2. Performance Indices - Pp/Cp (Normal Data)

This tool is used to evaluate the capacity of a process using the normal probability distribution.

Example 1:

The data set used in this example was taken from a statistical process with the specifications 37±13. We have that LSL = 24; μ = 37; USL = 50.

Sample	Reading1	Reading2	Reading3	Reading4	Reading5
1	36	35	34	33	32
2	31	31	34	32	30
3	30	30	32	30	32
4	32	33	33	32	35
5	32	34	37	37	35
6	32	32	31	33	33
7	33	33	36	32	31
8	23	33	36	35	36
9	43	36	35	24	31
10	36	35	36	41	41
11	34	38	35	34	38
12	36	38	39	39	40
13	36	40	35	26	33
14	36	35	37	34	33
15	30	37	33	34	35
16	28	31	33	33	33
17	33	30	34	33	35
18	27	28	29	27	30
19	35	36	29	27	32
20	33	35	35	39	36

We will upload the data to the system.

Configuring as shown in the figure below to perform the analysis.

In Select tests we can choose the tests we want to perform.

Then click Calculate to get the results. You can also generate the analyses and download them in Word format.

The results are:

Specifications

	Valor
Sample:	100
Lower Limit	24
Upper Limit	50

Estimates

	Estimate
Mean	33.550
Standard Deviation (Short term)	2.9724
Standard Deviation (Long term)	3.5377

Performace Indices (Long term)

	Performace Indices (Total Variability)
PP	1.225
PPL	0.8998
PPU	1.550
PPK	0.8998

Capability Indices (Short term)

	Capacity Indexes (Variability Inherent)
CP	1.4579
CPL	1.071
CPU	1.8448
CPK	1.071

Observed Indices

	Observed Indices
PPM < LSL	10000
PPM > USL	0
Total PPM	10000

Expected Indices (Long term)

	Expected Indice (Total Variability)
PPM < LSL	3471.964
PPM > USL	1.660
Total PPM	3473.624

Expected Indices (Short term)

	Expected Indicess (Inherent Variability)
PPM < LSL	656.9802
PPM > USL	0.0156
Total PPM	656.9958

SIGMA LEVEL

	SIGMA Level
Zbench (long term)	2.6994
Zbench (Short term)	3.2129
Zshift	1.500
Sigma metrics	4.1994

Out-of-control points - X-Bar Graph

Subgrupo	Valor	Teste
10	37.8	1 point more than 3 Sigmas from the center line
12	38.4	1 point more than 3 Sigmas from the center line
18	28.2	1 point more than 3 Sigmas from the center line

Out-of-control points - Standad-Deviation Graph

Subgroup	Value	Test
8	5.5045	1 point greater than 3 Sigmas from the center line
9	6.9785	1 point greater than 3 Sigmas from the center line

Exemplo 2:

Consider a process at the start of development, where we collected a sample of 30 units. These units were measured and the data is shown in the table below. For this case we have USL = 4.

Data
1.278258
0.017442
1.763441
0.350306
0.499543
0.009417
4.47932
0.096113
1.503284
3.618302
0.19454
1.845016
2.035204
0.992143
0.714152
1.084793
1.195303
1.707286
3.757334
5.958947
1.973829
0.680619
0.088677
0.360242
1.985193
3.193834
4.359103
0.645437
1.003296
0.309148