26 Statistical Process Control Methods: Control Chart for Attributes

Kajal Kiran

26.1 OBJECTIVES

This chapter will help the students to grasp:

• The concept of control chart for attributes
• The type of control charts
• Practical application of P charts, np charts and C charts.

26.2  INTRODUCTION

A control chart is a graphic presentation depicting whether a sample of data falls within the common or normal range of variation. Control charts can be classified as control chart for variables and control chart for attributes. There are certain limitations attached with control chart for variables like these can be used only when quality characteristic of a product can be measured quantitatively and expressed in numbers.

Thus where quality characteristic of a product cannot be quantified, control charts for attributes are used.

Attributes are those parameters which can only be identified by their presence or absence from the product such as air bubble, scratches, defective print on cloth etc.

Control charts for attributes are of three types:-

• Control charts for proportion of defective units (P-chart)
• Control charts for number of defectives (np-chart)
• Control charts for number of defects (C-chart)

26.3 TYPES OF CONTROL CHARTS FOR ATTRIBUTES

Various Control charts for attributes are

• Control charts for proportion of defective units (P-chart)

P-chart are known as fraction defective charts are useful when characteristic can not be quantified, for example hole in a cloth, absence of picture quality etc. These charts are meant to control the percentage of defective units in a lot.

The procedure to construct P-chart is :

Example 1

Construct a control chart for the proportion of defectives obtained in a repeated random sample of size 50 from a process which is considered to be under control when the average of proportion of defectives P i.e.

CONTROL CHART

EXAMPLE 2

Draw a P Chart from the following data

Sample No	Date	Number of Pieces Inspected	Number of Defective Pieces
1	2-2-2016	100	8
2	4-2-2016	100	10
3	5-2-2016	100	12
4	6-2-2016	100	14
5	7-2-2016	100	15
6	9-2-2016	100	12
7	11-2-2016	100	14
8	12-2-2016	100	10
9	13-2-2016	100	7
10	14-2-2016	100	16

Sol:-

Sample No	Date	Number of  Pieces Inspected	Number  of  Defective Pieces	Fraction Defectives (P) =   No.   of   Defective Piece/No.    of    Pieces Inspected
1	2-2-2016	100	8	0.08
2	4-2-2016	100	10	0.10
3	5-2-2016	100	12	0.12
4	6-2-2016	100	14	0.14
5	7-2-2016	100	15	0.15
6	9-2-2016	100	12	0.12
7	11-2-2016	100	14	0.14
8	12-2-2016	100	10	0.10
9	13-2-2016	100	7	0.07
10	14-2-2016	100	16	0.16
				∑P= 1.18

CONTROL CHART

• Control charts for number of defective units (np-chart)

These charts are modified form of  P-chart and are used when the analyst is more interested in number of defectives than fraction of defectives.

Steps to construct np-chart is :

np-charts are more preferred than P-charts as in np-charts, the number of defective can be directly plotted from the inspection report.

Example 3

Find the UCL and LCL for np chart for the following information and comment on the result:

Sample No. of 100	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
No. of Defectives	19	9	8	7	11	10	2	6	8	11	12	10	8	7	6

Since the number of defectives in each sample are within the two limits i.e. UCL and LCL so process is said to be under control.

CONTROL CHART

Example 4

A nationwide courier service desires to check the accuracy of its clerical work in completing invoices. A sample of 200 invoices is taken each day for 30 consecutive days for inspection. No. of defectives found in each day is as follows:

2	6	8	5	2	3	5	2	10	2	10	9	7	4	1
4	6	8	6	1	8	3	6	3	2	4	9	3	7	4

Determine the upper and lower control limits using np chart and also construct the control chart

CONTROL CHART

Control charts for number of defects (C-chart)

When the management is more interested in reducing number of defects per unit then c-charts are used. Sometimes, the products have more than one defect per unit e.g. number of air bubbles in a glass sheet, number of complaints in a restaurant. These charts enable the management to know whether number of defects is within the tolerance limit or not.

Example 5

Ten LEDs were inspected to locate defects in them. Each LED was having some defects as below. Draw C chart to arrive at conclusion.

LEDs	No. of Defects in the LED
1	2
2	3
3	4
4	0
5	1
6	3
7	5
8	2
9	0
10	1
Total	21

CONTROL CHART

Example 6

Ten pieces of cloth out of different roles of equal length contained the following number of defects:

2,5,1,0,3,4,6,8,1,0

Draw a control chart for the number of defects & state whether the process is in a state of statistical control.

CONTROL CHART

26.4 CASE STUDY: APPLICATION OF P CONTROL CHART IN PISTON MANUFACTURING

A piston manufacturer let’s call it Piston India Ltd. Is involved in manufacturing 3 types of pistons (A, B and C). The company caters to domestic and international market of pistons used both in two and four wheelers. The company has a turnover of more than 4 billion USD per annum. Thus it manufactures pistons in huge quantities. It is pertinent for the company to reduce cost in order to enhance its profitability. It was found that the manufacturing process of three types of pistons results in wastage of more than Rs.30 lakhs per annum in the form of scrap. It is understood that scrap cannot be reduced to zero. But the company wanted to apply a diligent effort to reduce scrap to the minimum so as to cut its wastage cost substantially. To do various steps were taken. Firstly, the case would present the process of manufacturing of pistons. Secondly, by using pareto chart analysis causes for defects in pistons of various types were found. Lastly, analysis was done by using various statistical technique including control charts to quantify the reasons and deduce where the error has occurred in the process which has resulted in defective item.

Process:

A piston in its manufacturing cycle goes through following phases:

Phase- 1 Material section

• Aluminium:- aluminium is consumed in two forms namely virgin metal and converted alloy. Purity is maintained up to 99.8% Al. and Iron Content is always kept to minimum. Daily consumption of 3.5 to 4 tons of aluminium in Federal Mogul is there.
• Copper and Phosphorous:- Copper was imported in the forms of long continuous wires earlier, but now metallic strips are used that are easy to use, usually copper phosphorous alloy as master alloy(8%) is used.

While melting process, these parameters are maintained. After every half hour, sample is sent to lab and analysis of constituents is done by machine Spectrometer. It is computer based machine, pre-programmed and displays all constituents of the specimen between five minutes. Infrared scanning is the main principle behind it. Also from composition table, we observe that Silicon is the main constituent of concern, as its slight change in the metal many cause defects.

Phase-2 Melting Sections

At S.T.P Pure Aluminium melts at 658 degree c. But once alloyed, its melting point varies from 750-850 degree C. Element is converted from soft, weak metal into hard strong metal, still retaining its light weight, and good conductivity and heat dissipation ability.

FURNACE: – Two types of furnaces are two types of furnaces are used for melting purpose:

Oil furnaces:- Kerosene oil is continuously supplied from height of about 5m, and air is pressured in (3.5kg/m2) by a nozzle. The oil furnace is used in Federal Mogul are SK-1,SK-2 of 400 kg each and SK-3 of 2 ton. Rear burners are used. The Curcible is supported on a block of refractory materials. Refractory or fire bricks are used here. Temperatures varies form composition of alloy, but generally it is 750-800degree C for 124 and 138 alloys and 860 degree C for 124 and 138 alloys and 860 degree C for A- 244 alloys.

Induction Furnace:- Junker and pioneer Induction Furnaces are used. Copper are used to produce eddy currents.

Metal provide resistance to the current produced eddy currents. Metal provide resistance to the current produced and hence melting occurs. Proper water circulation with temperature of outlet water less than 60 degree C. high speed blowers and auto-electric Control is used.

Phase-3 Melting Treatment in Holding Furnaces:

After tilting metal in holding furnaces, melt surface is covered with coverflux-350 GMS. Charge using fleering spoon. Then the slag produced is removed with (Slag) Skimming Spoon and put in trolley. Then preheated inverted umbrella type Graphite tube is lowered in melt, hood of suction system is positioned and duet for chlorine inlet is opened. Under proper pressure chlorine is passed for 10 minutes. Afterwards hood is removed and metal surface is skimmed with Skimming Spoon. Allow metal to stabilize for ten minutes. Sample is then casted in Brick mould to inspect blow holes and gas inclusion.

Phase-4 Casting

All the casting work is automated and timid for good quality and production and button coals get fixed. Then a bottom tool comes up. Guide bushes are provided with the central tool. Now the die is ready to take charge. With carry spoon, hot charge is taken from holding furnace and poured though runner in the die. Metal flows into the die, due to gravity. Then automatically, water circulation is given to coal down the piston. Each process is timid and hence, after solidifying of metal, the die opens and piston is taken out. Now, before repeating the operation, the die is heated to some extent, so that new charge does not come in the direct contact of a cold die. Whole process gets completed in 1 to 1.5 minutes

Phase-5  Heat treatment shop

Heat Treatment of Aluminum is done to:-

• Improve machinability
• Relieve internal stresses
• Improve mechanical properties
• Change grain size
• Increase resistance to corrosion
• Remove gases
• Change the ductility, strength, hardness and toughness.

Phase-6: Inspection and Quality Control

After complete finishing and machining of the piston pins, they all checked for their quality according to the ISO standards. The work of inspection is done by the foremen, supervisors and quality control officers. Inspection is done at two stages:-

• After every machining process.
• At the end of a cycle.

Quality control and inspection of foundry and piston plant shops are discussed in the respective shops. In this section we will discuss about the inspection of pistons in machine shop

Process 1: inspection meter is used to measure the diameter, is first standardize by masterpiece. Vernier caliper is used to measure the legs thickness, bottom thickness and wall thickness is also checked.

Process 2:

• total height of cavity is checked.
• Cavity taper from the centre of the bottom is checked.
• Limits of +0.1 mm are maintained.
• Roundness of piston is checked.
• Seat depth is checked, seat depth is depth of fixture seat to the leg.

Process 3: movement of fixture on piston base is checked.

Process 4:

• Holes alignment is checked by straight gauge.
• Hole diameter is checked by vernier caliper.
• Piston axis should coincide with hole axis.

Process 5: as grooving is done after making oil holes, so oil holes lie just in centre of the groove Process 6:

• Overturn diameter is checked again.
• Groove diameter is check by caliper.
• Groove angle is checked.
• Circlips width is checked by diameter gauge.

Process 7:

Finally compression height and surface roughness is checked in five measurement room.

Process 8:

Then the entire pistons are transferred to final quality central department. There, they are kept at 25 degree c and all the checking is done within the required limits. Then pistons are within the required limits.

Objective of the study:

Last 1 year Foundry Rejection in Machine Shop for Part numbers A, B and C is 20% resulting in Less Productivity, Excess Labor Cost and Material loss accounting for Approx.30.7 lacs per Annum.

Some of the main objective which are related to case study:-

• To identify the problems leading to scrap at casting stage
• To analyse the role of shift dependency on scrap
• To analyse the role of die coating thickness on scrap
• To analyse the role of in gate design on scrap
• To analyse the worker skills
• To analyse the discharge of cooling water

The study exhibited in this chapter includes simple approach in the analysis of rejection rate in particular production line in piston machine/casting shop. The production line consists of sequence of operation in making final product. Defects occur due to deficiency in machining/casting process. The study aims at analyzing the rejection rate using quality tools like check sheet, Pareto chart and cause and effect diagram.

Methodology:

Project managers, in just about any industry, are faced with the challenge of improving the efficiency and productivity of their businesses. To do this, they need to understand the best methodology and tools to study and analyse processes correctly. After all, to improve results, the best approach is to improve the process that gives you those results.

The concept of improvement is quite simple; to improve the outputs of a process, you simply improve the inputs and the process itself. To improve the output (also called the “Y” or the “Key Measure”), identify, measure and improve the inputs and process metrics (also known as the “X’s”). Focusing on the results, the output Y measures instead of the X’s is an after-the-fact, reactive, expensive and inefficient approach to improving results. The concept that Y is a function of X (Y=f(X1, X2 …Xn) is at the core of the: Define, Measure, Analyse, Improve and Control; also known as DMAIC steps.

DMAIC is an iterative process that gives structure and guidance to improving processes and productivity in the workplace. Project managers and Six Sigma practitioners apply the DMAIC steps and appropriate analysis tools under each step, to analyse and improve key metrics of a business. Metrics are established, variation is studied and reduced and processes are improved and optimized. The result is improved performance, fewer errors and increased efficiency and productivity.

1. Define

Essentially the purpose of the Define step is to set your project up for success. Project managers are familiar with the things that need to be done when starting off a project. Essential project elements are accomplished in this step, such as:

• Attaining sponsorship for the project
• Establishing the project charter and appropriate scope
• Identifying stakeholders and team members
• Establishing team ground rules
• Planning and conducting a successful kick-off meeting

In addition to the normal project deliverables listed above, for a process improvement effort, the project manager would facilitate his or her team in developing an “As-Is” process map. This will help the team not only get on the same page in terms of the process, but also will help the team identify problematic steps in the process.

Process maps, or Deployment maps (a.k.a. Swim-lanes), can also be useful in identifying non-value added steps and can be vital in determining process measures.

Lastly, the team may require some basic training on the application of the DMAIC steps so that everyone knows what to do and when to do it.

2. Measure

The Measure step is often a step which, unfortunately, is skimmed over by most teams. One of the biggest mistakes made when trying to improve results is to make decisions based on “gut” feeling, intuition or anecdotal information. Instead, what is imperative is to base decisions on facts and data and that is the main goal of the measure step. In the Measure step, the team should:

• Identify and operationally define key metrics
• Develop a data collection plan
• Conduct a measurement system analysis to verify that the data is accurate
• Stratify the data
• Establish baseline charts
• Make charts and graphs to help the team better understand what the process is currently delivering in terms of processing times.

3. Analyze

The Analyze step is all about getting to the root cause of the problem. Too often when trying to solve a problem, people or teams tend to focus on a symptom as opposed to the true root cause of the problem. The tools and techniques in the Analyze step lead project teams to gather clues for improvement and ascertain what the root cause, or causes, are that are the most important drivers. The Y is a function of X formula is at play in the Analyze step. A team will analyze the process, perhaps using value-added analysis, statistical analysis, or maybe a fishbone chart, a cause and effect diagram, to get to what they think are the root causes. Then the team would gather data on the root causes to determine if there is a cause and effect relationship with the problem. Verifying cause and effect is a crucial step in the Analyze phase; a step which many people, unfortunately, skip or simply take for granted based on their opinions.

4. Improve

Once a team moves through the Define, Measure and Analyze steps, they are now ready to use what they’ve learned about the process to be innovative when solving the problem at hand. Improve is the step where creative solutions to existing problems can be developed and tested, using various experiment or piloting techniques. The key deliverable in the Improve step is verifiable improvement through measurement. The best ideas for improvement, based on what was learned in Measure and Analyse, are tested and implemented on a limited basis to determine if there is statistical evidence of sustained improvement. Once a team improves a process, the results should become quite clear on a control chart. When stakeholders can see the proof of improved performance, they will be more likely to accept and actually implement the team’s recommendations.

Improve is about taking the emotion out of decision making. Improve is about verification and validation of recommendations. Often times, teams make the mistake of thinking they “know” what will work. Thus, they blindly implement what they think is the best solution without proper testing. The result, more times than not, is that there is no measurable or sustainable improvement.

5. Control

The real strength of the DMAIC steps is the Control step. Too often, teams do a lot of hard work, actually improve the process and results, and then implementation of the improved process doesn’t go smoothly. There is pressure to move on; time isn’t spent on having a smooth transition and the buy-in for full implementation just isn’t quite there. The result is that sustaining the improvement realized in the Improve step becomes difficult. The purpose of the Control step is to ensure a successful implementation of the team’s recommendation so that long- term success will be attained. The new and improved process will be flowcharted and these new methods will become the new standard operation procedures. Results will continue to be tracked so that any “drift” back to previous results can be monitored and addressed in a proactive manner. The Control step is about the transfer of responsibilities and establishing plans for long-term process control.

Findings

Reasons of Scrap

These are some reasons shown through pareto charts which shows us the total no/types of defects category pistons. These pareto charts also shows cumulative percentage Which will further help us to reduce scrap by focusing on a major defect to reduce that effect.

Pareto chart for piston A

This shows that there is dominance of B.T defect in piston category A as its on top rank.

This shows that there is dominance of shrinkage ring zone in B as its on top rank

Pareto chart for piston C

Shrinkage ring zone is the major reason of scrap in piston category C

Control Chart for overall Scrap Variation:

Days	Sample (n)	Scrap (np)	p-value (np/n)
1st Dec	425	42	0.10
2nd Dec	425	30	0.07
3rd Dec	425	47	0.11
4th Dec	425	60	0.14
5th Dec	425	77	0.18
6th Dec	425	79	0.19
7th Dec	425	77	0.18
8th Dec	425	68	0.16
9th Dec	425	60	0.14
10th Dec	425	43	0.10
11th Dec	425	43	0.10
12th Dec	425	43	0.10
13th Dec	425	34	0.08
14th Dec	425	38	0.09
15th Dec	425	43	0.10
16th Dec	425	42	0.10
17th Dec	425	42	0.10
18th Dec	425	41	0.10
19th Dec	425	39	0.09
20th Dec	425	38	0.09
21st Dec	425	41	0.10
22nd Dec	425	43	0.10
23rd Dec	425	43	0.10
24th Dec	425	30	0.07
25th Dec	425	34	0.08
26th Dec	425	34	0.08
27th Dec	425	38	0.09
28th Dec	425	38	0.09
29th Dec	425	30	0.07
30th Dec	425	34	0.08
31st Dec	425	30	0.07

The above shown p chart indicates Upper control and lower control limit of overall scarp of pistons under study. From the chart it can be deduced that during which days the scrap proportion is out of limit and rectification measures need to be taken.

26.5 SUMMARY

Control charts for attributes are an important tool in the hands of management to control the quality characteristics which cannot be measured in quantitative terms. P charts are used to exercise control over the fraction defectives in the process. nP charts are used when more concern is for number of defectives than the fraction of defectives. Similarly C charts are used when the parameter for deciding the quality of product is the number of defects per unit.

26.6 REFERENCES/ SUGGESTED READINGS

• Nair N G, Production and Operation Management, Tata McGraw- Hill Publishing Company Limited, New Delhi
• Chary, Production and Operations management, McGraw-Hill
• Robert Fetter B. , Quality Control Systems, Richard D. Irwin, Illinois, USA