Research

Industrial Engineer, Feb 2008 by Yano, Candace

Sometimes it's difficult to predict the moral of the story, which is true of quality-related decisions. In the first article highlighted below, the moralisthat most of the time, a simple approach (Shewhart charts) works nearly as well as a more complicated one (Cusum charts). The second article has the opposite message: Takinginto account degradation over a product's life when setting manufacturing specifications is much better economically and leads to much longer, useful lives. The articles from which these summaries are drawn appear in the February 2008 issue oF IIE Transactions (Vol. 40, No. 2).

Cusum or Shewhart?

Choosing the right quality monitoring process is not an easy task: there are many options, and the economic implications of implementing each of them is not obvious. This was the problem facing Philkeram-Johnson S.A., a major Greek manufacturer of ceramic tiles with a work force of more than 400 employees. The company needed to identify the economically optimal statistical online monitoring scheme for a critical quality characteristic during the tile formation stage in the press. This characteristic is related to the penetrability of tiles, which is directly related to the dimensions of the final product. The company sought the advice of a research team headed by George Tagaras, Ph.D., of the Aristotle University of Thessaloniki, Greece.

The research team initially attempted a comprehensive comparison of alternative process monitoring schemes from an economic point of view. At one end of the spectrum is the standard Shewharttype chart, and at the other end is the elaborate, fully adaptive Bayesian control chart. The cusum (or, cumulative sum control) chart falls in between.

The researchers discovered that published results of previous investigations regarding the relative economic effectiveness of Shewhart and cusum charts the two types most commonly used in practice - were contradictory and inconclusive. Consequently, they decided to explore the differences in more depth. Tagaras asked his then-doctoral student George Nenes, Ph.D., to participate in that project.

In "An Economic Comparison of Cusum and Shewhart Charts," Nenes and Tagaras present a new, accurate method to compute the average quality-related cost per unit time. Using this tool, they performed a systematic numerical investigation of the conditions under which it is worth using a cusum chart instead of the simpler Shewhart chart.

The main finding of their investigation is that the economic superiority of the cusum scheme is substantial only when the sample sizes must be unitary (i.e., when rational grouping of observations is infeasible) or when the sample sizes are restricted to be very small. Therefore, many firms can elect to use the easier-to-implement Shewhart charts with the confidence that they are not making a big sacrifice from an economic standpoint.

Contact George Tagaras; tagaras@auth.gr; 30-2310-996062; Department of Mechanical Engineering, Aristotle University of Thessaloniki, Thessaloniki 54124, Greece

Optimizing specifications

Many characteristics of a product, such as the diameter of a piston ring and the thickness of a brake pad, are subject to degradation. During product use, those characteristics degrade, resulting in the deterioration of the product's performance. How should one determine the manufacturing specifications for such characteristics? Traditionally they have been chosen to maximize the quality of the product when it is new. But if the characteristic is affected by degradation, then this may not be the optimal choice with respect to the performance of the product over time.

By sacrificing quality at the initial stage of the product's use, one might be able to improve the reliability of the product and increase its lifetime. Therefore, the specifications for degrading characteristics should be chosen to maximize the quality as well as the reliability. For example, the optimal manufacturing target for the diameter of a piston ring or the thickness of a brake pad should be determined not only by quality but also by accounting for the wear that can happen over time. Products designed this way will have better performance and will last longer, on average. The idea of integrating quality and reliability into product design is not a new concept, but a formal and scientific approach for developing manufacturing specifications is needed.

In "Optimal Specifications for Degrading Characteristics," professors V. Roshan Joseph of Georgia Institute of Technology and I-Tang Yu of Tunghai University in Taiwan provide a mathematical formulation of the problem and develop a method for finding the optimal manufacturing target using stochastic optimization methods. Their method uses a degradation model that quantifies how the key characteristic changes over time. The degradation model forms the foundation for a quality loss function that captures both quality and reliability of the product.

In applying their method to several examples, the authors show that products should be designed differently when degradation is taken into consideration. Manufacturers who adopt this strategy may be able to charge a premium and enjoy stronger market shares due to superior quality and greater durability of their products.