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Dr. Dipayan Das Assistant Professor Dept. of Textile Technology Indian Institute of Technology Delhi Phone: +91-11-26591402 E-mail: [email protected] Statistical Quality Control in Textiles Module 5: Process Capability Analysis

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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