Reporting quality-control

REPORTING QUALITY CONTROL

SUPERVISOR: Ms. Nguyen Nhu Phong

Monitoring Software Reliability using StatisticalProcess Control: An Ordered Statistics Approach

Hoàng Minh Công

21200393

Nguyễn Văn Bình

21200267

Nguyễn Trường Minh

Members:

Contents

4.CONLUCSION

3.STATISTICAL PROCESS CONTROL

2.ORDERED STATISTICS

1.INTRODUCTION

1. INTRODUCTION

Software Operation T/F = Reliable

Control

ORDERED STATISTICS

Goel-Okumoto model

SPC

M(t) : the random process representing the number of failures experienced by time t

- mean value function (the expected number of failures at time t): μ(t)=E[m(t)]

- failure intensity function (the instantaneous rate of change of the expected number of failures with respect to time) : λ(t)=

- software reliability function : R(t) = e-m(t)

1. INTRODUCTION

X denote a continuous random variable with:- Probability Density Function (PDF) f(x)- Cumulative Distribution Function (CDF) F(x)(X1 , X2 , …, Xn) denote a random sample of size n

drawn on X- X1 < X 2 <... <Xn

=> (X1, X2, …, Xn) are collectively known as the order statistics derived from the parent X.


The inter-failure time data - the time lapse between every two consecutive

failures.We can group the inter-failure time data into non

overlapping successive sub groups - size 4 or 5 - add the failure times within each sub group.The probability distribution of such a time lapse

= the rth ordered statistics in a subgroup of size r

= rth power of the distribution m (t)



Model Description

MODEL

Parameter estimation

and Control limits

2.1. Model DescriptionConsidering failure detection:- a non homogenous Poisson process - have an exponentially decaying rate function- the expected number of failures observed by time t

m(t)=a(1-e-bt)- the failure rate : λ(t)=m’(t)


Group the inter-failure time data into non overlapping successive sub groups of size r.

The mean value function can be written as

The likelihood function L


For the given observations using equations


2.2. Parameter estimation and Control limitsThe parameters “a” and “b” - computed by using the popular Newton Rapson

method- obtained from Goel-Okumoto model

Table 1: Parameter estimates and their control limits of 4 and 5 order Statistics


Control limits

These limits are convert at m(tu), m(tC) and m(tL)


3. STATISTICAL PROCESS CONTROL

Statistical process control- the application of statistical methods - provide the information necessary to continuously control - or improve processes throughout the entire lifecycle of a

product SPC techniques - help to locate trends, cycles, - irregularities within the development process and- provide clues about how well the process meets

specifications or requirements.


3.1. Control Chart

Control chart - displays sequential process measurements relative to the overall process average and control limits.

The upper and lower control limits (UCL & LCL)- establish the boundaries of normal variation for the

process being measured.- give the boundaries within which observed fluctuations

are typical and acceptable


3.2. Illustration

Table 2: Software failure data reported by Musa (1975)


Table 3: 4th order cumulative faults and their m(t) successive difference.



Table: 4: 5th order cumulative faults and their m(t) successive difference


4.CONCLUSION

The Mean value charts of Fig 1 and 2- out of control signals i.e. below LCL. - we identified that failures situation is detected at an early

stages.The early detection of software failure will improve the

software reliability. When the control signals are below LCL- have causes leading to significant process deterioration and - it should be investigated.

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