| Summary: | 碩士 === 中原大學 === 工業工程研究所 === 96 === We consider the design of X charts, where the quality characteristic measurements
are autocorrelated with and unknown marginal distribution and unknown autocorrelations,
but a set of data is given. Specifically, we assume that the data process
follows an ARTA (Autoregressive-To-Anything Process).
Then we apply the X chart, we need to decide the value of the X-chart design
parameters: the sample size n and the control limits. In practice, the data properties
are unknown.
Here we apply two steps to compute the ARL (Average Run Length). First, we
construct an empirical distribution for a given set of data. We use the mixture of
the original empirical distribution and exponential distribution (for the tails). Second,
we evaluate the performance of the model-free design based on the proposed
empirical distribution. The performance measurements are the in-control and out-ofcontrol
average run length (ARL). The ARL is the expected number of samples (or
observations if taking samples of one) required by the chart to signal.
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