Scrutinizing and Improving Process Capability Index by Application of Statistical Process Control...

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International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 6340(Print), ISSN 0976 6359(Online) Volume 3, Issue 2, May-August (2012), IAEME

551

SCRUTINIZING AND IMPROVING PROCESS CAPABILITY INDEX BY

APPLICATION OF STATISTICAL PROCESS CONTROL AND SIX-

SIGMA TOOLS

Piyush Kumar Soni*, M. K. Ghosh, Imtiyaz Khan, Himanshu Gangwal

Department of Mechanical Engineering, Mandsaur Institute of Technology

Mandsaur - 458001 (M.P.), India

*Corresponding Author- Piyush Kumar Soni,

H. No. D/2, Yatindra Vihar, Mandsaur - 458001 (M.P.), India

+91 7898060802, [email protected]

Abstract

In this paper, the process control of a CNC Grinder manufactured at PMTMachines Ltd. Halol, (Gujarat) India is discussed. The varying measurements have been

recorded for a number of samples of a Cam Roller Shoe obtained from a number of trials

with the CNC Grinder. SPC technique has been adopted, by which the process is finally

brought under control and the process capability index is improved. Quality control helps

industries in improvement of its product quality and productivity. Statistical Process

Control (SPC) is one of the tools to control the quality of products that practice in

bringing a manufacturing process under control.

Keywords: Statistical Process Control, Range and Standard Deviation, Control Charts,

Normal Distribution Curves, Process Capability.

Introduction

Statistical process control (SPC) describes a widely-used set of approaches used

to detect shifts in processes in, for example, manufacturing. Among these are control

charts" [1]. Statistics is a body of methods by which useful conclusions can be drawn

from numerical data. A process is a systematic series of actions directed to some end.

Statistical Process Control (SPC) refers to controlling a process (e.g., grinding) based on

INTERNATIONAL JOURNAL OF MECHANICAL ENGINEERING AND

TECHNOLOGY (IJMET)

ISSN 0976 6340 (Print)

ISSN 0976 6359 (Online)

Volume 3, Issue 2, May-August (2012), pp. 551-558

IAEME: www.iaeme.com/ijmet.html

Journal Impact Factor (2012): 3.8071 (Calculated by GISI)www.jifactor.com

IJMET

I A E M E


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responding to process data with statistical techniques and tools. Statistical Quality

Control (SQC) refers to controlling the quality of a product based on responding to

machine shop data with statistical techniques and tools [3]. PMT Machines Ltd., Halol is

one of the leading CNC Machine Tools manufacturers in India. The SPC methodology

have been adopted for grinding of Cam Roller Shoes, a component of one of its customercompanies, Delphi TVS, Chennai (India). The product was being ground by a CNC

Grinding machine which was solely manufactured and assembled at PMT Machines Ltd.

itself. As the thickness of shoes in different samples after grinding was found to be out of

tolerance limits asked by Delphi TVS, the process capability found to be less than the

standard value. This required the idea of SPC implementation and the techniques been

practiced.

Literature Review

SPC tools can be used by operators to monitor their part of production or service

process for the purpose of making improvements [2]. The use of statistical concepts in

the field of quality emerged in the United States in the beginning of the nineteenth

century. But its democratic use began only in the 1930s. W. Edwards Deming, who

applied SPC methods in the US during the Second World War, was the one responsible

for introducing this concept in Japan after the war ended. These methods were not used in

France until the 1970s. The 1980s saw the SPC methods being used frequently, due to the

pressure from large clients like automobile manufacturers and aircraft manufacturers.

Companies who have been operating in the market for a while already have a quality

control process in place. This process enables a company to meet four main objectives:

higher quality, more effectiveness, optimum cost savings and greater rigor, and produces

products of optimum quality [1]. Statistics is more applicable to measuring and

controlling variation from common cause (random) than from special causes [3].Control charts detects special causes of variation, measures and monitors common

causes of variation, helps to know when to look for problems and adjust or when to keep

hands off and when to make a fundamental change [3]. For normally distributed statistics,

the area bracketed by the control limits will on average contain 99.73% of all the plot

points on the chart, as long as the process is and remains in statistical control. A false-

detection rate of at least 0.27% is therefore expected. Control charts are also known as

Shewhart charts or process-behaviour charts. Variable control charts are used to study a

process when characteristics is a measurement, for example, cycle time, processing time,

waiting time, highest, area, temperature, cost or revenue [4].

Goals of SPC:

understand the process eliminate special cause variation reduce common cause variation and maintain a process that is in "statistical

control" and has high "process capability".


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Methodology

Recorded component details as furnished below:

Specifications : 8.07 + 0.02 (as per the customer drawing).

Upper Specification Limit (USL) : 8.09 mm

Lower Specification Limit (LSL) : 8.05 mmSeveral measurements of thickness ground by the CNC Grinder in different trials have

been recorded for every component in the observation tables. One of the observation

tables (trial no. 6) is given as under:Table 1: Component trial report

Component Details

Part Name TC Trial Date 13/09/2011

Trial Time 09:00 am 05:00 pm Each Sample Size (N) 05

Per Cycle Time 7 min 46 sec Dressing Amount 0.5mm

SampleNumber

Thickness (in mm)

Part 1(x1)

Part 2(x2)

Part 3(x3)

Part 4(x4)

Part 5(x5)

Mean(xi)

Range(Ri)

1 8.071 8.075 8.084 8.088 8.082 8.08 0.017

2 8.075 8.066 8.074 8.078 8.082 8.075 0.016

3 8.069 8.065 8.062 8.073 8.076 8.069 0.014

4 8.076 8.073 8.07 8.061 8.065 8.069 0.015

5 8.055 8.06 8.072 8.069 8.064 8.064 0.017

6 8.051 8.055 8.059 8.069 8.066 8.06 0.018

7 8.056 8.063 8.063 8.069 8.074 8.065 0.018

8 8.055 8.051 8.061 8.065 8.068 8.06 0.017

9 8.056 8.066 8.05 8.047 8.061 8.056 0.01910 8.04 8.044 8.045 8.055 8.061 8.049 0.021

11 8.035 8.041 8.048 8.057 8.044 8.045 0.022

12 8.046 8.045 8.061 8.056 8.042 8.05 0.019

13 8.045 8.048 8.053 8.055 8.064 8.053 0.019

14 8.055 8.052 8.057 8.07 8.061 8.059 0.018

15 8.076 8.069 8.069 8.061 8.065 8.068 0.015

16 8.063 8.064 8.074 8.062 8.057 8.064 0.017

n = 16 xi = 128.986 Ri = 0.282

To analyze the process capability, the statistical quality control chart techniques can beimplemented in the following way:

The arithmetic average (mean) of ranges,

=n

RR

i = 0.282 / 16 = 0.0176

Process (or population) Standard Deviation, = R/ D2 = 0.0176 / 2.326 = 0.0076where, D2 = 2.326 (from table of constants, for N = 5)


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purpose jig. After a close discussion, the team decided to provide a calibrated scale with

the drives in such a way that whenever machine starts to follow the command to move

fast in a direction, the drives should take a lead exactly with the calibrated values of the

scale. After the calibrated scale provided to the tool drives, all the first three sample trials

gave the dimensional values within specification limits (i.e. 8.07 + 0.2). It meant that theCNC Grinder was become capable of giving the dimensions of the components as per the

given tolerances. The same procedure of SPC was repeated again to determine the

process capability after the remedies were applied. One of the observation tables (trial no.

11) is given as under:Table 2. Component trial report

Component Details

Part Name TC Trial Date 16/09/2011

Trial Time 09:00 am 05:00 pm Each Sample Size (N) 5

Per Cycle Time 6 min 5 sec Dressing Amount 0.5mm

Sample

Number

Thickness (in mm)Part 1

(x1)

Part 2

(x2)

Part 3

(x3)

Part 4

(x4)

Part 5

(x5)

Mean

(xi)

Range

(Ri)

1 8.071 8.072 8.073 8.07 8.069 8.071 0.004

2 8.073 8.073 8.07 8.072 8.067 8.071 0.006

3 8.071 8.072 8.068 8.066 8.068 8.069 0.006

4 8.068 8.07 8.071 8.069 8.072 8.07 0.004

5 8.07 8.071 8.07 8.073 8.071 8.071 0.003

6 8.067 8.07 8.07 8.072 8.071 8.07 0.005

7 8.07 8.073 8.069 8.069 8.069 8.07 0.004

8 8.07 8.071 8.07 8.067 8.067 8.069 0.0049 8.067 8.067 8.068 8.074 8.069 8.069 0.007

10 8.069 8.072 8.073 8.073 8.073 8.072 0.004

11 8.07 8.07 8.067 8.07 8.073 8.07 0.006

12 8.073 8.074 8.07 8.071 8.072 8.072 0.004

13 8.07 8.072 8.069 8.07 8.069 8.07 0.003

14 8.073 8.072 8.071 8.068 8.071 8.071 0.005

15 8.074 8.072 8.072 8.071 8.071 8.072 0.003

16 8.072 8.072 8.071 8.071 8.069 8.071 0.003

Total

n = 16

xi =

129.128

Ri =

0.071

The arithmetic average (mean) of ranges,

=n

RR

i = 0.071 / 16 = 0.0044

Process (or population) Standard Deviation, = R/ D2 = 0.0044 / 2.326 = 0.0019where, D2 = 2.326 (from table of constants, for N = 5)[5]

Therefore, Standard Deviation of the sample mean, x = /N = 0.0019 /5 = 0.00085Average x (Process mean), x = xi / n = 8.0705


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International Journal of Mech6340(Print), ISSN 0976 6359(O

The control limits are, UCLx

Range = [Highest value Lo

The control limits for Range c

where, D4 = 2.114 and D3 = 0

Process Capability,

Capability Ratio, CR = 1 /

Let, CPU and CPL are Upper

CPU = USL - x = 3.42

3 Cpk= Minimum (CPU, CPL)

Plotted control charts with the

Fig. 4: X Chart for t

8.065

8.066

8.067

8.068

8.069

8.07

8.071

8.072

8.0738.074

1 2 3 4 5 6 7 8 9 10

AverageThickness(mm),X-bar

Sample #

anical Engineering and Technology (IJMETline) Volume 3, Issue 2, May-August (2012), I

556

x + 3 x = 8.0731; LCLx = x - 3est value] = 0.007 0.003 = 0.004

hart are, UCLR = D4 R = 2.114 X 0.0

LCLR = D3 R = 0 X 0.0044

(from table of constants, for N = 5)[5]

= (8.09 8.05)

6 X 0.0019

p = 0.28

and Lower Process Capabilities, respectivel

and, CPL = x - LSL

3 = Minimum (3.42, 3.59)

help of MS-Excel application software as s

able 2. Fig. 5: R Chart for

11 12 13 14 15 160

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

0.009

0.01

1 2 3 4 5 6 7 8 9 1

Range

Sample #

), ISSN 0976 EME

x = 8.0679

044 = 0.0093

= 0

= 3.51

.

= 3.59

= 3.42

own below:

table 2.

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Fig. 6: Normal Distribution Curve for table 2.

Results:Upper Control Limit, UCL = 8.0731; Lower Control Limit, LCL = 8.0679 ;

Range, R = 0.004 ; Average Range, R = 0.0044 ;

Process Capability, Cp= 3.51 ; Capability Ratio, CR = 0.28 ;

Upper Process Capability, CPU = 3.42 ; Lower Process Capability, CPL = 3.59 ;

Cpk= Minimum (CPU, CPL) = 3.42

Conclusion:

The control limits obtained after the remedial actions taken for the grinder arewithin specification limits and the thickness produced in all the components of every

sample lie under the control limits. The thicknesses of all the components are located

very close to the process mean. All these results are positive by which we conclude that

the process is under control. The process capability (Cp) increased to 3.51 which show

that implementation of SPC technique is proved to be successful in improving the

performance of grinding process thereby making it more capable of producing the

products with right dimensions. Capability Ratio (CR) is reduced to 0.28 which means

that the process spread now occupies 28 % of the given tolerance. The lower is the CR

the more is capable the process. The provision of a calibrated scale with the mechanical

drives of a CNC Grinder solved the backlash problems and increased its preciseness. Cpkis a better measure of process capability than Cp or CR since Cpk takes into account the

actual process center compared to the target [3]. Here, we got Cpk as 3.42 which is greater

than 2. Cpk of value greater than 2 was required by the customer company, Delphi TVS,

Chennai and their demand has been met satisfactorily. These all become possible with the

implementation of an SPC technique. Likewise, the SPC tools can be implemented to

solve so many real life problems of different machines and processes in future that may

0

50

100

150

200

250

8.064 8.066 8.068 8.07 8.072 8.074 8.076 8.078


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come up with meeting the demand of higher quality and productivity of different

manufacturing processes. The methods developed in the first half of this century by

Shewhart and others are still very useful in many current applications.

References1. Term papers (2011), Statistical Process Control spc management -1, businessand market, 34 pages.

2. Roberta Russell & Bernard W. Taylor (2006), III John Wiley & Sons, StatisticalProcess Control, Operations Management - 5th Edition, Inc.Beni Asllani,

University of Tennessee at Chattanooga.

3. SPC92b, file format: microsoft word statistical process control (spc) &statistical quality control (sqc) chemrat.com/chemhog2/spc_files/spc92b.doc

4. Rami Hikmat Fouad, Adnan Mukattash (2010), Statistical Process Control Tools:A Practical guide for Jordanian Industrial Organizations JJMIE, Volume 4,

Number 6, ISSN 1995-6665 Pages 693 700.

5. Institute of Quality and Reliability, Control Chart Factors Tables of Constantsfor Control charts, Page 1 - 3.

6. Goyat N.S., Ahmad S., Chahal M., and Garg U. (2011), Effect of MachiningParameters on Output Characteristics of CNC Milling using Taguchi Optimization

Technique IJIET, Vol.3, No.2, ISSN 0974-3146, pp.209-214.

7. M. Mahajan, (2011) Statistical Quality Control, Dhanpat Rai and Company,Chapter 6, pp. 172 195.

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