An "x-bar" control chart is developed for recording the mean value of a quality characteristic by use of a sample size of three. The control chart has control limits (LCL and UCL) of 1.000 and 1.020 pounds, respectively. If a new sample of three items has weights of 1.023, 0.999, and 1.025 pounds, what can we say about the lot (batch) it came from?

0.0879 or 8.79 % is the process capability of the batch and the batch doesn't meet the control limits.

Step-by-step explanation:

mean of three readings = (1.023+0.999+1.025) / 3 = 1.0157

standard deviation=√ ((1.023-1.0157) ² + (0.999-1.0157) ² + (1.025-1.0157) ²) / 3)

= 0.0163

Process Capability = min ((USL-mean) / 3SD, (Mean-LSL) / 3SD)

(USL-mean) / 3SD = (1.02-1.0157) / (3*0.0163) = 0.0879

(Mean-LSL) / 3SD) = (1.0157-1.00) / (3*0.0163) = 0.321

Process capability = (0.0879,0.321)

0.0879 or 8.79 % is the process capability