Ppt On S.Q.C.

STATISTICAL STATISTICAL

QUALITYQUALITY

CONTROLCONTROL

(S.Q.C.)(S.Q.C.)

PRESENTED BY-: PRESENTED BY-: NIKHIL GARGNIKHIL GARG ROLL NO- ROLL NO- 01296260129626

Contents-:Contents-:Meaning…………….Meaning…………….Definitions …………Definitions …………Characteristics………Characteristics………Causes of variations……….Causes of variations……….Methods of S.Q.C………..Methods of S.Q.C……….. Process Control-:Process Control-: Control Chart………..Control Chart……….. Purpose & uses of control charts……….Purpose & uses of control charts………. Types of control charts………Types of control charts……… Control charts for variables-:Control charts for variables-: Chart……Chart…… R Chart ……R Chart …… σσ Chart………Chart………

Control chart for attributes-:Control chart for attributes-: p-chart………… p-chart………… np-chart…...... np-chart…...... C-Chart………… C-Chart………… Product Control/Acceptance Sampling-:Product Control/Acceptance Sampling-: Meaning………….. Meaning………….. Definition…………. Definition…………. Risks in Acceptance Sampling-: Risks in Acceptance Sampling-: Producer’s Risk………. Producer’s Risk………. Consumer’s Risk………. Consumer’s Risk………. Types of Sampling Inspection plans-: Types of Sampling Inspection plans-: Single Sampling plan……… Single Sampling plan……… Double Sampling Plan…….. Double Sampling Plan…….. Multiple Sampling Plan……. Multiple Sampling Plan……. Advantages of S.Q.C……………Advantages of S.Q.C……………Limitations of S.Q.C…………….Limitations of S.Q.C…………….

Acknowledgement-:Acknowledgement-:

Mrs. Sheenu KhuranaMrs. Sheenu Khurana our our BusinessBusiness StatisticsStatistics lecturer. lecturer. Without her guidance & Without her guidance & suggestions this work is not suggestions this work is not possible…..possible…..

MEANING-:MEANING-:

manufactured Refers to the use of manufactured Refers to the use of statistical techniques in controlling statistical techniques in controlling the quality of goods.the quality of goods.

Means of establishing & achieving Means of establishing & achieving quality specification, which requires quality specification, which requires use of tools & techniques of use of tools & techniques of statistics.statistics.

DEFINATION-:DEFINATION-:

““Statistical quality control can be simply Statistical quality control can be simply defined as an economic & effective system defined as an economic & effective system of maintaining & improving the quality of of maintaining & improving the quality of outputs throughout the whole operating outputs throughout the whole operating process of specification, production & process of specification, production & inspection based on continuous testing inspection based on continuous testing with random samples.”with random samples.”

By-:By-:

YA LUN CHOUYA LUN CHOU

Definition-:Definition-:

““Statistical quality control should be Statistical quality control should be viewed as a kit of tools which may viewed as a kit of tools which may influence decisions to the functions of influence decisions to the functions of specification, production or inspection.specification, production or inspection.

By-:By-:

EUGENE L. GRANTEUGENE L. GRANT

CHARACTERISTICS OF S.Q.C.-:CHARACTERISTICS OF S.Q.C.-:

Designed to control quality standard of goods Designed to control quality standard of goods produced for marketing.produced for marketing.

Exercise by the producers during production to Exercise by the producers during production to assess the quality of goods.assess the quality of goods.

Carried out with the help of certain statistical Carried out with the help of certain statistical tools like Mean Chart, Range Chart, P-Chart, C-tools like Mean Chart, Range Chart, P-Chart, C-Chart etc.Chart etc.

Designed to determine the variations in quality of Designed to determine the variations in quality of the goods & limits of tolerance.the goods & limits of tolerance.

CAUSES OF VARIATIONS IN CAUSES OF VARIATIONS IN QUALITY-:QUALITY-:

1.1. ASSIGNABLE CAUSES-:ASSIGNABLE CAUSES-: It refers to those It refers to those changes in the quality of the products changes in the quality of the products which can be assigned or attributed to any which can be assigned or attributed to any particular causes like defective materials, particular causes like defective materials, defective labour, etc.defective labour, etc.

2.2. CHANCE CAUSES-:CHANCE CAUSES-: These causes take These causes take place as per chance or in a random place as per chance or in a random fashion as a result of the cumulative effect fashion as a result of the cumulative effect of a multiplicity of several minor causes of a multiplicity of several minor causes which cannot be identified. These causes which cannot be identified. These causes are inherent in every type of production.are inherent in every type of production.

METHODS OF S.Q.C.-:METHODS OF S.Q.C.-:

1.1. PROCESS CONTROL-:PROCESS CONTROL-: Under this the Under this the quality of the products is controlled while quality of the products is controlled while the products are in the process of the products are in the process of production.production.

The process control is secured with theThe process control is secured with the technique oftechnique of control chartscontrol charts. . Control Control chartscharts are also used in the field of are also used in the field of advertising, packing etc. They ensures advertising, packing etc. They ensures that whether the products confirm to the that whether the products confirm to the specified quality standard or not.specified quality standard or not.

A control chart is a time plot of a statistic, such as a sample mean, range, standard deviation, or proportion, with a center line and upper and lower control limits. The limits give the desired range of values for the statistic. When the statistic is outside the bounds, or when its time plot reveals certain patterns, the process may be out of control.

A control chart is a time plot of a statistic, such as a sample mean, range, standard deviation, or proportion, with a center line and upper and lower control limits. The limits give the desired range of values for the statistic. When the statistic is outside the bounds, or when its time plot reveals certain patterns, the process may be out of control.

A process is considered in statistical control if it has no assignable causes, only natural variation.

A process is considered in statistical control if it has no assignable causes, only natural variation.

UCL

LCL

CenterLine

Time

ValueThis point is out of the control limitsThis point is out of the control limits

3

3

Control ChartControl Chart

PURPOSE & USES OF CONTROL PURPOSE & USES OF CONTROL CHARTSCHARTS

1.1. Helps in determining the quality standard Helps in determining the quality standard of the products.of the products.

2.2. Helps in detecting the chance & Helps in detecting the chance & assignable variations in the quality assignable variations in the quality standards by setting two control limits.standards by setting two control limits.

3.3. Reveals variations in the quality Reveals variations in the quality standards of the products from the standards of the products from the desired level.desired level.

4.4. Indicates whether the production process Indicates whether the production process is in control or not.is in control or not.

5.5. Ensures less inspection cost & time in the Ensures less inspection cost & time in the process control.process control.

Types-:Types-:

Types of Control Charts

Control Charts

for Variables

Chart

Control Charts for Attributes

R-Chart σ-Chart p-Chartnp-

ChartC-Chart

CONTROL CHATS FOR CONTROL CHATS FOR VARIABLESVARIABLES

CHART/ MEAN CHART-:CHART/ MEAN CHART-: This chart is constructed for controlling the variations in the average quality standard of the products in a production process.

R-CHART-: This chart is constructed for controlling the variations in the dispersion or variability of the quality standards of the products in a production process.

EXAMPLE-:EXAMPLE-:

Sample No.Sample No. WeightsWeights

11

22

33

44

55

2020 15 10 11 1415 10 11 14

2121 18 10 8 2218 10 8 22

2121 19 17 10 1319 17 10 13

2222 12 19 14 2012 19 14 20

20 19 26 12 2320 19 26 12 23

Conversion factors for n=5, AConversion factors for n=5, A2 2 =0.577, D=0.577, D33 =0, =0, DD44=2.115=2.115

Solution-:Solution-:Sample Sample no.no.

Weights (X)Weights (X) TotalTotal

Weights Weights ((ΣΣX)X)

=(=(ΣΣX/5)X/5)

RangeRange

R=(L-R=(L-S)S)

11

22

33

44

55

K=5K=5

2020 15 10 11 1415 10 11 14

2121 18 10 8 2218 10 8 22

2121 19 17 10 1319 17 10 13

2222 12 19 14 2012 19 14 20

20 19 26 12 2320 19 26 12 23

7070

7070

8080

8080

100100

1414

1414

1616

1616

2020

Σ Σ =80=80

1010

1414

1111

88

1414

ΣΣR=57R=57

GrandGrand = = ΣΣ/K = 80/5=16/K = 80/5=16

GrandGrand Chart Chart GrandGrand = 16 (Central line)= 16 (Central line)

Control limits-: Control limits-:

UCL =UCL = Grand + A Grand + A2 2 = 16 + 0.577 x 11.4 = 16 + 0.577 x 11.4 = 22.577 = 22.577

LCL =LCL = Grand - Grand - AA22 = 16 – 0.577 x 11.4= 16 – 0.577 x 11.4 = 9.423 = 9.423

= = ΣΣR/K = 57/5 = 11.4R/K = 57/5 = 11.4

Range ChartRange Chart = 11.4 (Central line)= 11.4 (Central line)

Control limits-:Control limits-:

UCL = DUCL = D44. . = 2.115 x 11.4= 2.115 x 11.4 = 24.09= 24.09

LCL = DLCL = D33.. = 0 x 11.4= 0 x 11.4 = 0= 0

σσ Chart-: Chart-: This chart is constructed to get a better This chart is constructed to get a better picture of the variations in the quality standard in a process picture of the variations in the quality standard in a process than that is obtained from the range chart provided the than that is obtained from the range chart provided the standard deviation(standard deviation(σσ) of the various samples are readily ) of the various samples are readily available.available.

Example-:Example-: Quality control is maintained in a factory Quality control is maintained in a factory with the help of standard deviation chart. Ten items are with the help of standard deviation chart. Ten items are chosen in every sample. 18 samples in all were chosen chosen in every sample. 18 samples in all were chosen whose whose ΣΣS was 8.28. Determine the three sigma limits S was 8.28. Determine the three sigma limits of of σσ- chart. - chart. You may use the following-: You may use the following-:

n = 10, Bn = 10, B33 = 0.28, B = 0.28, B44 = 1.72, K = 18. = 1.72, K = 18.

Solution-:Solution-: = = ΣΣS/K = 8.28/18 = 0.46S/K = 8.28/18 = 0.46

UCL = BUCL = B44. LCL = B. LCL = B33. . = 1.72 x 0.46 = 0.28 x 0.46= 1.72 x 0.46 = 0.28 x 0.46 = 0.7912 = 0.1288= 0.7912 = 0.1288

Control Charts for Attributes-:Control Charts for Attributes-:

p-chart-:p-chart-: This chart is constructed for This chart is constructed for controlling the quality standard in the average controlling the quality standard in the average fraction defective of the products in a process fraction defective of the products in a process when the observed sample items are classified when the observed sample items are classified into defectives & non-defectives.into defectives & non-defectives.

np-chart-:np-chart-: This chart is constructed for This chart is constructed for controlling the quality standard of attributes in controlling the quality standard of attributes in a process where the sample size is equal & it is a process where the sample size is equal & it is required to plot the no. of defectives (np) in required to plot the no. of defectives (np) in samples instead of fraction defectives (p).samples instead of fraction defectives (p).

Example-:Example-:

Sample No. Sample No.

Size of sample Size of sample (n)(n)

No. of No. of defectives (d)defectives (d)

Fraction Fraction defectives defectives (d/n)(d/n)

11

22

33

44

55

66

77

88

99

1010

100100

100100

100100

100100

100100

100100

100100

100100

100100

100100

55

33

33

66

55

66

88

1010

1010

44

0.050.05

0.030.03

0.030.03

0.060.06

0.050.05

0.060.06

0.080.08

0.10.1

0.10.1

0.040.04

K = 10K = 10 ΣΣd = 60d = 60

= = Total no. of defectives/Total no. of units Total no. of defectives/Total no. of units = 60/1000 = 0.06= 60/1000 = 0.06»q»q̅̅ = 1-= 1- = 1- 0.06 = 0.94= 1- 0.06 = 0.94 = 0.06 (central line)= 0.06 (central line)

UCL =UCL = + 3 + 3√ √ . q. q̅̅/n/n = 0.06 + 3√0.06x0.94/100= 0.06 + 3√0.06x0.94/100 = 0.1311 = 0.1311LCL = LCL = - 3- 3 √ √ . q. q̅/n̅/n = 0.06 - 3= 0.06 - 3 √ √ 0.06x0.94/1000.06x0.94/100 = -0.0111 = 0 = -0.0111 = 0

Example-:Example-:An inspection of 10 samples of size 400 each from 10 lots An inspection of 10 samples of size 400 each from 10 lots

reveal the following number of defectives:reveal the following number of defectives:17, 15, 14, 26, 9, 4, 19, 12, 9, 1517, 15, 14, 26, 9, 4, 19, 12, 9, 15Calculate control limits for the no. of defective units.Calculate control limits for the no. of defective units.

Solution-:Solution-: n = 400, k (No. of samples) = 10, n = 400, k (No. of samples) = 10, ΣΣd (total no. of d (total no. of defectives) = 140defectives) = 140

nn = = ΣΣd/k = 140/10 = 14d/k = 140/10 = 14

Now, = Now, = nn/n = 14/400 = 0.035,/n = 14/400 = 0.035,

»q»q̅ = 1- ̅ = 1- = 1- 0.035 = 0.965 = 1- 0.035 = 0.965

nn = 14 (central line) = 14 (central line)

UCL= UCL= nn + 3 + 3√ n√ n q q̅ LCL= ̅ LCL= nn - 3 - 3√ √ nn qq̅̅ ̅̅ = 14 + 3= 14 + 3√400x0.035x0.965 = √400x0.035x0.965 = 14 - 14 -

33√400x0.035x0.965 √400x0.035x0.965 = 25.025 = 2.975= 25.025 = 2.975

C-Chart-:C-Chart-: This chart is used This chart is used for the control of no. of for the control of no. of defects per unit say a piece defects per unit say a piece of cloth/glass/paper/bottle of cloth/glass/paper/bottle which may contain more which may contain more than one defect. The than one defect. The inspection unit in this chart inspection unit in this chart will be a single unit of will be a single unit of product. The probability of product. The probability of occurrence of each defect occurrence of each defect tends to remain very small.tends to remain very small.

USES-:USES-:

The following are the field of The following are the field of application of C-Chart-:application of C-Chart-:

Number of defects of all kinds of Number of defects of all kinds of aircraft final assembly.aircraft final assembly.

Number of defects counted in a roll Number of defects counted in a roll of coated paper, sheet of of coated paper, sheet of photographic film, bale of cloth etc.photographic film, bale of cloth etc.

ACCEPTANCE SAMPLINGACCEPTANCE SAMPLING

Meaning-:Meaning-:Another major area of S.Q.C. is Another major area of S.Q.C. is

“Product Control” or “Acceptance “Product Control” or “Acceptance Sampling”. It is concerned with the Sampling”. It is concerned with the inspection of manufactured products. inspection of manufactured products. The items are inspected to know The items are inspected to know whether to accept a lot of items whether to accept a lot of items conforming to standards of quality or conforming to standards of quality or reject a lot as non- conforming.reject a lot as non- conforming.

DEFINATION-:DEFINATION-:

“ “ Acceptance Sampling is concerned with Acceptance Sampling is concerned with the decision to accept a mass of the decision to accept a mass of manufactured items as conforming to manufactured items as conforming to standards of quality or to reject the mass standards of quality or to reject the mass as non-conforming to quality. The decision as non-conforming to quality. The decision is reached through sampling.”is reached through sampling.”

By-:By-:

SIMPSON AND SIMPSON AND KAFKAKAFKA

Risks in Acceptance samplingRisks in Acceptance sampling

1.1. Producer’s risk-:Producer’s risk-: Sometimes inspite of Sometimes inspite of good quality, the sample taken may show good quality, the sample taken may show defective units as such the lot will be defective units as such the lot will be rejected, such type of risk is known as rejected, such type of risk is known as producer’s risk.producer’s risk.

2.2. Consumer’s Risk-:Consumer’s Risk-: Sometimes the quality Sometimes the quality of the lot is not good but the sample of the lot is not good but the sample results show good quality units as such the results show good quality units as such the consumer has to accept a defective lot, consumer has to accept a defective lot, such a risk is known as consumer’s risk.such a risk is known as consumer’s risk.

Types of Sampling Inspection PlanTypes of Sampling Inspection Plan

Single Sampling Plan-:Single Sampling Plan-: Under single Under single sampling plan, a sample of ‘n’ items sampling plan, a sample of ‘n’ items is first chosen at random from a lot is first chosen at random from a lot of N items. If the sample contains, of N items. If the sample contains, say, ‘c’ or few defectives, the lot is say, ‘c’ or few defectives, the lot is accepted, while if it contains more accepted, while if it contains more than ‘c’ defectives, the lot is rejected than ‘c’ defectives, the lot is rejected (‘c’ is known as ‘acceptance (‘c’ is known as ‘acceptance number’).number’).

Single Sampling PlanSingle Sampling Plan

Count the no. of defectives, ‘d’ in the sample of size ‘n’

Is ‘d’ ≤ ‘c’

If yes, than accept the lot If no, then reject the lot

Double Sampling Plan-:Double Sampling Plan-:

Under this sampling plan, a sample of ‘nUnder this sampling plan, a sample of ‘n11’ ’ items is first chosen at random from the lot items is first chosen at random from the lot of size ‘N’. If the sample contains, say, ‘cof size ‘N’. If the sample contains, say, ‘c11’ or ’ or few defectives, the lot is accepted; if it few defectives, the lot is accepted; if it contains more than ‘ccontains more than ‘c22’ defectives, the lot is ’ defectives, the lot is rejected. If however, the number of rejected. If however, the number of defectives in the sample exceeds ‘cdefectives in the sample exceeds ‘c11’, but is ’, but is not more than ‘cnot more than ‘c22’, a second sample of ‘n’, a second sample of ‘n22’ ’ items is take from the same lot. If now, the items is take from the same lot. If now, the total no. of defectives in the two samples total no. of defectives in the two samples together does not exceed ‘ctogether does not exceed ‘c22’, the lot is ’, the lot is accepted; otherwise it is rejected. (‘caccepted; otherwise it is rejected. (‘c11’ is ’ is known as acceptance no. for the first sample known as acceptance no. for the first sample & ‘c& ‘c22’ is the acceptance no. of both the ’ is the acceptance no. of both the samples taken together)samples taken together)

Double Sampling Plan-:Double Sampling Plan-:Count the no. of defectives, d1in the first sample of size

n1

Is d1 ≤ c1 ?

Draw another sample of size n2

If No, then check If c1 ≤ d1 ≥ c2 ?

Count the no. of defectives d2

in this sample

Is d1 + d2 ≤ c2

If No, reject the lot

If yes, accept the lot

If yes, then accept the lot.

Multiple Sampling Plan-:Multiple Sampling Plan-:

Under this sampling plan, a decision to Under this sampling plan, a decision to accept or reject a lot is taken after accept or reject a lot is taken after inspecting more than two samples of inspecting more than two samples of small size each. In this plan, units are small size each. In this plan, units are examined one at a time & after examined one at a time & after examining each unit decision is examining each unit decision is taken. taken. “However, such plan are very “However, such plan are very complicated & hence rarely used in complicated & hence rarely used in practice.”practice.”

ADVANTAGES OF S.Q.C.-:ADVANTAGES OF S.Q.C.-:

Helpful in controlling quality of a Helpful in controlling quality of a productproduct

Eliminate Assignable causes of Eliminate Assignable causes of variationvariation

Better quality at lower inspection costBetter quality at lower inspection cost Useful to both consumers & producersUseful to both consumers & producers It makes workers quality consciousIt makes workers quality conscious Helps in earn goodwillHelps in earn goodwill

LIMITATIONS-:LIMITATIONS-:

Does not serve as a ‘PANACEA’ for all Does not serve as a ‘PANACEA’ for all quality evils.quality evils.

It cannot be used to all production It cannot be used to all production process.process.

It involves mathematical & statistical It involves mathematical & statistical problems in the process of analysis & problems in the process of analysis & interpretation of variations in quality.interpretation of variations in quality.

Provides only an information services.Provides only an information services.

THE THE END END