Development of robust design optimization using incomplete data

In robust design, the main goal is to select the levels of the controllable factors to obtain the optimal operating conditions. To this end, Taguchi recommends that statistical experimental design methods be employed. To adopt his approach, we need to observe a number of replicated observations at each design point. A commonly used assumption behind the data collection procedure is that all the data are fully observed. However, in many industrial experiments, interval-censored observations are frequently available in addition to the fully observed observations. For example, the products are often inspected by a ‘go or no-go’ inspection system which typically provides interval-censored data. Even though fully observed observations are preferred, only partially observed or interval-censored observations are available in practice owing to inherent limitations or time/cost considerations. When a data set consists of both partially and fully observed observations, it is commonly referred to as ‘incomplete’ in the statistics literature. In this paper, we calculate the optimal operating conditions for the process based on a dual response approach using incomplete data. For robust design optimization problems, the dual response approach is a commonly used technique but the novel approach in this study is that we estimate the process mean and variance with incomplete data using the EM algorithm. Thus, it is possible to find the optimal operating conditions using all of the information available. The applicability of the proposed method is illustrated for a case study incorporating incomplete data. The performance of the proposed method is compared with the ordinary method through Monte Carlo simulations and this substantiates the proposed method.