1 Statistical Quality Control & Monitoring

BY: ER. DAMANI MITAL.

2What is Quality ?

Quality : Degree of excellence a product or service provides.. ..Like Design , execution , plumbing, masonry , elevation ,r.c.c , concrete, materials , many other s too .In short we can say quality mean each and every things which relate to our field and which going to use for construction or execution of all our idea in reality or practically in that good work and delivery of assurance should be in it .

3Step to achieve quality

If we think for Low budget > Poor quality . The responsibility of quality is not only on builder

but on project team , owner , consultant , contractor , supervisor , people , …all of us .

The structure are good or not quality wise that assurance point is listed as follow :

Architecture design & building design should be sound .

Testing of structure on scale model should be carry out & result must be satisfactory .

Use of material should be choice by its usage . Methodology , workmanship , team work ,

supervisor ….everybody must having sound knowledge

4Quality control

Q.C depend on workmanship , material , person , Type of project .. Etc

Q.C is important part of project body but its important given to this point is too less ….

In civil engineering the quality comprises of 3 things :

Material used in construction Methodology used in project Testing of items

5Factor affecting quality control

Staff of Organization Methodology Skills of executive Supervisor standards Quality of raw material Quality control plan Machinery used for construction

6Advantage of quality control

Costing of project Wastage of material Less monitoring or inspection Firm reputation Technical knowledge became sound Complains from client reduced a lot speeding project get complete Override or penalty expenses reduced Machinery & staff complete in ideal time

7Objectives of quality control

Quality assurance :reliability ,durability , maintainability , interchange ability , safety , life of the structure

Project completion must happen as Costing & valuation made for it

The defect in project must be reduced The quality work should be as per decide by client

and standard must be fulfilled If change I design wants from client then that

should be done at a time of construction for good quality control

The list of defect & problem happen while doing project must be noted down and that should be not repeated

8Attributes & Variables

Attributes : any physical changes Like temperature ,weight of material , size , measurement , etc ….

Variables : abstraction belonging to entity or the assumption made to happen is not fulfllied Like Number of block in testing of conc cube , finishing of plaster , cracks in conc work ,

9What is SQC ?

Statistical quality control (SQC) is the term used to describe the set of statistical tools used by quality professionals.

In the process of Q.C of material , method , testing material , … this all can be assured by standards and that is to be maintained through out project .

Variables , attributes , unit & universe .

10Advantage of S.Q.C

Free from sources of variation By recognizing the fatal point and solve the

things The safety of product increases inspection at different stages reduces Solve errors in Experimental Usage of scrap decrease a cost of production The notable changes in project seems good

in development

11Objectives of S.Q.C

To notice the changes happens in quality and note down that for future use

Take good step to improve a quality work Mark a goal to achieve a quality Reduced a wastage of material

12Statistical process control

The process use for monitoring a process of quality performance and its technics that what mean S.P.C

Statistical : collecting , representation & analyzing data

Process : a sequence of operations Control : measuring performance Objectives : - collect the feedback to improve

work , find a source of problem created, predict about future step for improvement ,reduce weak point ….

13Tools /Techniques for SPC

Process flow chart Cause & effect diagram Check list Scatter diagram Pareto diagram Histogram Control charts Sampling

14Process flow chart

Material

receiveIncoming inspection Delivery

to stores

Verification at stores Entered in

ledgerstored

15Cause & effect diagram

people Materials Work method

Material received

Measurement Equipment Environment

16Tools & techniques cont….

Check list Scatter diagram Pareto diagram

0 1 2 301234

Y-Values

Y-Val-ues

Catego

ry 1

Catego

ry 3

0246

Series 1Series 2Series 3

17Methods of statistical quality control (S.Q.C)

Frequency distribution Control chart Acceptance sampling Special methods

18SQC Categories

Descriptive statistics

Statistical process control (SPC)

Acceptance sampling

19Characteristic measures of frequency distribution

Central tendency

Spread

20Descriptive Statistics

Descriptive statistics are used to describe quality characteristics and relationships.

21Descriptive Statistics

The Mean- measure of central tendency Median - the mid numeric Mode - the variable whose numeric value is

highest Variance - the difference of single numeric

and summation of numeric Co-efficient of variance The Range- difference between

largest/smallest observations in a set of data Standard Deviation measures the amount of

data dispersion around mean

22The Mean

To compute the mean we simply sum all the observations and divide by the total no. of observations.

23The Range

Range, which is the difference between the largest and smallest observations.

24Variance

V= (x – ŦŦ ) x = numeric value Ŧ = summation of value V = Variance Co – efficient of variance :- C= s/x x10 Range :- R = xmax – xmin

25Standard Deviation

Standard deviation is a measure of dispersion of a curve.

It measures the extent to which these values are scattered around the central mean.

26

• Extend the use of descriptive statistics to monitor the quality of the product and process

• Statistical process control help to determine the amount of variation

• To make sure the process is in a state of control

Statistical process control

26

27Variation in Quality

No two items are exactly alike.

Some sort of variations in the two items is bound to be there. In fact it is an integral part of any manufacturing process.

This difference in characteristics known as variation.

This variation may be due to substandard quality of raw material, carelessness on the part of operator, fault in machinery system etc..

28Important terms

Sample Sample size Sampling fraction Item Sampling Lot Lot size Inspection

29Sampling techniques

Simple random samplingStratified sampling Systematic sampling Cluster sampling Two stage sampling Refer book content ….

30

100% inspection Sampling inspection

Lot inspection More cost Less cost

Machines Required modern machines

Feasible in routine machines

Inspection Damaging more Less

Inference No perdition Predictable

Destructive test Not valid Valid

Risk in choice material Valid Not valid

31

Inspection by attributes

Inspection by variable

Define

Inspection Visual Measurement

Inference More material Less material

Item quality Sample quality made easily

Difficult

Inspection process Subjective Objective

At time More Point consideration

Less

32Acceptance sampling

Dividing whole lot into small part

Take a random sample from lot Inspect that sample and come

to result Based on inspection result take

decision to accept or reject the lot

33Pros & Nros of acceptance sampling

Low costing in inspection process Easy & feasible This method is convent for big lot Less stressful Time consuming is less Decrease the chance of lot

acceptance by supplier Supplier may accept Poor quality of

lot

34Sampling plan

Single sample plan Double sample plan Multiple sampling plan Sequential sampling plan

35Symbol used for sampling plan calculation

N = total number of product n = sample number C = acceptance number r = rejected number For eg : n= 7 N= 100 C=0

36Types Of Variations

Variation due to “CHANCE CAUSES”

Variation due to “ASSIGNABLE CAUSES”

37Variation due to chance causes/common causes

Variation occurred due to chance. This variation is NOT due to defect in machine,

Raw material or any other factors. Behave in “random manner”. Negligible but Inevitable The process is said to be under the state of

statistical control.

37

38Variation due to assignable causes

Non – random causes like:

Difference in quality of raw materialDifference in machinesDifference in operatorsDifference of time

38

39

40Specification and control limits

No item in the world can be a true copy of another item.

It is not expressed in absolute values but in terms of a range.

For Eg: The diameter of a pen is expected by its manufacturer not as 7mm but as 7mm ± 0.05. Thus, the diameter of a pen produced by the manufacturer can vary from 6.95 mm to 7.05 mm.

41Setting Control Limits

42HOW CONTROL LIMITS ARE USEFUL…..?

43SPC Methods-Control Charts

Control Charts show sample data plotted on a graph with CL, UCL, and LCL

Control chart for variables are used to monitor characteristics that can be measured, e.g. length, weight, diameter, time

Control charts for attributes are used to monitor characteristics that have discrete values and can be counted, e.g. % defective, number of flaws in a shirt, number of broken eggs in a box

44Control Charts for Variables

x-bar charts It is used to monitor the changes in the mean of a process (central tendencies).

R-bar charts It is used to monitor the dispersion or variability of the process

45Constructing a X-bar chart ( sigma is not given)

A factory produces 50 cylinders per hour. Samples of 10 cylinders are taken at random from the production at every hour and the diameters of cylinders are measured. Draw X-bar and R charts and decide whether the process is under control or not.

(For n=4 A2= 0.73 D3= 0, D4=2.28)

46

Sample no.

x1 x2 x3 x4

1 230 238 242 2502 220 230 218 2423 222 232 236 2404 250 240 230 2255 228 242 235 2256 248 222 220 2307 232 232 242 2428 236 234 235 2379 231 248 251 27110 220 222 224 231

47Sample no.

x1 x2 x3 x4 SigmaXi

MeanX-bar

Range R

1 230 238 242 250 960 240.00 202 220 230 218 242 910 227.50 243 222 232 236 240 930 232.50 184 250 240 230 225 945 236.25 255 228 242 235 225 930 232.50 176 248 222 220 230 920 230.00 287 232 232 242 242 948 237.00 108 236 234 235 237 942 235.50 39 231 248 251 271 1001 250.25 4010 220 222 224 231 897 224.25 11Total 2345.7

5196

48Calculation of x-bar and R-bar

Now,

75.2341075.2345

m x

x

6.1910196

mR

R

49

Factor for x-Chart

A2 D3 D42 1.88 0.00 3.273 1.02 0.00 2.574 0.73 0.00 2.285 0.58 0.00 2.116 0.48 0.00 2.007 0.42 0.08 1.928 0.37 0.14 1.869 0.34 0.18 1.8210 0.31 0.22 1.7811 0.29 0.26 1.7412 0.27 0.28 1.7213 0.25 0.31 1.6914 0.24 0.33 1.6715 0.22 0.35 1.65

Factors for R-ChartSample Size (n)

50Control limits of X-Bar Chart Central line C.L =

U.C.L = =234.75 + (0.73) (19.6) =249.06

L.C.L= =234.75- (0.73) (19.6) =220.72

RAx *2

RAx *2

75.234x

51X-Bar Chart

52Control limits of R-Bar Chart

Central Line =

U.C.L = =45.50

L.C.L = =0

6.19R

)96.19(*)28.2(4 RD

)96.19(*)0(3 RD

53R-Bar Chart

54Constructing a X-bar Chart (Sigma is given) A quality control inspector at the Coca-Cola soft drink

company has taken twenty-five samples with four observations each of the volume of bottles filled. The data and the computed means are shown in the table. If the standard deviation of the bottling operation is 0.14 ounces, use this information to develop control limits of three standard deviations for the bottling operation.

55

56Equations

2dRs

nsx

xzXLCL

xzXUCL

57

58X-Bar Control Chart

59Control Charts for Attributes Attributes are discrete events; yes/no, pass/fail

Use P-Charts for quality characteristics that are discrete and involve yes/no or good/bad decisions

Number of leaking caulking tubes in a box of 48 Number of broken eggs in a carton

Use C-Charts for discrete defects when there can be more than one defect per unit

Number of flaws or stains in a carpet sample cut from a production run

Number of complaints per customer at a hotel

60P-Chart Example

A Production manager of a BKT tire company has inspected the number of defective tires in five random samples with 20 tires in each sample. The table below shows the number of defective tires in each sample of 20 tires. Calculate the control limits.

61

62

63P- Control Chart

64C - Chart Example

The number of weekly customer complaints are monitored in a large hotel using a c-chart. Develop three sigma control limits using the data table below.

65

66

67C - Control Chart

68Process Capability

Evaluating the ability of a production process to meet or exceed preset specifications. This is called process capability.

Product specifications, often called tolerances, are preset ranges of acceptable quality characteristics, such as product dimensions.

69Two parts of process capability

1) Measure the variability of the output of a process, and

2) Compare that variability with a proposed specification or product tolerance.

70Measuring Process Capability

To produce an acceptable product, the process must be capable and in control before production begins.

6LSLUSLC p

71Example

Let’s say that the specification for the acceptable volume of liquid is preset at 16 ounces ±.2 ounces, which is 15.8 and 16.2 ounces.

72Figure (a)

The process produces 99.74 percent (three sigma) of the product with volumes between 15.8 and 16.2 ounces.

1pC

73Figure (b)

The process produces 99.74 percent (three sigma) of the product with volumes between 15.7 and 16.3 ounces.

1pC

74Figure (c)

the production process produces 99.74 percent (three sigma) of the product with volumes between 15.9 and 16.1 ounces.

1pC

75

76

77Process capability ratio (off centering process)

There is a possibility that the process mean may shift over a period of time, in either direction, i.e., towards the USL or the LSL. This may result in more defective items then the expected. This shift of the process mean is called the off-centering of the process.

3

,3

min LSLUSLCkp

78Example

Process mean:

Process standard deviation: LSL = 15.8 USL = 16.2

9.15

067.0

1)067.0(6

4.0pC

79

3

,3

min LSLUSLCkp

33.0

33.0,00.1min

)1(.38.159.15,

)1(.39.152.16min

pk

pk

kp

C

C

C

80

Thank You…