420

Pignatiello & Ramberg

Table 1. Estimates of Process Capability Indices and Their Standard Errors

Statistic

X

S

c_P

ć__L

Standard Error

S

s

V²("-i)

V²*"-¹)

c.

Figurę 5 shows that a capable process having a C_p = 1.33 can yield Ć_p values that give the impression that the process is not particularly good. In this Monte Carlo study, 55 of the 1000 Ć_p values from the normal process with the true C_p value of 1.33 were less than 1.10 and 196 were less than 1.20. Perhaps somewhat disturbing is the fact that processes with Iow true C_p values can easily produce C_p values that give the impression that the process is capable. In Figurę 6, the normal process with the true C_p value of 1.00 produced 112 out of 1000 C_p values that were greater than 1.20 and 43 out of the 1000 were greater than 1.30.

Simple ‘^oint estimates” of process capability indices can be extremely misleading. Instead, “interval estimates” or “confidence intervals”