Chapter 17, Problem 42E

1.

To determine

Calculate the value of k in the Taguchi loss function, the cost coefficient.

Explanation of Solution

Operational control is the power to carry out those functions of orders over subordinate forces concerning the organization and use of instructions and compels the assignment of tasks, the assignment of goals and the giving of the instructive path requisite for the task.

Total Quality Management (TQM) is the unyielding and ongoing effort by all in the organization to understand, meet and exceed customer’s expectations.

Quality is defined as customer satisfaction with the overall product or service experience, that is, the difference (or gap) between customer expectations and actual experience product performance or service.

The Taguchi quality loss function depicts the relationship between costs in terms of quality and variance from target quality.

Taguchi and Wu show that for a quality characteristic with the target value T, the loss from having an observed quality characteristic x can be estimated by the following quadratic function:

$L(x)=k{(x-T)}^2$

Where,

x = the observed value of the quality characteristic

T = the target value of the quality characteristic

k = the cost co-efficient, determined by the firm’s costs of failure

Value of k, the cost coefficient, in the Taguchi Loss Function, L(x):

$\begin{array}{c}L(x)=k{(x-T)}^2\\ k=\$20÷{0.0002}^2\\ k=\$20÷0.00000004\\ k=\$500,000,000\end{array}$

Therefore, the value of k in the Taguchi loss function, i.e., the cost coefficient is $500,000,000.

2.

To determine

1. a. Assess estimated loss of quality for each of the measurements observed.
2. b. Calculate the anticipated (i.e., average) loss for the whole production process.

Explanation of Solution

Operational control is the power to carry out those functions of orders over subordinate forces concerning the organization and use of instructions and compels the assignment of tasks, the assignment of goals and the giving of the instructive path requisite for the task.

Total Quality Management (TQM) is the unyielding and ongoing effort by all in the organization to understand, meet and exceed customer’s expectations.

Quality is defined as customer satisfaction with the overall product or service experience, that is, the difference (or gap) between customer expectations and actual experience product performance or service.

The Taguchi quality loss function depicts the relationship between costs in terms of quality and variance from target quality.

Taguchi and Wu show that for a quality characteristic with the target value T, the loss from having an observed quality characteristic x can be estimated by the following quadratic function:

$L(x)=k{(x-T)}^2$

Where,

x = the observed value of the quality characteristic

T = the target value of the quality characteristic

k = the cost co-efficient, determined by the firm’s costs of failure

The estimated loss of quality for each of the measurements observed and the anticipated (i.e., average) loss for the whole production process is shown below from the following table:

x	Quality Loss L(x)	Probability f(x)	Expected Loss
0.1996	$80.00	0.02	$1.60
0.1997	$45.00	0.05	$2.25
0.1998	$20.00	0.12	$2.40
0.1999	$5.00	0.11	$0.55
0.2000	$0.00	0.45	$0.00
0.2001	$5.00	0.10	$0.50
0.2002	$20.00	0.08	$1.60
0.2003	$45.00	0.05	$2.25
0.2004	$80.00	0.02	$1.60
		1.00	$12.75

3.

To determine

1. a. Determine the variance in the measured distance between two pins.
2. b. Calculate the expected loss of the process using the calculated variance.

Explanation of Solution

Operational control is the power to carry out those functions of orders over subordinate forces concerning the organization and use of instructions and compels the assignment of tasks, the assignment of goals and the giving of the instructive path requisite for the task.

Total Quality Management (TQM) is the unyielding and ongoing effort by all in the organization to understand, meet and exceed customer’s expectations.

Quality is defined as customer satisfaction with the overall product or service experience, that is, the difference (or gap) between customer expectations and actual experience product performance or service.

Cost of quality (COQ) is a performance measurement reporting framework for the classification of costs associated with quality.

The Taguchi quality loss function depicts the relationship between costs in terms of quality and variance from target quality.

Taguchi and Wu show that for a quality characteristic with the target value T, the loss from having an observed quality characteristic x can be estimated by the following quadratic function:

$L(x)=k{(x-T)}^2$

Where,

x = the observed value of the quality characteristic

T = the target value of the quality characteristic

k = the cost co-efficient, determined by the firm’s costs of failure

Albright and Roth show that, using variance and the square of the mean deviation from the target value, the expected or average loss per unit can be determined as follows.

$EL(x)=k({\sigma }^2+D^2)$

Where,

$EL(x)=\text{Expected }\left(\text{average}\right)\text{ loss from having a quality characteristic equal to }x$

${\sigma }^2=\text{variance of the quality characteristic about the target value}$

$\begin{array}{c}D=\text{the deviation of the mean value of the quality characteristic from the target value}\\ =\overline{x}-T\end{array}$

X	Probability, f(x)	$x\cdot f(x)$	(x − 0.199991)2f(x)
0.1996	0.02	0.003992	0.00000000305762
0.1997	0.05	0.009985	0.00000000423405
0.1998	0.12	0.023976	0.00000000437772
0.1999	0.11	0.021989	0.00000000091091
0.2000	0.45	0.090000	0.00000000003645
0.2001	0.10	0.020010	0.00000000118810
0.2002	0.08	0.016016	0.00000000349448
0.2003	0.05	0.010015	0.00000000477405
0.2004	0.02	0.004008	0.00000000334562
		$\overline{x}=0.\text{199991}$	0.00000002541900

Calculate the variance:

$\begin{array}{c}D=\text{the deviation of the mean value of the quality characteristic from the target value}\\ =\overline{x}-T\end{array}$

$\begin{array}{c}{D}^2={(0.199991-0.2)}^2\\ =0.\text{000000000081}\end{array}$

Where 0.20 = target value and 0.199991 = (mean value of the quality characteristic).

b. Calculate the expected loss of the process using the calculated variance:

$\begin{array}{c}EL(x)=k({\sigma }^2+D^2)\\ =\$\text{500,000,000 × (0}\text{.000000025419 + 0}\text{.000000000081)}\\ \text{=\$12}\text{.75}\end{array}$