HP 9g Instruction Manual page 3

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HP 9g Statistics – Process Capability
Practice solving process capability problems
Example 1: As part of a process optimization effort, an industrial manager had to determine whether their
manufacturing process, for which µ = 19.35 and σ = 2.05, was capable. The population of data values is
assumed to be normally distributed. The upper and lower specification limits of the process are 23.3 and
11, respectively. How could the HP 9g help her?
Solution: By calculating the C
previous statistical data in memory (press `1, then select D-CL and finally press =). Since it is
one single process, we'll carry out all calculations in 1-VAR mode (i.e. `1, select 1-VAR and press
=). No data set is provided. Therefore, in order to enter µ and σ into the calculator, we'll have to use
the method described in the HP 9g learning module Statistics – Normal Distribution., that is to say: create a
data set consisting of two values µ + σ and µ – σ. To do this press:
E=19.35+2.05‡‡19.35-2.05‡
It is very important to bear in mind that, when using this trick, those variables shown in the STATVAR
menu that depend on the actual data or the number of data, n, will be meaningless. Only those which only
depend on the average and the population standard deviation (that is, in which n is not explicitly used in
their calculation) will be correct; namely:
and t . Any other variable involves the value of n or the data in their calculation. Particularly, note that 'ppm'
is calculated by the HP 9g using the actual value of n, not the one 'embedded' in µ.
The next step is to input the LSL and USL values. Press:
E, select LIMIT, =11‡23.3‡
Let's determine if the process is located at the midpoint of the specification range. We can do it graphically
by plotting the process control chart: press ~e P2. The x-axis range is automatically set to
(LSL, USL). The resulting bell-shaped curve is clearly off-center. Alternatively, we can do it numerically:
Or simply by finding the value of
~e ‡‡‡‡
C =0.3577 ≠ 0. Therefore, the capability index that we must find is C
a
for a shift in the mean of the process to either specification limit. All these statistics are in the STATVAR
menu, so press ~e ‡‡‡†† to display C
Answer: C = 0.6423 (rounded to four decimal digits). Since C
pk
process is incapable: the process spread exceeds the tolerance spread, which assures that out-of-
tolerance products will be made.
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and C statistics to measure the process capability. First of all, let's clear any
p pk
x
,
+ +
USL LSL .
23 3
=
2 2
C
, which is displayed by pressing:
a
C C C
y , σx, σy,
, ,
px pkx
11
= ≠ µ =
. .
17 15 19
.
pk
is clearly smaller than 1.33 (even than 1, in fact) the
pk
- 3 -
C C C
, , , ,P(t), Q(t), R(t)
ax py pky ay
35
because C , unlike C
pk pk
HP 9g Statistics – Process Capability - Version 1.0
accounts
p,