# Pacific Gas & Electric (PCG)

## PCG»Topics» Figure 4.3.1 Sample Control Chart

This excerpt taken from the PCG 10-K filed Feb 18, 2005.

Figure 4.3.1 Sample Control Chart

Index 1: Annual Average Forced Outage(IMS) Frequency for All Transmission Line Circuits.

Index 2: Annual Average Accumulated Forced Outage(IMS) Duration for those Transmission Line Circuits with Forced Outages(IMS).

Index 3: Annual Proportion of Transmission Line Circuits with No Forced Outages(IMS).

The control charts incorporate a center line (CL), upper and lower control limits (UCL and LCL, respectively), and upper and lower warning limits (UWL and LWL, respectively). The CL represents the average annual historical performance for a period prior to the current year. The UCL and LCL define a range of expected performance extending above and below the CL. For the annual proportion of Transmission Line Circuits with no Forced Outages(IMS), the limits are based on standard control chart techniques for binomial proportion data. For the other two indices, bootstrap resampling techniques are used to determine empirical UCL and LCL at 99.75% and 0.25% percentile values, respectively, for means from the historical data. The bootstrap procedure is described in Section 4.3.2. Similarly, the UWL and LWL define a range of performance intending to cover the percentiles from 2.5% to 97.5%. The bootstrap algorithm is also used to determine these values. Thus, the UCL and LCL will contain about 99.5% of resampling means from the Voltage Class of interest. UWL and LWL will contain about 95% of the resampling means. These limits coincide with the usual choices for control charts when the means are approximately normal. Bootstrap estimation procedures are used here since the sampling means do not follow the Normal distribution model. The bootstrap estimation procedures ensure consistent control chart limits by using a starting base number("seed") for it's random number generator. Accuracy or reduced variances in the control chart limits are attained by using the average control chart limits generated from applying ten repetitions or cycles of the bootstrap sampling method. Collectively, the CL, UCL, LCL, UWL and LWL provide reference values for use in evaluating performance as described in Section 4.3.3.

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For the special case where there is a Voltage Class with only one Transmission Line Circuit, individual and moving range control charts should be used for Index 1 and 2. The method used herein for calculating Index 3 is not applicable for those Voltage Classes containing less than six Transmission Line Circuits. Maintenance procedures recommended by the MCC and approved by the ISO Governing Board will be used by the PTOs to calculate Index 1, 2, or 3 where the methods provided herein do not apply.More information on the individual and moving range control charts can be found in the user manuals of the statistical software recommended by the MCC and approved by the ISO Governing Board for use in creating the control charts .