5. Performance Indices - Pp/Cp (Automatic)

In many cases it is advisable to have a tool that allows the capacity of a process to be assessed automatically, using the model that best fits the data under study.

Example:

The following data refers to checking the distance between the teeth of a transmission gear. Every thirty pieces produced, the last piece was taken to the laboratory to be measured on a coordinate measuring machine. For this example we have LSL = 98.25 e USL = 98.15.

Date	Timetable	Nro Pieceº	Exter Diame
3/10/2007	09:16:47	1	98.212
3/10/2007	11:50:33	30	98.23
3/10/2007	13:39:07	60	98.218
3/10/2007	13:42:14	90	98.215
3/10/2007	18:12:52	120	98.216
3/10/2007	19:29:54	150	98.22
3/10/2007	21:28:47	180	98.219
3/10/2007	22:26:35	210	98.216
4/10/2007	08:41:10	240	98.207
4/10/2007	08:50:53	270	98.208
4/10/2007	08:55:51	300	98.216
4/10/2007	13:23:37	330	98.215
4/10/2007	13:26:14	360	98.192
4/10/2007	22:49:48	390	98.193
5/10/2007	08:50:18	420	98.171
5/10/2007	08:57:52	450	98.186
5/10/2007	12:45:56	480	98.187
5/10/2007	13:13:10	510	98.197
5/10/2007	13:24:35	540	98.191
5/10/2007	18:23:46	570	98.198
5/10/2007	21:43:05	600	98.187
5/10/2007	21:46:40	630	98.199
5/10/2007	22:59:42	660	98.192
8/10/2007	07:18:23	690	98.207
8/10/2007	09:09:06	720	98.21
24/10/2007	06:50:06	1	98.209
24/10/2007	10:59:44	30	98.193
24/10/2007	12:50:13	60	98.204
24/10/2007	15:08:16	90	98.202
24/10/2007	18:13:40	120	98.222
24/10/2007	22:07:46	150	98.214
25/10/2007	07:24:32	180	98.204
25/10/2007	09:24:54	210	98.166
25/10/2007	12:26:39	240	98.168
25/10/2007	16:49:41	270	98.169
25/10/2007	19:38:17	300	98.175
25/10/2007	22:44:45	330	98.175
26/10/2007	08:51:41	360	98.191
26/10/2007	11:49:26	390	98.19
29/10/2007	06:14:28	420	98.181
29/10/2007	06:17:54	450	98.179
29/10/2007	08:39:19	480	98.187
29/10/2007	12:43:09	510	98.192
29/10/2007	17:11:26	540	98.208
29/10/2007	17:48:53	570	98.195
29/10/2007	20:48:24	600	98.196
30/10/2007	06:47:31	630	98.176
30/10/2007	09:30:37	660	98.186
30/10/2007	13:05:12	690	98.194

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 carry out.

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

The results are:

Automatic Analysis

Process Analysis	Situation
Normality Test	Accept a 0.05 significance level.
Box-Cox Transformatiion	Not Applicable
Johnson Transformatiion	Not Applicable
Non-Normal Distribution	Not Applicable
Non-Parametric Distribution	Not Applicable

Normality Teste

	Statistics	P-values
Anderson - Darling	0.413	0.326
Kolmogorov - Smirnov	0.091	0.402
Shapiro - Wilk	0.973	0.316

Specifications

	Value
Sample:	49
Lower Limit	98.15
Upper Limit	98.25

Estimates

	Estimate
Mean	98.198
Standard Deviation (Short term)	0.008
Standard Deviation (Long term)	0.016

Performance Indices (Long Term)

	Performance Indices (Total Variability)
PP	1.040
PPL	0.989
PPU	1.092
PPK	0.989

Capability Indices (Short term)

	Capacity Indixes (Variability Inherent)
CP	2.160
CPL	2.052
CPU	2.267
CPK	2.052

Observed Indices

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

Expected indices (Long term)

	Expected Indices (Short term)
PPM < LSL	1509.777
PPM > USL	525.358
Total PPM	2035.136

Expected Indices (Short Term)

	Expected indices (Inherent Variability)
PPM < LSL	0
PPM > USL	0
Total PPM	0

SIGMA LEVEL

	SIGMA Level
Zbench (long term)	2.873
Zbench (short term)	6.154
Zshift	1.500
Sigma Metrics	4.373