Question

a process in statistical control has a mean of .3119 and specification limit of .307 to .317. if the standard deviation of the process is .0013, what percent of the process output is expected to be below the specification limit?

Answer 1

Specification Limits - Maximum and minimum allowable dimensions of some quality of characteristics are to be decided, so the process/product can be utilised for which it is intended. These maximum and minimum limits of variations are known as specification limits.

Mean = 0.3119

Max. Specification Limit = 0.317

Min. Specification Limits = 0.307

Standard Deviation of the process = 0.0013

The percentage of process output that is expected to be below the specification limits will be calculated by the below formula using the Z-Values(from the standard normal distribution table).

Thus, we will calculate the number of estimated standard deviations exist between the Mean and Specification Limit. This number of standard deviation calculated is called the Z value. This, Z- value will help us determine the percentage of output outside the specification limit.

Since, we have to calculate the percentage output below the specification limit, we calculate (Z lower),

=> Zlower = (Mean - LSL) / SD = (0.3119-0.307)/0.0013 = 3.77(rounded to 2 decimal places)

The value corresponding to Z= 3.77 from standard normal table is = 0.00008

The percentage of process output that is expected to be below the specification limits = 0.00008*100 = 0.008% which is almost negligible.