| Methods |
| ======= |
|
|
| CUSUM parameters |
| ---------------- |
|
|
| .. csv-table:: CUSUM parameters |
| :file: ../../assets/params.csv |
| :header-rows: 1 |
|
|
| CUSUM chart |
| ----------- |
|
|
| A two-sided CUSUM control chart computes the cumulative differences or |
| deviations of individual observations from the target mean (or |
| in-control mean, :math:`\mu_{in}`). The positive and negative cumulative |
| sums are calculated: |
|
|
| .. math:: |
|
|
| \\ S_{hi}(d) = max(0, S_{hi}(d-1) + x_d - \hat{\mu}_{in} - K) |
| \\ S_{lo}(d) = max(0, S_{lo}(d-1) - x_d + \hat{\mu}_{in} - K) |
|
|
| where *d* denotes a unit of time, :math:`x_d` is the value of quantity |
| being monitored at time :math:`d`, :math:`\hat{\mu}_{in}` is the |
| in-control mean of :math:`x_d`, and :math:`K` is a "reference value" |
| related to the magnitude of change that one is interested in detecting. |
| :math:`S_{hi}` and :math:`S_{lo}` are the cumulative sum of positive and |
| negative changes. To detect a change in the observed values from the |
| in-control mean, the CUSUM scheme accumulates deviations that are |
| :math:`K` units away from the in-control mean. Let :math:`\sigma_{in}` |
| denote the in-control standard deviation of :math:`x_d`. |
