This paper studies an attribute control chart for monitoring the number of nonconforming items using a triple sampling (TS-np) which has not yet been applied to attribute control charts. The chart design and procedure for the decision about the state of the process are given. Mathematical expressions for the average run length (ARL) for in-control and out-of-control processes and the average sample number (ASN) are given. A bi-objective genetic algorithm that seeks to minimize the ASN and the probability of type 2 error is implemented in order to optimize the design of the TS-np control chart. A comparison between TS-np, single sampling np (SS-np), double sampling np (DS-np), and multiple dependent state repetitive sampling (MDSRS) control charts is carried out in terms of the out-of-control average run length (). Tables of values for TS-np are presented in comparison with MDSRS and DS-np for various scenarios. The operation of the proposed control chart is shown through simulated data. Finally, it is concluded that the proposed TS-np chart has a better performance in terms of detecting small and moderate shifts in the process nonconforming rate in-control () compared with MDSRS and DS-np.

In statistical process control, the Shewhart c chart is the most used tool to monitor the mean number of nonconformities. This chart is easy to use but its ability to detect small shifts in the process is low. To improve its an inspection on a larger unit is required, increasing sampling-related costs. This paper proposes a new double sampling scheme for c control chart (DS-c) that can be designed to improve the performance of c or to reduce the inspection cost. The mathematical expression required to do an exact evaluation of Average Run Length (ARL) and Average Sample Size (ASN) is deduced. Further, a bi-objective genetic algorithm is implemented to obtain the optimal design of the DS-c scheme. This optimizatión is aimed to simultaneously minimizing the error probability type II (β) and the ASN , guaranteeing a desired level for the error probability type I (α). A performance comparison between the Double Sampling (DS), Fixed Parameters (FP), Variable Sample Size (VSS) and Exponential Wigthed Moving Average (EWMA) schemes for the c control chart is carried out. The comparison shows that with the implementation of DS-c scheme is obtained a significant reduction of the out of control ARL (ARL1) with a lower ASN respect to FP scheme and a better ARL profile than VSS scheme.

This paper compares different methods (Kragten, Guide to the expression of uncertainty in measurement -GUM-and Relative Uncertainty) to evaluate the measurement uncertainty in bimetallic thermometers. The motivation for the development of the work is based on a need detected in the industry to increase the metrological reliability of thermometers for temperature control in the most diverse measurement processes. The applied methodology is based on the concepts enshrined in the classical literature about the GUM, Kragten and Relative methods. The consolidated results confirmed that, for temperature measurement applications, the GUM method is more appropriate for estimating the measurement uncertainty. The value obtained was equal to 1.22 o C throughout the calibration range of the instrument. In conclusion, this work showed that an increase in metrological reliability for the measurement of temperature, fundamental magnitude in industrial processes, can be obtained by evaluating different methods for estimating the measurement uncertainty.