Page 237 - DMGT524_TOTAL_QUALITY_MANAGEMENT

Total Quality Management

Notes Research Methodology
Process Capability determines whether a process with normal variation, is capable of
meeting customer requirements. It compares the output of an in-control process to the
specification limits by using capability indices. These are obtained by using the ratio of
the “specification width” to the “process width”.

There are several statistics that can be used to measure the capability of a process, e.g. Cp,
Cpu, Cpl and Cpk. Most of the capability indices estimates are valid only for large samples,
i.e. at least 100. These also assume that the sampled populations are normal. If μ and σ are
the mean and standard deviation of the normal data respectively. The USL and LSL are the
upper and lower specification limits, respectively. Then, the Process Capability Ratios
(PCRs) defined by Montgomery (2001) are as below:

PCR = Cp = (USL - LSL)/6 σ
PCR (Upper Sided) = CPU = (USL - µ)/3σ
PCR (Lower Sided) = Cpl = (µ - LSL)/3σ
Cpk = min (Cpu, Cpl)
The Cp, CPU, Cpl and Cpk are obtained by using HLF’s specification limits and estimates
of µ and σ.
Statistical Analysis
The process capability of six machines i.e. A, B, C, D, E and F model TBA-19 of HLF is
calculated and analyzed. The data of one week is collected from 3rd to 8th January, 2005
and the timings are from 9:00 a.m. to 15:00 p.m. From each machine 100 samples are taken
during one hour. The process is considered capable which has Cpk = 1.33 or large and a
process having Cpk between 1.0 and 1.33 as marginal. The Cpk exactly equals to 1.0
implies that the process variation exactly meets the specification requirements. The Cpk <
0 implies that the process mean lies outside the specification limits. The Cpk < -1 implies
that entire process lies outside the specification limits and portrays the extreme situation
of variability. If Cp = Cpk the process is centred at the mid point of the specifications, and
if Cpk < Cp the process is off centred. The magnitude of the ratio Cr = Cpk/Cp shows
degree of off-centre. The lower the value of Cr, the higher is the degree of off- centre . The
capability indices Cp, Cpu, Cpl and Cpk of six machines are as given in Appendix.
Process capability Cpk of 6 machines at the 1st day of production from 9:00 to 10:00 a.m.
shows that machine A and D are not capable with the process. The Cpk < -1 of machine D
shows that entire process lies outside the specification limits and portrays the extreme
situation of variability. It is also confirmed by the lowest value of Cr = -8.474. Machine B
shows Cpk = 1.354 a capable process. Machine E and F show Cpk = 1.263 and 1.032,
respectively, a marginal process. Machine C has Cpk = 0.937 which can be considered
approximately a marginal process. There is need to watch the process of machines A and
D carefully to reduce variability.
Process capability Cpk on the 2nd day from 10:00 to 11:00 a.m. shows that only machines
A and D give Cpk greater that 1.33. The process is capable only for these 2 machines. Other
machines show that process is not capable of meeting specification. The Cpk < 0 of machines
B, C and F implies that the process mean lies outside the specification limits.

Process capability Cpk on 3rd day from 11:00 to 12:00 shows that machine A and C give
Cpk 1.034 and 1.156, respectively. It implies that process is marginal. Machines B, C, D, E
and F must be carefully watched.
Contd...

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