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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?

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hafsaabdulhai

Answer:

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

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