**The relationship**

Xbar control charts are equivalent to sampling plans for the mean carried out
repeatedly, and the results plotted and analyzed in sequence. The control limits are
exactly the same as the acceptance limits for a targeted (two-sided) sampling plan for the
mean.

To be equivalent to a Shewhart chart, the sampling plan for the mean must have these
risks:

alpha=0.0027 (two-sided) or alpha=0.00135(one-side) and

Beta=0.5.

**How to calculate the sample size for arbitrarily
chosen control limits:**

You can use TP414 to calculate the sample size for Xbar charts, starting with the
control limits as input.

Calculate the sample size required for selected control limits by entering these
performance requirements into TP414 using: [Mean] [Both] [Performance]

0.00135, 0.5, LCL, Target, Target, UCL

Where LCL and UCL are chosen control limits, and Target is the center line.

**How to calculate control limits for arbitrary chosen
sample size:**

You can use TP414 to calculate the control limits of an Xbar chart (starting with the
sample size as input) by:

Use options [P] [L] and enter: alpha=0.00135, Beta=0.5, 1,2

Now use the up-arrow to back up(alpha and beta defaults have been set to the proper
values).

Use options [D] [L], and enter n,0

Calculate the control limits as: center line +- AQLML.

**How to calculate the OC-Curve and ARL-Curve of an
Xbar chart:**

You can use TP414 to calculate the OC-Curve and ARL-Curve of an existing Xbar
chart by entering it into the program as follows:

Use options [M] [B] [D] and enter the values for n,LCL,UCL

View the OC-Curve and ARL-Curve table. The OC-Curve will show that the population mean can
be outside of the control limits and still have a Pa=0.5 (50 percent probability of
acceptance). For this reason, Shewhart charts are not suitable for product acceptance.