Functional control charts and health monitoring of steam sterilizers

In this paper, motivated by a multiple profile monitoring problem, we introduce general functional exponentially weighted moving average (EWMA) control charts. When functional data to be monitored are smooth enough to be representable by a finite dimensional basis, a particular version of these functional EWMAs is shown to be a multivariate EWMA applied to basis coefficients. Hence, it is called f-EWMA for monitoring single profiles and f-MEWMA for multiple profiles. The use of f-MEWMA is illustrated in connection to health monitoring of a steam sterilizer during its life cycle. Indeed, each sterilization run gives several profiles related to machine health, and degradation of the steam sterilizer during its life cycle modifies profile curvature in an unpredictable way. Hence, a control chart capable to monitor multiple sterilization profiles during the sterilizer life cycle is needed. The f-EWMA thresholds or control limits have been computed using Monte Carlo simulations. Moreover, the f-EWMA performance has been assessed using experimental data generated in laboratory according to anomalies considered relevant to the sterilizer maintenance program. Consequently, the average run length for these anomalies has been computed applying Monte Carlo simulation to experimental results.