely adopted to address this issue by exposing materials to elevated stressors-such as temperature, moisture, or voltage-to speed up degradation and measure degradation responses, allowing for earlier data collection. Accelerated destructive degradation tests (ADDTs) obtain degradation measurements through destructive sampling, often before a unit has failed, providing earlier insights into aging behavior. These tests are particularly useful when studying material-level degradation, offering more precise modeling of how experimental variables influence degradation rates. This study aims to model the degradation behavior of a rubber compound under accelerated conditions and to derive the induced failure-time distribution based on the fitted degradation model that supports predictive reliability analysis.
Accelerated destructive degradation tests (ADDTs) have been devised to obtain reliability informations regarding highly reliable products that do not survive the measurement process. Majority of existing ADDT models consider independent effects of various stress factors, ignoring their possible interactions. Various studies in engineering evident that these interactions significantly affect the degradation process. This article introduces an ADDT framework to study the effect of multiple stress factors and their interactions on a product's life. The degradation process is formulated using Wiener process and a generalized log-linear (GLL) stress-life relationship. The estimates of the model parameters and quantile lifetimes are obtained using approximation as well as numerical methods. Optimal test plans are obtained under D-optimality and V-optimality criteria. Simulation study is carried out for numerical illustrations, and a real data set concerning the thermal damage in a sandstone is analyzed. Robustness of the proposed model is examined under stress-dependent diffusion parameter.
In the practical implementation of experimental designs, randomizing the order of runs often results in numerous level changes for factors and does not necessarily mitigate the influence of nuisance factors. Consequently, the literature highlights that using a pre-established sequence with few level changes and strong protection against external effects is advantageous, because it lowers costs and reduces estimation bias. This paper introduces the rob library, an R package, and its associated Shiny web app, which together generate run orders for full factorial designs that simultaneously control bias and the number of level changes, providing an accessible computational framework for run order generation in real experimental settings. Both tools are based on the Assignment-Expansion method.
Statistical Process Control (SPC) is traditionally based on a two-phase framework: a reference sample is required to estimate in-control parameters (Phase I) before active monitoring (Phase II) begins. However, in many contemporary industrial and service settings, such a sample is either unavailable or heavily contaminated by heterogeneity, structural changes, or sporadic anomalies. Under these conditions, classical Phase I and Phase II schemes are difficult to justify. This challenge arose while attempting to remotely monitor industrial printers, prompting a search for alternatives that led to the Bayesian outlier framework proposed by Box and Tiao. This article revisits that framework and argues that its core principles provide a coherent basis for SPC when reliable Phase I data are absent. In the Box and Tiao formulation, observations arise from a mixture of two components sharing a common mean but differing in dispersion; this allows for simultaneous parameter estimation and outlier identification through posterior probabilities. Using the industrial printer case as a primary example, this article demonstrates how this logic can be extended from the original Normal distribution to Poisson data - such as error counts - which are frequently encountered in SPC applications.
Monitoring changes in the occurrence probability of target events is crucial in many fields, such as healthcare and industrial systems, to ensure timely and effective management decisions. Risk-adjusted models, which incorporate covariate information, are commonly used to estimate these probabilities. However, when actual risk increases, relying solely on event outcomes may delay the detection of potential changes, affecting management decisions. To address this issue, various risk-adjusted control charts have been proposed. Most existing schemes focus on monitoring changes in risk-adjusted model coefficients (e.g., slope and intercept), which may limit their flexibility when risk fluctuations deviate from parametric assumptions. In this study, we propose a risk-adjusted exponentially weighted moving average control chart based on a Bayesian framework. By integrating risk-adjusted expected values as prior information, this scheme directly monitors risk levels, providing a more intuitive and flexible detection mechanism. This newly proposed control chart is designed to monitor small shifts in the failure rate of a Bernoulli distribution. Monte Carlo simulations demonstrate that the proposed method outperforms the existing charts in monitoring small and moderate shifts. Finally, two real-world case studies on ICU patient monitoring and displacement monitoring are used to illustrate the practical applicability of the proposed approach.
The traditional Six Sigma toolkit presents significant limitations for problem solving in Industry 4.0 settings. To address these limitations, it can be extended with latent variable-based multivariate statistical techniques such as Principal Component Analysis (PCA) and Partial Least Squares (PLS), in what has been referred to as multivariate Six Sigma. In this work, this approach is applied to address vibration performance issues in the caliper, a key component of a car's braking system. By appropriately integrating these techniques into the five-step DMAIC cycle, the root cause was satisfactorily identified, an effective corrective action was implemented, and the objectives of the project were successfully achieved. This case study provides further evidence of the practical utility of multivariate Six Sigma and demonstrates its potential for broader adoption in industrial projects.
This study presents a comprehensive framework for designing and evaluating split-plot order-of-addition (SP-OofA) experiments. The proposed method aims to develop D-optimal SP-OofA designs to maximize the efficiency of estimating both whole-plot and subplot effects. We introduce a systematic algorithm that incorporates a point-exchange method to iteratively refine the design, ultimately identifying the D-optimal design. Through an example in pharmaceutical formulation, the D-optimal SP-OofA design achieved an improvement of nearly 50% in D-efficiency compared to the original design. A simulation study further demonstrates the superiority of D-optimal SP-OofA designs in terms of statistical power and design efficiency. This research contributes to the methodology of OofA experiments with split-plot structures, providing a practical solution for high-efficiency experimental design in fields, such as pharmaceuticals, material science, and manufacturing.
Ron Kenett is an applied statistician with a career in industry, in academia and in consulting. This perspective provides a unique point of view on the role and future of statistics in industry, healthcare, services and academia. He earned a B.Sc. in mathematics, with first class honors, at Imperial College in London, and took his Ph.D. under Prof. Samuel Karlin at Stanford and the Weizmann Institute in Israel. He is a recipient of the Greenfield Medal of the Royal Statistical Society in the UK, Box Medal of the European Network of Business and Industrial Statistics (ENBIS) and life achievement award by the Israel Society for Quality. Ron is past President of ENBIS and of the Israel Statistical Association and author and coauthor of 18 books and over 250 papers. This discussion provides a glance at Ron's career and his views on statistics.
In multivariate statistical process control, Hotelling's T2 control chart (HT chart) is a powerful tool for detecting shifts in a process's overall mean. However, when a process falls out of control, the HT chart only signals an issue without identifying the specific variables responsible for the deviation. To address this limitation, traditional approaches decompose the overall T2 statistic into T2 statistics of individual variables or higher-order interaction terms. While informative, this approach becomes computationally challenging and less effective as the number of variables increases. In this study, we propose a new procedure based on the Shapley value, widely applied in machine learning to quantify variable importance in predictions. In this approach, we consider the T2 statistic as a value function for each subset of variables and employ Shapley sampling and KernelSHAP to estimate Shapley values in high dimensional data. Most importantly, we develop a procedure to identify variable causing the out of control signal using Shapley values, demonstrating that Shapley values serve as an e-value. We numerically compare the performance of this new Shapley-based procedure with two existing procedures: the Mason-Tracy-Young and the adaptive step-down procedures. Finally, we apply these procedures to detect changes in the monthly temperature of Seoul after the year 2000.
The design, monitoring, improvement, and control of processes of all types creates a continual flow of problems that must be solved for processes to perform as designed, and effectively and efficiently serve customers. As a result, various types of problems arise, and numerous problem-solving methods have been developed to address these problems. Using the principles of statistical engineering, this research develops a framework that integrates problem types and problem-solving strategies. The proposed framework introduces a structured decision logic based on several dimensions, including: the fundamental intent of intervention (fixing, improving, or creating), whether the solution direction is known or must be discovered, and the availability of sufficient problem-relevant data. The framework is designed to help practitioners choose the most effective problem-solving methodology for each unique challenge. This work emphasizes that the problem and its characteristics should drive the selection of tools, not the other way around. While this framework can be useful in practice, it should serve only as a guide to problem-solving, not the dictator of the approach. That is, the framework should work for the practitioner, not the other way around. The framework is illustrated using four real problems from our collective experience.
Ronald J.M.M. Does is Professor Emeritus of Industrial Statistics at the University of Amsterdam and was founder and director of IBIS UvA, the Institute for Business and Industrial Statistics for many years. He has supervised 25 PhD research students, focusing on control charts, Lean Six Sigma, healthcare, and statistical engineering. In addition, he has educated and mentored more than three thousand Green and Black Belts.
Problem-solving is central to contributions that statisticians and data scientists can make as part of collaborative interdisciplinary teams. Mastering getting up to speed quickly with a problem, identifying the critical aspects of a problem, as well as assessing how statistics can improve the solution are all important aspects of becoming a valued and valuable contributor to solving complex problems. In this article, we explore three general problem-solving tactics that can increase the impact of statisticians and build confidence with tackling messy multi-stage problems. Problem decomposition focuses on breaking large messy problems into manageable pieces. Approximation identifies key components of a complex problem that can help prioritize resources, maximize improvement opportunities improvement and identify areas of weakness. Analogies leverage successful results used in closely or more-distantly related areas that provide ideas or lead to potential paths to solutions. We discuss aspects of these general approaches where statisticians can make unique contributions. A complex problem tackled by a team including the two authors illustrates how the different tactics were used and combined for an enhanced solution. We also share ideas for how teaching and practicing these skills can be incorporated into statistics/data science training and our daily lives.
Process capability indices are commonly used to summarize a process's capability based on a single quality characteristic. However, modern production processes usually involve multivariate and often correlated quality characteristics, rendering univariate indices insufficient to fully assess the capability of a process. This has led to the development of multivariate process capability indices (MPCI). Even though various index formulations have been proposed in the literature, they differ greatly in their approach, interpretation and sensitivity to the parameters such as the "non-centeredness" of the process and the number of the quality characteristics as well as their correlation structure. In this Quality Quandaries, we examine a selection of the available MPCI. We then conduct a sensitivity analysis to examine how these indices respond to changes in certain process parameters. Finally, we illustrate these findings using a case study and emphasize the need for careful interpretation when applying MPCI in practice.
