UNIVERSITY OF AGRICULTURE,

FAISALABAD

Department of Mathematics and

Statistics

(Synopsis

for M. Phil degree in Statistics)

Title: Comparison

of Robust Techniques in Process of Capability Index by Dealing Outlier

Name of the Student : Muhammad Zeeshan Mustafa Shah

Registration Number : 2016-ag-1777

ABSTRACT

Process

capability indices used to measure the variability and reduced the variability

of the data. One technique is that convert non normal data in to normal data by

using any transformation technique. Results of the process capability indices

compare with the Box-

Plot and Percentile methods. We will use the Burr Percentile method, weighted

variance method, distribution independent, tolerance independent interval,

probability graphs and root transformation technique. When the target value of

one product characteristic coincides with the mid-point of tolerance interval

the tolerance is called asymmetric. The case study results provide the insights

about the process in the term of process variation. The location of the mean in

the specification interval and fraction non confirming.

Introduction:

Process

capability indices used for reduced and measures the variability. If outliers

are available then many indices will be unreliable. The outlier makes cause of

variability. Process capability indices have been discussed by many

researchers. Only two are the basis approaches estimating process capability

indices for non-normal process. First is to convert non-normal data into normal

data using any transformation technique. Used any conventional methods are easy

to deploy. Non-normal percentile may be another approach for transformation non

normal data to the normal data. This

approach is not easy for converting non-normal data in to the normal data. Convert

non-normal into normal data by transformation technique called root transformation.

The effect of the technique by conducting simulation study using any

statistical distribution applies on the simulated data. Results compared with

process capability indices obtain using exact Box-plot and percentile methods.

The conventional methods give lead to erroneous interpretation of process

capability many methods may be proposed for computing process capability

indices under non normality. The improvement and quality improvement the

quality products control chart are consider compulsory tool. For control chart

used variables and attributes are unsatisfactory for process monitoring. For

this difficulty proposed monitoring scheme that is an improved technique based

on the joint matrices of the variables as well as attributes control chart.

Multivariate process capability indices are applied to the capability of the

process which quality of the product depends upon two or more related

characteristics. Process capability indices are widely used to the measure of

process potential and process performance. Used sample data to estimate process

capability indices means that any error in sampling consider uncertainty into

the assessment of process capability.

The

process capability indices or the process capability ratio measure how much

natural variation in the process. The process capability indices include upper

specification limits and lower specifications limits. The term T is the measure

of the trend process.

Is the estimated mean and is the estimated standard deviation.

=

=

=

This expression is for suitable if mean

may not be center between the specifications limits. The term specifications

are same as requirements.

The specification limits communicate to

the customer’s requirements desire and need for the process. The control limits

equal to prediction variation that the process will exhibit in the near future.

If the value of are equal then means that producing product

meeting to the specifications.

The meaning of robust techniques as well

as to the resistance to errors in the results. Robust data make cause of the

bias. If the sample size tends to infinity then Bias will be equal to zero.

REVIEW OF LITERATURE:

Aslam

et al., (2017) urged that the compulsory

tool for monitoring were control charts. Through control chart quality improve

of any product. Variable control chart commonly used for overcome the

difficulty proposed monitoring scheme that the merits were improved the techniques based on the merits of attributes

same to the control chart has been determined for out of control and in control

situations for specified average by using

simulation. The efficiency of control chart was evaluated through

average. This technique practical example implementation on practical example

has been studied.

Chen

et al., (2017) urged that process

capability indices widely used as measure of process potential and process

performance. Use sample data to estimate process capability indices means any

error in sampling can introduce considerable uncertainty into the assessment of

process capability. Used of the lower confidence limit in estimation of minimum

process capability. The complexity of the sampling distribution of process

capability indices greatly hinder interval estimation only an approximation

only lower class limit can achieved. This paper purpose a novel approach to

deriving the 100( 1 – ? ) % lower class limit of indices, and by used Boole’s inequality and DE Morgan’s

Theorem. This technique is based on the sample data calculated from the stable

process. The quality for determine the process capability that satisfied the customers requirements there

for this purpose used hypothesis testing.

Kovarik

and Sarga (2014) urged that the probability distribution of a process

characteristic was non-normal and indices estimated by using conventional

methods often lead to erroneous interpretation of process capability. Many

methods available have proposed for process capability indices of

non-normality. But for literature sources offer comprehensive evaluation and

comparison they were suitable process capability under severe departure form

normality. Overview nine methods to their preference when identified the

process capability indices non normality so carried out by the lognormal data

use box plots for results.

Mondal

et al., (2010) urged that the concept

of process capability indices was given in early 1970 with the introduction of

“capability ratio” by Juan world known. He was quality expert. After the death

of Juan indices, and were developed. Many researchers concern about

the application of the diversified indices owing to the three reasons. First

was theoretical for practitioners. Second was mismatching with preference

values measure through many indices. Third was inadequacy to mimic the reality.

This study focused on the application of different indices developed. Results

obtained by comparing with percent conforming products as well as amongst the

indices themselves.

Hossein

et al., (2009) is stated that non

normal process estimates the process capability indices has discussed by many

researchers. There were two approaches for process capability indices. First is

that transformation the non-normal data into normal data using any transformation

techniques and used any conventional method for calculating principal component

indices for transformation data. This approach was very simple to the second

method used non-normal percentiles to calculate the process capability

analysis. Second method was not easy to implement on the data for calculated

the principal component indices. In this paper used root transformation method

for calculating the process capability indices. The method transformation based

on simulation study on the gamma, weibull and beta distribution apply root

transformation on the simulation data.

Anis

(2008) urged that the four basis process capability indices have been made. The

relationship in these indices has been highlighted. The sample size has been

emphasized. Used non-normal distributions, skewed distributions and auto

correlated data were presented. Effects of measurement errors on process

capability indices have been dealt with in great detail.

Bothe

(2006) urged that a procedure for determining the process capability indicates

was whole centers within a circular tolerance zone. In this procedure the and index practitioners can compare the two matrix.

Determine process capability is lacked due to the poor centering excessive

variation.

Ortiz

et al., (2006) studied that

analytical procedure validation means the evaluation of some performance

criteria as accuracy, linear range and capability detection. For checking there

procedures are robust or not we can applied many statistical techniques. If

outlier available then significant effect on the determination of sensitivity.

Wang.

C (2004) urged that the short run facilities of production were become rapidly the

consumer requirements increased techniques of production improved. The product

was lie in the small lot. The researcher cannot collect sufficient samples for

determine the distribution of quality characteristics estimated process

parameters. The multiple quality characteristics must be simultaneously

evaluated for determine product quality. The complexity of the product design

on the high value. Conventional process capability indices as and not satisfy requirements. Multiple process

capability indices have been studied. This study focus on the characteristics

and mass production assumed that quality characteristic was normally

distributed in developed the multiple process capability indices. The multiple

process capability indices used the techniques of principal component analysis.

Zhao

et al., (2004) stated that the

deduction of outlier based on radical basis functions partial least squares

approach. Prescott test apply was used for detection of the outlier in complex

system. Weighted error back propagation algorithm proposed to keep the training

of multi-layer forward networks from the disturbance of outlier.

Palmer

et al., (1999) urged that the

industrial statistics was generally familiar with the and process capability indices. Many additional

indices have been proposed and knowledge of there is less widespread. Regarding

the indices comparative behavior was lacking. In this study the behavior of

various indices under shifting process conditions. Both have been studied

useful and misleading characteristic of the indices are identified. Many

process capability indices have been reviewed. Application of capability

indices is also summarized. The indices are grouped according to the loss

functions which used in interpretation. Recommendations were made for selection

of indices at different levels of process performance.

Parsad

(1998) studied that many organizations used process capability analysis was

estimated and measured the variability the used of indices as unreliable. The

integration of dependency structure and outliers may be caused of variations.

The monitoring was proposed that effectively classifies a first variability

into the component. There underlying correlation structure. Third unexplained

variance indices proposed to distinguish in these three components. The

approach helps to identify the appropriate corrective action to be taken to

reduced variability.

Choi

et al., (1996) stated that the

process capability index was recently proposed to the measured the

degree of process capability of a system, . In this paper present

the estimators of and derived its asymptotic distribution also

utilized the asymptotic variance of estimator of to divide the two sided confidence interval

for based on the percentile t bootstrap technique.

The new confidence intervals are shown to outperform the ones based on the

percentile and standard bootstrap on the basis of simulation.

MATERIALS AND METHODS:

The

process capability indices measure how much natural variation in the data. For

this purpose we will use different methods for checking variability and outlier

in the given data. The methods are given blew. The method

transformation based on simulation study on the gamma, weibull and beta

distribution (life time distributions) apply root transformation on the

simulation data.

1. John

transformation

2. Burr

Percentile method.

3. Weighted

variance method.

4. Distribution

independent Tolerance interval.

5. Bool’s

Inequality.

6. Use and conventiol methods.

7. Probability

graph.

8. Non

normal percentile.

9. Root

transformation.