# statistical quality control in textiles

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IntroductionTRANSCRIPT

Statistical Quality Control in Textiles

Module 5:Process Capability Analysis Dr. Dipayan Das Assistant
Professor Dept. of Textile Technology Indian Institute of
Technology Delhi Phone: Introduction Process Capability
Analysis

When the process is operating under control, we are often required
to obtain some information about the performance or capability of
the process. Process capability refers to the uniformity of the
process. The variability in the process is a measure of uniformity
of the output. There are two ways to think about this variability.
Natural or inherent variability at a specified time, Variability
over time. Let us investigate and assess both aspects of process
capability. 3 Natural Tolerance Limits

The six-sigma spread in the distribution of product quality
characteristic is customarily taken as a measure of process
capability. Then the upper and lower natural tolerance limits are
Upper natural tolerance limit = + 3 Lowe natural tolerance limit =
- 3 Under the assumption of normal distribution, the natural
tolerance limits include 99.73% of the process output falls inside
the natural tolerance limits, that is, 0.27% (2700 parts per
million) falls outside the natural tolerance limits. 4 Techniques
for Process Capability Analysis Techniques for Process Capability
Analysis

Histogram Probability Plot Control Charts 6 Histogram It gives an
immediate visual impression of process performance. It may also
immediately show the reason for poor performance. Poor process
capability is due to poor process centering LSL USL Poor process
capability is due to excess process variability LSL USL 7 Example:
Yarn Strength (cN.tex-1) Dataset

8 Frequency Distribution

Class Interval (cN.tex-1) Class Value xi Frequency ni (-) Relative
Frequency gi Relative Frequency Density fi (cN-1.tex) 10.50 2
0.0044 11.50 8 0.0178 12.50 37 0.0822 13.50 102 0.2267 14.50 140
0.3111 15.50 104 0.2311 16.50 43 0.0956 17.50 13 0.0289 18.50 1
0.0022 TOTAL 450 1.0000 9 Histogram Mean = 14.57 cN tex-1 Standard
deviation = 1.30 cN tex-1

The process capability would be estimated as follows: If we assume
that yarn strength follows normal distribution then it can be said
that 99.73% of the yarns manufactured by this process will break
between cN tex-1 to cN tex-1. Note that process capability can be
estimated independent of the specifications on strength of yarn.
0.1 0.2 0.3 0.4 10 Probability Plot Probability plot can determine
the shape, center, and spread of the distribution. It often
produces reasonable results for moderately small samples (which the
histogram will not). Generally, a probability plot is a graph of
the ordered data (ascending order) versus the sample cumulative
frequency on special paper with a vertical scale chosen so that the
cumulative frequency distribution of the assumed type (say normal
distribution) is a straight line. The procedure to obtain a
probability plot is as follows. The sample data is arranged aswhere
is the smallest observation,is the second smallest observation, and
is the largest observation, and so forth. The ordered
observationsare then plotted again their observed cumulative
frequency on the appropriate probability paper. If the hypothesized
distribution adequately describes the data, the plotted points will
fall approximately along a straight line. 11 Example: Yarn Strength
(cN.tex-1) Dataset

Let us take that the following yarn strength data 12.35, 17.17,
15.58, 10.84, 18.02, 14.05, 13.25, 14.45, 12.35, j xj (j-0.5)/10 1
10.84 0.05 2 11.09 0.15 3 12.35 0.25 4 13.25 0.35 5 14.05 0.45 6
14.45 0.55 7 15.58 0.65 8 16.19 0.75 9 17.17 0.85 10 18.02 0.95 The
sample strength data can be regarded as taken from a population
following normal distribution. 12 Measures of Process Capability
Analysis Measure of Process Capability: Cp

Process capability ratio (Cp), when the process is centered at
nominal dimension, is defined below where USL and LSL stand for
upper specification limit and lower specification limit
respectively and refers to the process standard deviation.
100(1/Cp) is interpreted as the percentage of the specifications
width used by the process. 3 USL LSL Cp>1 Cp=1 Cp