Page 238 - DMGT524_TOTAL_QUALITY_MANAGEMENT

Unit 14: Statistical Process Control

Process capability Cpk on 4th day from 12:00 to 13:00 shows that machine A has Cpk=1.276 Notes
a marginal process, machine D has Cpk =1.413 a capable process. All other machines show
that process is not capable with these specifications. Moreover, Cpk < 0 of machines E
implies that the process mean lies outside the specification limits.
Process capability Cpk on 5th day from 13:00 to 14:00 shows that machines C & F have Cpk
=1.696 & Cpk = 1.352, respectively show capable process. Machine E has Cpk =1.016, a
marginal process. The Cpk < 0 of Machines A implies that the process mean lies outside
the specification limits. The Cpk < -1 of Machine B shows that entire process lies outside
the specification limits and portrays the extreme situation of variability. It is also confirmed
by the lower value of Cr = -2.738. Therefore, Machines A and B give losses in production
and are not capable with the process.
Process capability Cpk on 6th day shows that machines B, D & F gives Cpk =1.089, Cpk
=0.967 & Cpk = 1.130, respectively, show a barely marginal process. All other machines
have process spread greater than specification limits. The Cpk < 0 of Machines A implies
that the process mean lies outside the specification limits.
Conclusions
It is a remote probability of a capable process. For machines A, B, C and F it is 1/6. Only for
machine B and D this probability is 1/3. The chance that machine E will achieve a process
capability is zero.
The categories marginal and capable process is combined. The probabilities for combined
processes are as: For machines A and F ½, B, C, D and E 1/3.
The probability that Cpk < 0 is 1/6 for machines C, D, E & F and 1/3 for machines A and B.
It shows the chance that process mean can go beyond the specification limits. The probability
that Cpk < - 1 for machines B and D is 1/6. It shows the chance that entire process lies
outside the specification limits. It should be taken care off.

Thus, in general, position of machines is good with reference to the process capability. But
to take care of isolated points, i.e. Cpk < -1 for machines B and D, HFL is suggested to
introduce high technology to reduce the variability and insure the process capability.

Questions
1. Based on the case discussed above bring out the importance of process capability
2. Do a brief analysis of the case in your own words
Source: http://www.gcu.edu.pk/fulltextjour/stat/stat-journal2005/sarwatzahra-article2.pdf

Appendix: Table of Control Chart Constants
X-bar Chart For Sigma R Chart S Chart
Constants Estimate Constants Constants
Sample A2 A3 d2 D3 D4 B3 B4
Size = m
2 1.880 2.659 1.128 0 3.267 0 3.267
3 1.023 1.954 1.693 0 2.574 0 2.568
4 0.729 1.628 2.059 0 2.282 0 2.266
5 0.577 1.427 2.326 0 2.114 0 2.089
6 0.483 1.287 2.534 0 2.004 0.030 1.970
7 0.419 1.182 2.704 0.076 1.924 0.118 1.882
Contd...

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